Cristina M. Pinotti

Channel assignment with separation for interference avoidance in wireless networks

Given an integer /spl sigma/>1, a vector (/spl delta//sub 1/, /spl delta//sub 2/,..., /spl delta//sub /spl sigma/-1/), of nonnegative integers, and an undirected graph G=(V, E), an L(/spl delta//sub 1/, /spl delta//sub 2/,..., /spl delta//sub /spl sigma/-1/)-coloring of G is a function f from the vertex set V to a set of nonnegative integers, such that |f(u)-f(v)|/spl ges//spl delta//sub i/, if d(u,v)=i, for 1<i<(/spl sigma/-1), where d(u, v) is the distance (i.e., the minimum number of edges) between the vertices u and v. An optimal L(/spl delta//sub 1/, /spl delta//sub 2/,..., /spl delta//sub /spl sigma/-1/)-coloring for G is one using the smallest range /spl lambda/ of integers over all such colorings. This problem has relevant application in channel assignment for interference avoidance in wireless networks, where channels (i.e., colors) assigned to interfering stations (i.e., vertices) at distance i must be at least /spl delta//sub i/ apart, while the same channel can be reused in vertices whose distance is at least /spl sigma/. In particular, two versions of the coloring problem - L(2, 1, 1) and L(/spl delta//sub 1/, 1,..., 1) - are considered. Since these versions of the problem are NP-hard for general graphs, efficient algorithms for finding optimal colorings are provided for specific graphs modeling realistic wireless networks, including rings, bidimensional grids, and cellular grids.

Efficient use of radio spectrum in wireless networks with channel separation between close stations

This paper investigates the problem of assigning channels to the stations of a wireless