AoI-based Multicast Routing over Voronoi Overlays with Minimal Overhead
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AoI-based Multicast Routing overVoronoi Overlays with Minimal Overhead
MICHELE ALBANO , (Senior Member, IEEE), MATTEO MORDACCHINI , and LAURA RICCI Department of Computer Science, Aalborg University, Denmark (e-mail: [email protected]) Institute for Informatics and Telematics (IIT-CNR), Via Moruzzi 1, 56124, Pisa, Italy (e-mail: [email protected]) Universitá di Pisa, Italy (e-mail: [email protected])
Corresponding author: Michele Albano (e-mail: [email protected]).The research has received funding from the EU ECSEL JU under the H2020 Framework Programme, JU grant nr. 737459 (Productive4.0project).
ABSTRACT
The increasing pervasive and ubiquitous presence of devices at the edge of the Internetis creating new scenarios for the emergence of novel services and applications. This is particularlytrue for location- and context-aware services. These services call for new decentralized, self-organizingcommunication schemes that are able to face issues related to demanding resource consumption con-straints, while ensuring efficient locality-based information dissemination and querying. Voronoi-basedcommunication techniques are among the most widely used solutions in this field. However, when usedfor forwarding messages inside closed areas of the network (called Areas of Interest, AoIs), these solutionsgenerally require a significant overhead in terms of redundant and/or unnecessary communications. This factnegatively impacts both the devices’ resource consumption levels, as well as the network bandwidth usage.In order to eliminate all unnecessary communications, in this paper we present the MABRAVO (MulticastAlgorithm for Broadcast and Routing over AoIs in Voronoi Overlays) protocol suite. MABRAVO allowsto forward information within an AoI in a Voronoi network using only local information, reaching all thedevices in the area, and using the lowest possible number of messages, i.e., just one message for each nodeincluded in the AoI. The paper presents the mathematical and algorithmic descriptions of MABRAVO, aswell as experimental findings of its performance, showing its ability to reduce communication costs to thestrictly minimum required.
INDEX TERMS
Area of Interest, multicast, Voronoi networks I. INTRODUCTION
We are witnessing a fast and vast expansion of the Internetat its edges [1]. This is mainly due to the pervasive diffusionin the environment of smart objects, like sensors, Internet ofThings (IoT) devices, user personal devices, etc.This scenario allows the emergence of novel services andapplications [2]–[8], supported by potentially large networksof highly distributed and autonomous devices. Traditionalcentralized control and communication techniques do not suitthe needs and requirements of such an environment.In particular, these devices are usually equipped withcomputing and communication capabilities, that allow themto create and exchange information both among themselvesand with other remote services. One of the most challengingproblems is related to the fact that this kind of systemstypically requires frequent exchanges of information among a large number of geographically dispersed devices. Thecommunication complexity is further increased by the factthat devices cannot always count on the support of centralcommunication infrastructures, posing the need to applyautonomous, self-organizing forms of communication andinteraction among devices [9]–[12].Location- and context-aware services [13] in this scenarioare faced with additional issues. In fact, these services arecharacterized by the fact that most of the messages aredirected (and of interest) only to limited/specific areas ofthe network. This is the case of communications directedto bounded regions of the space, like Areas of Interest [14],validity regions [15], [16], and safe regions [17].As a consequence, effective and efficient communicationschemes for this kind of application are of utmost relevance.This fact poses the challenge to devise information dissemi-nation mechanisms that are able to face locality-based com-munication needs, while coping efficiently with demanding
VOLUME 4, 2016 a r X i v : . [ c s . N I] A ug . Albano, M. Mordacchini, L. Ricci: AoI-based Multicast Routing over Voronoi Overlays with minimal overhead requests in terms of scalability, responsiveness, performanceand resource consumption constraints. A. CONTRIBUTION
In this paper, we focus on Voronoi-based overlay networksfor data communication and data dissemination among de-centralized, autonomous entities. This is a widely used solu-tion [18]. In fact, Voronoi-based techniques have been pre-sented as effective solutions for disseminating and queryingdata in decentralized, distributed systems. This kind of tech-niques have been successfully applied in the IoT [19], wire-less sensor networks [20], [21], underwater networks [22],[23], embedded computing systems [24], vehicular net-works [25], and even distributed virtual environments [26],[27].More specifically, this paper presents a solution for infor-mation dissemination within bounded areas of the network.This communication paradigm can be relevant for a widespectrum of applications for context-aware services at theEdge [28]–[30]. Following the literature on this subject, inthis paper these bounded regions are called Areas of Interest(AoIs) [14]. Issues with decentralized communications to-ward nodes in a AoI are related to the fact that the entitiesin the system have to coordinate autonomously in order todetermine the involvement of other nodes in the propagationand delivery of the information, without relying on any formof centralized/global support. Geometric routing techniquesare generally used in this kind of systems to deliver messagesand queries towards interested areas. However, previousworks highlight the risk for the system to incur in redundantmessages (i.e., the same message is delivered to some nodesmore than once) and/or unnecessary communications (i.e.,messages are sent to nodes not related to the AoI) [31], [32].In order to overcome these issues, state-of-the-art solutionsrequire that nodes in a Voronoi network should use additionaldata, such as the positions of the neighbors of a node’simmediate neighboring nodes (e.g. [31]–[33]). All these factscompromise the efficiency of the system. In fact, all thesecommunications (both redundant and unnecessary messages,and the ones needed for maintaining an updated neighbors-of-neighbors list) are expensive in terms of nodes’ resourceconsumption and bandwidth usage.The contribution of this paper is to present a solution that isable to avoid all these costs by defining a novel decentralizedcommunication scheme for AoIs that is able: • to rely only on strictly local information (i.e., the posi-tion of immediate neighbors and their identifiers, whichwill be called IDs for short in the rest of the paper ); • to always deliver a message to all the nodes in an AoI; • to totally avoid all redundant communications; • to totally avoid all unnecessary communications.With our approach, the number of messages required todeliver data within an AoI is reduced to its minimum, thussaving nodes’ battery and computational resources, as wellas bandwidth usage. The proposed solution is based on geometric properties of Voronoi networks. At the best of ourknowledge, this is the first technique that is able to achieveall these objectives.In order to present our solution, in this paper we provide: • a mathematical description of the proposed approach; • mathematical proofs of the correctness of the proposedsolution; • an algorithmic description of the approach.This paper does not deal with the decentralized main-tenance of a Voronoi network, since several solutions arealready available in the literature [34]–[36] and can be usedfor this purpose. We do not deal either with the dynamicbehavior of nodes (i.e., churning nodes). This paper presentsthe very first completely decentralized solution that allowsto forward information within a delimited AoI using onlylocal information, and achieving the lowest possible numberof messages (i.e., just one message for each node includedin the AoI). The purpose of this paper is to present such asolution, prove it is mathematically sound, and explain howto implement it. Discussing possible dynamic behaviors ofthe nodes would have added too much material to this paper,making the presentation of this work less coherent and lessfocused with respect to the main goal of the paper. We thusdecided to leave the issues related to dynamic nodes to furtherresearch and future investigations.The rest of this paper is organized as follows: Section IIpresents the model of the overlay network we consider.Section III defines the algorithms of the MABRAVO protocolsuite, and proves that they are correct and computationallyefficient. Section IV presents our simulation environment andthe results it provided. Section V presents an overview of theliterature about the topic of this paper. Finally, Section VIpresents our conclusions about the topic at hand. II. NETWORK MODEL
Given a set of sites S = s ...s n that are points in a plane, a2-dimensional Voronoi tessellation is a partition of the planeinto cells, which assigns to each site s i a cell V s i that is the setof points closer to s i than to any other site s j ∈ S , accordingto a given definition of distance. In this paper we consider theclassical Voronoi tessellation, which uses the L metric as adistance: || p i , p j || = (cid:113) ( x i − x j ) + ( y i − y j ) where ( x i , y i ) are the coordinates of the point p i , and ( x j , y j ) are the coordinates of the point p j . The cell V s i associated tothe site s i = ( x i , y i ) is the locus of all the points in the planethat are closer to s i than to any other site, formally p k ∈ V s i ⇔ ∀ s j : || p k , s i || ≤ || p k , s j || (1)Figure 1 shows an example of a Voronoi tessellation. Eachinequality in Equation 1 is equivalent to dividing the planeinto half-spaces, thus the cell is obtained by intersectinghalf-spaces, resulting in the cell being a convex polygon.A cell V s i may be characterized either by a finite area, or VOLUME 4, 2016 . Albano, M. Mordacchini, L. Ricci: AoI-based Multicast Routing over Voronoi Overlays with minimal overhead
FIGURE 1.
Classical Voronoi tessellation. by an infinite area if some of the cell’s sides are segmentsdegenerated into half-lines.A side l i,j of a Voronoi cell is a segment that lays betweentwo adjacent Voronoi cells V s i and V s j , and a vertex v i,j,k of a Voronoi cell is a point that is intersection between twosides of the Voronoi cell, and that lays between Voronoi cells V s i , V s j and V s k . Should a segment degenerate into a half-line, the formalism still holds, except that the "segment" isadjacent to one vertex only. A Voronoi Overlay is an overlaynetwork that assigns the links among the sites following theVoronoi tessellations, i.e. a link exists in the overlay if andonly if the sites are Voronoi neighbors [31], [32], [37].In this paper, an Area of Interest (AoI) is a finite 2-dimensional convex region in the plane. We consider a site s i to be in the AoI if and only if the intersection I s i betweenits Voronoi cell V s i and the AoI is not empty, formally I s i = V s i (cid:84) AoI (cid:54) = ∅ .Let us consider a point D , not necessarily co-located witha site. We define Z s i ( D ) as the union of the points of the seg-ments that connect points of I s i to D ; S s i ( D ) (the Segmentsof Interest of s i towards D ) is defined as the intersectionbetween s i ’s cell sides, and Z s i ( D ) ; N s i ( D ) is defined as theset of neighbors of s i whose sides share with V s i at least onepoint ∈ S C ( D ) . Finally, we define V s i ,s j , I s i ,s j , Z s i ,s j ( D ) , S s i ,s j ( D ) and N s i ,s j ( D ) in a manner analogous to V s i , I s i , Z s i ( D ) , S s i ( D ) and N s i ( D ) , but computed with only thelocal information of s j . Table 1 summarizes the definitionspresented in this section.An AoI-cast is a routing protocol that delivers a packetto all the sites whose cells intersect the AoI. The generalstrategy for an efficient AoI-cast is routing a packet fromthe sender to a site s i located into the AoI, and afterwardsto create a distribution tree from s i . The lower limit for thenumber of required packets, corresponding to performing anAoI-cast over a tree, is equal to the number of sites in theAoI minus . The rest of the paper considers that a packethas already reached one site in the AoI, and we are concerned TABLE 1.
Definitions D either the destination of a routing message, orthe originator of a AoI-cast requestAoI convex area on the plane p i = ( x i , y i ) point i of coordinates x i and y i s i site iV s i Voronoi cell of a site s i l i,j side between cells V s i and V s j v i,j,k vertex between cells V s i , V s j and V s k I s i the intersection between V s i and the AoI s i is considered “into”the AoI if I s i is not empty Z s i ( D ) union of the points of the segments that con-nect points of I s i to D , with extremes notincluded, plus DS s i ( D ) ( Segments of In-terest of s i towards D ) intersection between s i ’s cell sides, and Z s i ( D ) N s i ( D ) neighbors of s i that share with V s i a side withat least one point ∈ S s i ( D ) V s i ,s j and I s i ,s j V s i and I s i computed in the local vision of s j Z s i ,s j ( D ) , S s i ,s j ( D ) and N s i ,s j ( D ) Z s i ( D ) , S s i ( D ) and N s i ( D ) computed inthe local vision of s j with either routing it to another site in the AoI (unicast), orreaching all the sites in the AoI (AoI-cast). III. MABRAVO ALGORITHMS
This section presents the MABRAVO protocol suite. Recallfrom SectionII that we define that site s i is part of the AoI if and only if the intersection of its Voronoi cell V s i and theAoI is not the empty set.The MABRAVO routing algorithms consider the di-chotomy between a “global vision” of the network and the“local vision” of a particular site, by defining the local visionof a site as the Voronoi tessellation computed by the site usingonly the location data of its immediate neighbors. Some pre-vious works, for example VoRaQue [32], make use of non-local information such as knowledge regarding neighbors ofneighbors. The maintenance of such information is prone toeither a big communication overhead or data obsolescence. Infact, in order to have up-to-date information for the routing,each site needs to exchange a high number of messages withits neighbors, and this constitutes a burden on the overallperformance of the system. Otherwise, there is an increasedrisk to incur in wrong forwarding decisions due to aged data.In order to overcome these problems, we propose routingalgorithms based uniquely on local information, i.e. a siteknows only about its own location, and its Voronoi neigh-bors’ locations and IDs. In doing this, we face issues likethe ones presented in Fig. 2, and in Fig. 3, which are mainlydue to the discrepancies between one site’s local vision ofthe network, and the real topology of the Voronoi diagram(global vision).Left part of Fig. 2 presents the local vision of site A , whileright part of Fig. 2 presents the global vision of the samearea. Let us suppose that an AoI-cast is being performed, forexample using the routing protocol from [38], that A receiveda packet to be delivered to C , and that A believes that B VOLUME 4, 2016
3. Albano, M. Mordacchini, L. Ricci: AoI-based Multicast Routing over Voronoi Overlays with minimal overhead
AB CD
AB CD E
FIGURE 2.
Comparison between the local vision of site A (left) and the real vision of the system (right). Site A wrongly believes that B and C are neighbors A B C
AoI
A B C D
AoI
FIGURE 3.
Comparison between the local vision of site A (left) and the real vision of the system (right). Site A wrongly believes that C is inside the AoI received the packet already. A may wrongly believe that sites B and C are mutual neighbors, and A may consider that site B is in charge of forwarding a packet it received to C , thus A will not forward the packet to C itself. In this particular case,it can happen that site C will not receive the packet from anysite, since B and C are not neighbors and E could not lay inthe AoI.Another possible case is presented in Fig. 3, where the leftpart of the figure is the local vision of A and the right partrepresents the global vision. In this case, A could believethat its neighbor C has a non-void intersection with the AoI .Thus, A decides to send the packet to C . The result is auseless message, since C ’s Voronoi cell has no intersectionwith the AoI and C should not receive any message.The purpose of the MABRAVO protocol suite is to over-come both the above problems, and to realize algorithms that,using the local vision of any site, are able to perform correctunicast and AoI-cast communication. Both communicationmodes avoid to contact unrelated sites (sites whose cellshave no intersection with the AoI), and the AoI-cast uses theminimal number of packet transmissions, equal to the numberof sites in the AoI minus 1.The rest of this section describes the proposed MABRAVOprotocol suite, starting with a discussion on the requirementsthat must be satisfied by the sites in terms of available primi-tives to allow an efficient implementation of unicast and AoI-cast routing (Subsection III-A), then presenting the unicast protocol MABRAVO D and proving its correctness (Subsec-tion III-B and Subsection III-C), and then doing the same forthe AoI-cast protocol MABRAVO R (Subsection III-D andSubsection III-E). A. REQUIREMENTS FOR THE ALGORITHMS
Recall from Section II the definition of side and vertex of aVoronoi cell. To be able to efficiently execute the algorithms,each site s i has to maintain a data structure with its Voronoicell’s vertices and sides. For each vertex v i,j,k , the datastructure must be able to provide s j and s k , which are thetwo Voronoi neighbors of s i that are at the same distancefrom v i,j,k . For each side l i,j , the data structure must be ableto provide s j , which the neighbor of s i that is adjacent to l i,j .Moreover, given a neighbor s j , the data structure must beable to provide the side l i,j that is adjacent to both s i and s j ,and the two Voronoi vertices v i,j,k and v i,j,l that are sharedby the Voronoi cells of s i and s j .We propose to use circular lists for the neighbors, sides,and Voronoi vertices of s i . The data structures get updatedwhenever a new site is inserted or removed from the Voronoidiagram, and the cost of querying and updating the datastructures of site s i is proportional to the number of neighborsof s i . Since we are considering Voronoi diagrams in theplane, it has been proven that the mean number of neighborsof a site has an expected value lower than (see for exam-ple [39]) over large Voronoi diagrams. Thus, the expected VOLUME 4, 2016 . Albano, M. Mordacchini, L. Ricci: AoI-based Multicast Routing over Voronoi Overlays with minimal overhead cost for querying and updating the data structure used by theMABRAVO routing protocols is O (1) .We consider that each node is assigned a unique ID, whichwill be used to break ties in the MABRAVO algorithms.Various techniques are available for creating unique IDsin decentralised, distributed systems (e.g. [40]–[42], just toname some recent examples).On a final note, we consider that the MABRAVO routingprotocols can use a Time to Live (TTL) mechanism similar tothe one of the AODV protocol [43]. In fact, the MABRAVOrouting protocols are proved to work properly only whenthe topology is maintained timely, and the TTL mechanismprotects the network in case the protocols are used in verydynamic networks before the topology gets maintained. B. UNICAST ALGORITHM MABRAVO D Let us consider a site C that is forwarding a packet towardsthe point D . D can be co-located with a site or not; in thelatter case, it must still belong to the AoI, and thus to the cellof a site belonging to the AoI. Site C can be the initiator ofthe routing process, or an intermediate (and potentially final)hop. Let us consider the actions performed by C to decidewhich site to route the packet to and let us, with an abuseof notation, consider that C is also the C ’s index among thesites of the diagram (i.e.: C = s C , sides of V C are l C,i , andvertices of V C are v C,i,j ).A unicast routing process will necessarily terminate withsuccess if it respects the following properties: • each site that has to forward the message shall be ableto identify at least one other site to forward the messageto (existence of next hop); • each site that has to forward the message shall uniquelyidentify the next forwarding site (unicity of next hop); • each routing step shall bring the packet closer (accord-ing to a given metric) to the destination point than thecurrent site (implying the finiteness of the route).If the current site C is the closest to D among its neigh-bors, the packet can be delivered and the routing processis completed. If not, it is necessary to route the packet toanother site, and the quantities Z C ( D ) , S C ( D ) and N C ( D ) (please refer to Section II for their definitions) cannot beempty: Z C ( D ) contains at least one point x since C is inthe AoI, S C ( D ) contains at least the intersection y betweenone side of V C and the segment xD , N C ( D ) contains at leastthe neighbor of C adjacent to the side containing y .The unicast routing algorithm builds N C ( D ) by consid-ering the vertices of V C laying in the AoI, and adding allneighbors that have a vertex in common with C that is locatedin the AoI. This way of computing N C ( D ) can lead either toa non-empty set, or an empty set. If N C ( D ) appears to beempty, it means that the AoI crosses a side twice (see leftpart of Fig. 4), and there is only one potential next hop in N C ( D ) , which will receive the packet.If the N C ( D ) was not empty (see right part of Fig. 4), thealgorithm moves on the circular list of neighbors in N C ( D ) if ∀ s i neighbors of C , DC < Ds i then Deliver the packet to C returnend Let L = the set of all neighbors of C foreach s i ∈ L doif DC < Ds i then Remove s i from L elseif ( v C,i,j / ∈ AoI ) and ( v C,i,k / ∈ AoI ) then Remove s i from L endendif L = 0 thenforeach s i neighbor of C doif Ds i < DC then for all q ∈ sides ( AoI ) doif q ∩ l i,C (cid:54) = 0 then Send packet to s i returnendendendelseforeach s i ∈ L do Compute a i = ∠ DCs i end Send packet to neighbor s m with lowest a m , andlowest ID in case of a tie returnendAlgorithm 1: Algorithm MABRAVO D , executed by C ,having D as destinationuntil it finds the one with lowest angle ∠ DCs i , and sendsthe packet to s i ; in case of a tie, C chooses the site withthe lowest ID. For the latter case, an example is given in theright part of Fig. 4. Site A wants to send a packet towards thedestination point D . Vertices y and t are in the AoI, thus thesites that will be considered as potential next hops are E, F and C , since the three of them are also closer to D than A .Site B has a non-empty intersection with the AoI in A ’s localvision, but the side between A and B is not included in the segments of interest and thus B is discarded. Among the threesites, F is selected since DAF < DAE and
DAF < DAC .The formal algorithm is reported in Algorithm 1, and nextsubsection proves that the MABRAVO D algorithm is correct. C. PROOF OF CORRECTNESS FOR THE UNICASTALGORITHM MABRAVO D Theorem III.1.
Given a site C that is not the destination fora message, if C receives a packet, there exists a site detectedby the algorithm which is the next destination of the packet.Proof. Take a point P in I C , which cannot be the empty setsince C ∈ AoI . Connect P to D with a straight segment, andconsider the segment’s intersection with C ’s Voronoi sides. VOLUME 4, 2016
5. Albano, M. Mordacchini, L. Ricci: AoI-based Multicast Routing over Voronoi Overlays with minimal overhead d ( B , D ) A B D d ( A , D ) AoI
FIGURE 4.
Unicast routing step when N A ( D ) appears to be empty (left) and non-empty (right). Considering the definition of Voronoi cell V C as given byEquation 1, we can have two possible cases: • if there is no intersection, P D lies in C ’s Voronoi cell V C . In this case, D ∈ V C ( D ) , site C owns point D , andthe routing process is completed with success; • otherwise, notice that the segment lays in I C since both V C and the AoI are convex. Consider the intersection q between P D and V C ’s borders. q ∈ S C ( D ) , hence N C ( D ) comprises at least the site on the other side of q ,which is closer to D than C . Thus, there exists at leastone possible site to forward the message to. Theorem III.2.
The fact that MABRAVO D forwards thepacket from a site C to a site B , implies that B is closerto D than C .Proof. The chosen site B is in N C ( D ) . From definitionof N C ( D ) , at least one of the segments connecting I C to D crosses the border between C and B . Hence, using thedefinition of a cell’s borders presented in Eq. 1, since D resides on the other side of the border between B and C ,we have proved that BD < CD . Theorem III.3.
Unicast route is unique, and finite.Proof.
Since the algorithm for unicast routing is determinis-tic (it has no random component), at each step it can chooseonly one site as the next hop to go towards the routingdestination D. Hence, the routing path is uniquely defined bythe routing algorithm. Each routing step brings the packet toa site that is closer to D than the preceding site. Thus, a routecan have at most as many hops as the number of sites in thenetwork. Thus, the route is finite. D. AOI-CAST ALGORITHM MABRAVO R This subsection presents MABRAVO Reverse (MABRAVO R ),which is an AoI-cast protocol that builds over the results presented in subsection III-C to compute AoI-cast treesin a distributed manner with local information only. Therationale is that the algorithm MABRAVO R , formalized inAlgorithm 2, understands if MABRAVO D would route apacket from C to D , and in that case D sends the packetto C while executing MABRAVO R . The algorithm performscorrect routing and minimizes the number of exchangedmessages, by delivering • one message - and one message only - to each site whoseVoronoi cell has a non-void intersection with the AoI,and • no messages to sites outside the AoI.Let us start the presentation with an example regarding theexecution of MABRAVO R on Fig. 5, where a site s i verifiesif it should send the packet originated in D to site s j . Thealgorithm will do that if site s j would send a packet to s i toreach the destination D when using the MABRAVO D . Firstof all, if s i D > s j D , s j can not be child of s i in the AoI-cast tree. Let us now call s k and s l the two sites that arecommon neighbors of s i and s j (it is possible that one ofthe sites or both do not exist). Let also be v i,j,k the Voronoivertex adjacent to s i , s j and s k and let be v i,j,l the Voronoivertex adjacent to s i , s j and s l . Algorithm 2 considers twomain cases: • Neither v i,j,k nor v i,j,l are in the AoI. In this case, s i checks if its border with s j crosses the AoI boundaries,in line with the routing performed in Fig.4. If this is true, s i is the only feasible next hop of s j in MABRAVO D ,thus s i sends the packet to s j ; • v i,j,k or v i,j,l or both lay into the AoI. In this case, s k or s l or both sites are compared with s j . Let us considerfor example that only v i,j,k ∈ AoI. s i sends the packetto s j unless both – s k D > s i D – ∠ Ds j s k < ∠ Ds j s i , or ∠ Ds j s k = ∠ Ds j s i andID of s k < ID of s i VOLUME 4, 2016 . Albano, M. Mordacchini, L. Ricci: AoI-based Multicast Routing over Voronoi Overlays with minimal overhead D s i s j s l s k AoI ? v i,j,l v i,j,k FIGURE 5.
Example of MABRAVO R routing. since it would mean that s k is better off than s i insending the packet to s j according to MABRAVO D unicast routing algorithm.Next section provides correctness proof for theMABRAVO R algorithm. E. PROOF OF CORRECTNESS FOR THE AOI-CASTALGORITHM MABRAVO R Theorem III.4. If A computes a non-empty (local vision) V C,A of the Voronoi cell of C , then V C ⊆ V C,A . Moreover, if I C,A exists, I C ⊆ I C,A .Proof.
Given two sites C and A , the Voronoi area of C in thelocal vision of A , called V C,A , exists if and only if A and C are neighbors. Let us consider point P , and the algorithm thatis used to decide if P ∈ V C,A . Let us call S the set of all sitesin the Voronoi tessellation (global vision of the overlay), and S ( A ) the set of sites in the local vision of A , which contains A and A ’s neighbors. From the definition of a Voronoi cell,we have that: P ∈ V C,A if and only if ∀ s i ∈ S ( A ) : d ( P, C ) ≤ d ( P, s i ) P ∈ V C if and only if ∀ s i ∈ S : d ( P, C ) ≤ d ( P, s i ) Since the set of the sites in a local vision is a subset of theset of all the neighbors ( S ( A ) ⊆ S ), the set of conditionsfor P ∈ V C,A is subset of the set of conditions for P ∈ V C ,and P ∈ V C ⇒ P ∈ V C,A . Thus, V C ⊆ V C,A . Consideringnow the intersection between the AoI and the Voronoi cells,since I C = V C (cid:84) AoI and I C,A = V C,A (cid:84)
AoI, and we justshowed that V C ⊆ V C,A , it holds that I C ⊆ I C,A . Theorem III.5. Z C ( D ) and Z C,A ( D ) are convex.Proof. First of all, since both Z C ( D ) and Z C,A ( D ) are com-puted in the same way, the proof will be shown considering Deliver the packet to s i foreach s j neighbor of s i doif Ds i > Ds j then Jump out to the main foreach cycle end
Let s k and s l be the common neighbors of site s i and site s j if ( v i,j,k / ∈ AoI ) and ( v i,j,l / ∈ AoI ) thenforeach q ∈ side ( AoI ) doif q ∩ v i,j,k v i,j,l (cid:54) = 0 then Send packet to s j Jump out to the main foreach cycle endendendif v i,j,k ∈ AoI and s k D > s i D thenif ( ∠ Ds j s k < ∠ Ds j s i ) or ( ∠ Ds j s k = ∠ Ds j s i and ID of s k < ID of s i ) then Jump out to the main foreach cycle endendif v i,j,l ∈ AoI and s l D > s i D thenif ( ∠ Ds j s l < ∠ Ds j s i ) or ( ∠ Ds j s l = ∠ Ds j s i and ID of s l < ID of s i ) then Jump out to the main foreach cycle endend
Send packet to s j Jump out to the main foreach cycle endAlgorithm 2:
Algorithm MABRAVO R , executed by site s i ,having D as source of the AoI-cast VOLUME 4, 2016
7. Albano, M. Mordacchini, L. Ricci: AoI-based Multicast Routing over Voronoi Overlays with minimal overhead Z C ( D ) only, but it applies to both sets. If D ∈ I C , since I C is convex, all segments connecting points of I C to D are internal to I C , hence Z C ( D ) = I C , which is convex. If D / ∈ I C , building Z C ( D ) is analogous to applying a step ofan Incremental Convex Hull algorithm (see for example GiftWrapping [44], or Incremental Convex Hull [45]), startingfrom I C , which is convex and is the convex hull of itsvertices, and adding the point D . Theorem III.6.
Locus S C ( D ) and locus S C,A ( D ) are aconnected component each.Proof. If D ∈ I C , S C ( D ) is the empty set. Let us considerthat D / ∈ I C . From the computation of Z C ( D ) using anIncremental Convex Hull algorithm [44], [45], the S C ( D ) isconstituted by the segments linking the vertices of I C thatare not vertices of Z C ( D ) , plus the two vertices of I C thatwere linked to D . Thus, S C ( D ) is a succession of adjacentsegments, thus S C ( D ) is a connected component. The proofregarding S C,A ( D ) is analogous. Corollary 1.
Considering sites A , B and C that are mutualneighbors of each others, it holds that B ∈ N C ( D ) (cid:86) A ∈ N C ( D ) if and only if the common vertex of V A , V B and V C lays into S C ( D ) . Corollary 2.
Consider now local visions. The commonvertex of v A,B,C three sites A, B and C that are mutualneighbors, is computed in the same way by the three sites.Thus, since the knowledge about the AoI is global, all A , B and C agree on the belonging of the common vertex to thesegments of interest S C ( D ) , S C,A ( D ) and S C,B ( D ) . Corollary 3.
As a consequence of the previous corollary, A , B and C agree on • C sending a packet to A – or not – to get to D withMABRAVO D algorithm, and • A sending a packet to C – or not – for a AoI-castgenerated in D with MABRAVO R algorithm. Theorem III.7.
Existence for MABRAVO R routes (each sitein the AoI receives the packet at least once).Proof. Let us consider that D generates a MABRAVO R AoI-cast, that A must receive the packet because its Voronoi cellowns points included in the AoI, and that B decides not toforward a packet to A . Let us prove that there will be anothersite forwarding the packet to A .Site B can take the decision not to forward the packet to A for two motivations: • Site
B / ∈ N A,B ( D ) , which is the set of the neighborsof A that are towards D in the local vision of B .Since I A,B ⊇ I A (see Theorem III.4), B can not be in N A ( D ) , and since the unicast route from A to D exists(see Theorem III.1), there must be at least another sitethat will forward the packet to A during MABRAVO R routing. • Function ∠ Ds i B has not a minimum in s i = A . Thecause is that one common neighbor of A and B (let . . . . . . A s i s i-1 s i+1 D B
FIGURE 6.
Unicity of MABRAVO R AoI-cast routes. us call it C ) is into N A,B ( D ) and it has a smallerangle. Since A , B and C agree if C ∈ N A,B ( D ) (seeCorollary 3), C will either select itself to send the packetto A , or it will repeat the same reasoning for a commonneighbor (let us call it F ) of C and A , but on the otherside with respect to B . Since the number of neighbor of A is finite, this chain will end up on a site (let call it G )that will actually send the packet to A .Thus, if B decides not to forward a packet to A , there willbe at least another site that will forward the packet to A , andhence there exists at least one MABRAVO R route reaching A . Theorem III.8.
Unicity for MABRAVO R route (each site inthe AoI receives the packet at most once).Proof. Let us prove that a generic site A can not receivea packet from more than one MABRAVO R route. First ofall, as a consequence of Theorem III.2, we have to considerthat any site that will forward a message to A should lay inthe half of the plane that is closer to D than A itself. Letus now suppose that site B decides to send a packet to site A during a MABRAVO R routing originated in point D . Inthe following, we use Fig. 6 as a possible representation ofthe situation. A necessary condition is that B ∈ N A,B ( D ) ,and thus B ∈ N A ( D ) . Moreover, B should see that ∠ DAB is smaller that the angle formed by any of its neighborsin N A ( D ) . This fact implies that B is the site in N A ( D ) that is closer to the half-plane A − D bisector line, thatconnects D and A . Otherwise, since Theorem III.6 statesthat all the sites in S A ( D ) form a connected locus on theplane, there exists a series of other sites s , ..., s i that startsfrom a B ’s neighbor s , and where a site s k is neighbor of s k +1 . These sites should be closer to the bisector line than B , as shown in Fig. 6. However, this also implies that eachof these sites forms an angle with D and A that is lowerthan ∠ DAB . Therefore, B cannot consider itself as the bestcandidate to forward a message to A , since it determines thatat least one of its neighbors is a better candidate. The samedecision would be taken by all the sites s , ..., s i − . This VOLUME 4, 2016 . Albano, M. Mordacchini, L. Ricci: AoI-based Multicast Routing over Voronoi Overlays with minimal overhead leads to the conclusion that only one site ( s i in the example)considers itself as the site in charge to deliver a message to A ,thus demonstrating the unicity of the selection of a messageforwarder in MABRAVO R . F. CONSIDERATIONS ABOUT THE COMPLEXITY OFTHE ALGORITHMS
This section discusses briefly the complexity of theMABRAVO routing algorithms, both in terms of messages,and of computational complexity.As proven in the previous subsections, the MABRAVOprotocol suite allows for correct unicast and AoI-cast routingif the sites have up-to-date information regarding their ownlocations, and the location of their neighbors in the Voronoidiagram. As discussed in Section I-A, we consider that atopology maintenance algorithm is already in place in thenetwork, since several solutions are already available in theliterature [34]–[36]. For example, the VoroNet [36] topologymaintenance algorithm has a message complexity for eachsite that is proportional to the number of its neighbors. Sincethe expected number of neighbors of a site is lower than [39], the amortized message complexity for each site tomaintain the topology is O (1) .The message complexity for the MABRAVO R AoI-castalgorithm was proven to be optimal in Section III-E. Thealgorithm is able to create a routing tree over the sites in theAoI in a distributed manner, and the total number of messagesis equal to the number of sites in the AoI minus .In the rest of this section, let us call n the number of neigh-bors of a site s i , and m the number of sides defining the AoI.The computational complexity of both the MABRAVO D algorithm (Algorithm 1) and the MABRAVO R algorithm(Algorithm 2) depends (i) on the expected number of neigh-bors of each site s i being less than [39], thus O (1) ; (ii)on the operations discussed in Section III-A being able toaccess the set of neighbors of each site s i in linear time inthe number of neighbors; (iii) on the fact that the numberof sides of the AoI is an external parameter set by the userdefining the AoI, and in most applications this value can beconsidered sufficiently small. For instance, in many location-based applications, areas/regions of interest are defined asrectangles (e.g. [46]–[48]).With regards to the MABRAVO D algorithm (Algo-rithm 1), its first loop of the algorithm is repeated for eachneighbor of a site s i (thus O ( n ) times), and each time itaccesses the list of neighbors of s i (complexity O ( n ) ) andit compares the location of each neighbor with each AoIside, whose cardinality is O ( m ) . Thus, the complexity ofthe first loop is O ( n m ) . The second loop is executed whenno vertices of the Voronoi cell of s i are into the AoI, it isrepeated for each neighbor of s i ( O ( n ) times), its internalloop is repeated for each side of the AoI ( O ( m ) times),thus the complexity of the second loop is O ( nm ) . Thethird loop is repeated over the neighbors of s i , which are O ( n ) , it performs only operations with constant complexity,thus the complexity of the third loop is O ( n ) . Thus, the computational complexity of the MABRAVO D algorithm is O ( n m + nm + n ) = O ( n m ) . It is worth noticing that,in the average case, n has an expected value that is equalor less than the constant . Therefore, in the average casethe complexity reduces to O ( m ) . In addition, as observed inthe previous paragraph, m has generally a small value, thusleading to an overall low complexity.With regards of the MABRAVO R algorithm (Algo-rithm 2), its most external loop is repeated for each neighborof s i , thus O ( n ) times. The first condition in the algorithm(the neighbors being located outside the AoI) requires torepeat basic geometric operations for each side of the AoI(thus, O ( m ) times), then it extracts v i,j,k and v i,j,l (cost O ( n ) ), and then executes a loop on the sides of the AoI(thus, O ( m ) times), each time performing operations havingconstant execution time. If at least one of the neighborsof s i is located into the AoI, whose test costs O ( m ) , thealgorithm executes in the worst case the two if clauses,which require to perform basic geometric operations. Thus,the computational complexity of the MABRAVO R algorithmis O ( n ( m ( n + m ) + m )) = O ( n m + nm ) . Applying thesame reasoning used for MABRAVO D , in the average casethe value of n is equal or less than . The overall complexityis thus a function of m only (i.e.: O ( m ) ), where m isgenerally a small value. IV. EVALUATION OF THE MABRAVO SUITE
This section describes the experimental evaluation of thealgorithms of the MABRAVO suite. The evaluation is madethrough a simulation implementation of the proposed so-lution. The results shown in the rest of this section havebeen selected in order to better highlight the features ofMABRAVO and to allow to experimentally corroborate thecorrectness of the algorithms.
A. IMPLEMENTATION
In this section, we provide a description of the simula-tor we used to derive the results presented in the restof the section. This description makes it possible to usethe related software. Thus, it allows to make the resultswe present verifiable and fully reproducible by the sci-entific community. The simulator is available on github(https://github.com/michelealbano/mabravo) and it was pub-lished on Code Ocean (DOI: 10.24433/CO.1722184.v1).The algorithms were implemented using the Java pro-gramming language and are accessible as a supplementarymaterial of this paper. This subsection describes the code,shows how to compile it, and what it does when executed.The implementation makes use of the VAST library, awell-known library used in the literature to help evaluateVoronoi-based solutions (e.g., the proof-of-concept in [31]).The novel code comprises 4 classes: • AreaOfInterest maintains a convex AoI on the plane.When instantiated, it receives a number of points inthe plane, and it makes use of the Gift Wrapping [44]
VOLUME 4, 2016
9. Albano, M. Mordacchini, L. Ricci: AoI-based Multicast Routing over Voronoi Overlays with minimal overhead algorithm to organize them as a clockwise sequence ofpoints that define the AoI; • VoronoiArea is a thin wrapper over the mechanismsprovided by the VON codebase; • VoronoiNetwork implements all the routing algorithmsof the MABRAVO suite, and a breadth first visit that isused to compute e.g. the number of sites that lie into anAoI; • Mabravo contains all the parameters that are used tospecify the simulations to be performed, it drives theexecution of the experiments, it can provide a simplegraphical representation of the routing processes, and itcan compute performance parameters to summarize theresults of routing processes.To deploy the system, it is sufficient to issue a make com-mand on the command line. After that, the software can beexecuted in two modes.The first one is named the graphical mode. It isexecuted if the user provides parameters on thecommand line. An example of the invocation of thismode of execution is java -cp mabravo-1.1.0.jarmabravo.Mabravo 100 10 1000 . These parametersare: the number of sites; the number of points defining theAoI; a random seed. This execution mode allows the userto have a visual representation of the system and of theexecution of the MABRAVO protocol suite. Specifically, theMabravo application creates a number of sites coordinates atrandom in the plane, and it instantiates an AoI with a givennumber of vertices. After that, it selects two points at randomin the AoI and performs a routing process from the first to thesecond. Finally, a graphical representation of the process isprovided to the user. If the user presses the return key, theprocess will start once again with new random coordinates.The second execution mode is the batch mode. It doesnot provide any graphical representation, but it is designedto allow to perform a series of different simulations of thesystem, and to extract performance indicators. To performthe simulations, five parameters are passed from the com-mand line when invoking the main class (e.g.: java -cpmabravo-1.1.0.jar mabravo.Mabravo 100 10100 10 100 ). These parameters are: the number of sites;the number of points defining the AoI; the number of routingprocesses to be performed over each network; the number ofnetworks to be simulated; a random seed.For each of the routing processes, the system print out datato both evaluate the proposed solution, and to compare itagainst an “oracle", i.e. a solution that computes the routingtree by exploiting a breadth first visit and the full knowledgeabout the structure and topology of the system. The valuesthat are used for evaluation and comparison that are returnedby the simulator are: • site where the unicast routing process starts; • site where the unicast routing end / site where the AoI-cast starts; • number of nodes in the whole network; • nodes in the AoI; • number of hops for the unicast routing using the “ora-cle"; • average length of the AoI-cast routes using the “oracle"; • average length of the AoI-cast using MABRAVO R ; • unicast route computed using MABRAVO D .These are the values used in the next section for the overallevaluation of MABRAVO.When executing the MABRAVO D algorithm, the simu-lator verifies that the routes goes from the source to thedestination, and that no site outside the AoI is reached by therouting process. When executing the MABRAVO R algorithmthe simulator verifies that all the sites in the AoI receive themessage once, and that no site outside the Aoi receives themessage. B. RESULTS
In the following, we present the results obtained by using thesimulator described in the previous section. The experimentsfocus on the more relevant characteristics of the MABRAVOsuite, and aimed to: • verify that the MABRAVO R algorithm is always ableto deliver a packet from a source site in the AoI to adestination site in the AoI, without using relays outsidethe AoI; • proof that the MABRAVO R algorithm sends a packet toall the sites in the AoI and no one else, and that the sitesreceive the packet only once; • compare the length of both MABRAVO D andMABRAVO R routes against the “oracle", as defined inthe previous subsection.In order to present an example of the execution ofMABRAVO, Figure 7 shows the output of the simulator whenexecuted in graphical mode, for networks comprising and sites, respectively. In both these cases, the AoI isdefined by points. The meanings of the colors in the figureare the following: the red lines are the borders of the AoI; theVoronoi cells of sites in the AoI have green borders, whilesites outside the AoI have Voronoi cells with blue borders; themagenta line connects source and destination of the unicastrouting process (the sites case shows clearly that sourceand destination points do not have to be co-located witha site), and the sites touched by the routing process arehighlighted with cyan circles.In order to present a meaningful evaluation, the resultswe show are the average of a series of repeated executionsof the system. Specifically, the system was run in batchmode to simulate different networks and perform MABRAVO D and MABRAVO R routing processes on them.The experiments were executed on networks of and sites, respectively. In both the scenarios, the AoIs are definedby points.For the sake of clarity, in the following we will show ex-perimental results by means of their Cumulative DistributionFunction (CDF) [49], meaning that the graphs will show thepossible values of the variable under study on the x axis, VOLUME 4, 2016 . Albano, M. Mordacchini, L. Ricci: AoI-based Multicast Routing over Voronoi Overlays with minimal overhead
FIGURE 7.
Routing process on a network comprising 100 (left) and 1000 (right) sites.
FIGURE 8.
CDF of the number of sites in the AoI, and of the number of sites receiving an AoI-cast with MABRAVO R , in networks comprising 100 (left) and 1000(right) sites. and the probability that the output of an experiment is lessor equal to the value on the y axis.The simulator confirmed that, in all the scenarios, theMABRAVO suite sent messages exclusively to sites that areincluded in the AoI. With regard to the AoI-cast algorithm,we counted the number of sites in the AoI from a globalvision, and we compared that to the number of sites thatreceive the AoI-cast message with MABRAVO R algorithm.We present the results of the experiments in Figure 8, whoseoverlapping curves ensure that MABRAVO R delivers theAoI-cast message exactly to the sites comprised (fully orpartially) within the AoI.We first show the results related to the unicast protocolof MABRAVO, i.e. MABRAVO D . As we anticipated, whenperforming unicast communication, using the MABRAVO D algorithm the routing process was always able to route thepackets using only sites in the AoI as relays. Figure 9 showsthe CDF of the route length when MABRAVO D is employed,presenting the results for networks of and sites.The results are compared with the “oracle", showing tworemarkably close and similar behaviors. It is worth noticingthat the “oracle" can exploit full knowledge of the geometryof the system, while MABRAVO D can only rely on partial and local information, and it is the result of autonomousdecisions of independent components of the system.The same considerations are valid for the AoI-cast protocolMABRAVO R . Also in this case, the AoI-cast performed bythe MABRAVO R algorithm is able to reach each site in theAoI with a packet by crossing only sites comprised in theAoI. Figure 10 compares the length of the routes for AoI-cast routing by showing the CDF of the average length of theroutes, when the two algorithms are used on networks of and sites. V. RELATED WORKS
Geometric routing techniques are among the most commonlyused strategy for forwarding messages and information inVoronoi networks. Compass Routing is the most importantsolution in this class of routing protocols. The use of Com-pass Routing in Voronoi networks has been first proposedin [50], which considers a connected graph and assumesthat a message is generated at one of its nodes n with thegoal to reach a destination node d . [50] shows that the beststrategy is to look at the edges incident in n and choose theedge whose slope is minimal with respect to the segmentconnecting n and the destination d . [50] also shows that while VOLUME 4, 2016
11. Albano, M. Mordacchini, L. Ricci: AoI-based Multicast Routing over Voronoi Overlays with minimal overhead
FIGURE 9.
CDF of the number of hops in the unicast routing in networks comprising 100 (left) and 1000 (right) sites.
FIGURE 10.
CDF of the average number of hops in the AoI-cast in networks comprising 100 (left) and 1000 (right) sites.
Compass Routing is not cycle free for general graphs, it canalways find a finite path between two nodes of a DelaunayTriangulation. The work in [51] suggests to exploit CompassRouting to define a Spanning Tree supporting an applicationlevel multicast.This class of solutions is very relevant in this field, since itforms the basis of many other routing protocols on Voronoinetworks. However, they do not face the problems relatedto multicast routing within delimited AoIs. These issues arefaced by the approaches described in the following of thissection.As far as its applications are concerned, Voronoi networkshave recently been exploited in several contexts, but mostlyfor the definition of routing algorithms in sensor and wirelesssensor networks.An approach which shares some features with our proposalis introduced in [52]. Indeed, Overlay Geocast, besides for-warding messages toward a given destination, is also able toroute messages to all the nodes belonging to a given area A .To reach a node in A , it exploits greedy routing, then eachnode in A forwards the message to all its neighbors in A anddiscards duplicates by utilizing a Bloom Filters. This impliesa large number of unnecessary messages, while MABRAVOtotally avoids unnecessary communications.[53] introduces sensing-covered networks, which are net-works where every point in a geographic area must be withinthe sensing range of at least one sensor. The paper intro-duces a new routing algorithm, Bounded Voronoi GreedyForwarding (BVGF), that combines Greedy Forwarding andand Voronoi diagrams. When a node forwards a packet, it considers its eligible neighbors, where a neighbor is eligibleif the line segment joining the source and the destinationintersects the Voronoi region of the neighbor or coincideswith one of the boundaries of the Voronoi region. BVGFchooses the neighbor that has the shortest Euclidean distanceto the destination among all eligible neighbors.[54] proposes a Voronoi diagram based on semi-distributed algorithms for coverage holes detection in WSNs.The Voronoi diagram is built by considering the locationof the sensor nodes which have the task of monitoring andcollecting information on the Region of Interest (ROI). Fur-thermore, the proposed algorithms decide if there are holesin the ROI.[55] investigates the use of wireless sensor networks inIoT environments, to monitor and collect data in some geo-graphic area. In this case, spatial range queries with locationconstraints are employed. To reduce the communication costand the storage requirements, the work presents an energy-and time-efficient multidimensional data indexing schemewhich exploits a Voronoi tessellation. VI. CONCLUSIONS & FUTURE WORKS
This paper presents an algorithm to perform AoI-cast inVoronoi-based distributed networks. The proposed solutionis able to construct AoI-cast trees in a completely distributedmanner, where each agent that supervises a Voronoi cellknows only its own coordinates and the ones of its immediateneighbors. Working in totally decentralized manner, the pro-posed algorithms are able to deliver packets by reaching all(and only) the sites in a convex AoI, thus requiring a minimal VOLUME 4, 2016 . Albano, M. Mordacchini, L. Ricci: AoI-based Multicast Routing over Voronoi Overlays with minimal overhead number of messages. In this work we gave a formal specifi-cation of MABRAVO, as well as a formal demonstration ofits properties.An open issue to investigate is whether it exists an algo-rithm that is able to minimize the route lengths depth, whilepreserving the optimal properties of the algorithms presentedin this work (only local knowledge required, minimum num-ber of packets). More future work has been planned: • Port the algorithm to another language (currently it ispure Java), which comprises studying how to use theexisting libraries of target language. For example, thiswill allow to access high-performance libraries for thecomputation of the Voronoi diagrams, and possibly touse hardware accelerations; • Implement the algorithm into a mainstream system sim-ulator, such as ns-3, to experiment the algorithm againstphysical properties of the wireless links, loss of packets,presence of metal walls and other obstacles that hindercommunication; • Study the effect of mobility and high churn of units,and the behavior of the algorithms against obsoleteinformation regarding a unit’s neighbors; • Implement a testbed, where the algorithms are usedto enable communication between robots in industrialsettings, for example basing the exchange of messagesbetween neighbors over the Arrowhead framework [6].
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MICHELE ALBANO (M’11-SM’19) is a tenure-track Assistant Professor for the Department ofComputer Science of Aalborg University, Den-mark. He got his Ph.D. in Computer Science fromthe University of Pisa, Italy, and his research isfocused on distributed systems and embedded sys-tems. He has been active in more than 10 Europeanresearch projects, and he acted as technical man-ager for CELTIC project Green-T; work packageleader for FP7 IP ROMEO, ITEA2 CarCoDe, andECSEL MANTIS. Michele is editor of the Open Access book ”The MAN-TIS book: Cyber Physical System Based Proactive Maintenance”, and he isEditor in Chief for the Journal of Industrial Engineering and ManagementScience, River Publishers.
MATTEO MORDACCHINI is a Researcher atthe Ubiquitous Internet Lab, IIT-CNR, Italy. Cur-rently, his main research areas include Edge com-puting, the Internet of People paradigm, and adap-tive, self-organizing distributed solutions. Specif-ically, he is investigating how models of humancognitive processes, coming from the cognitivepsychology domain, can be exploited to deviseautonomic and adaptive solutions for autonomousagents. Other research directions include Cloudcomputing and Opportunistic Networks. Matteo has also worked in severalEU projects and has served in the TPC of many international conferencesand workshops.
LAURA RICCI received the M.Sc. degree in com-puter science and the Ph.D. degree from the Uni-versity of Pisa, Pisa, Italy, in 1983 and 1990, re-spectively. She is currently an Associate Professorwith the Department of Computer Science, Uni-versity of Pisa. She has been involved in several re-search projects. She is also the Local Coordinatorof the H2020 European Project Helios: A Context-aware Distributed Networking Framework. Hercurrent research interests include distributed sys-tems, peer-to-peer networks, cryptocurrencies and blockchains, and socialnetwork analysis. She has coauthored over 100 articles published in in-ternational journals and conference/workshop proceedings in these fields.Dr. Ricci has served as a program committee member and the chair forseveral conferences. She has been the Program Chair of the 19th editionof International Conference on Distributed Applications and InteroperableSystems (DAIS). She is an Organizer of the Large Scale Distributed VirtualEnvironments (LSDVE) Workshop held in conjunction with EUROPARconference.14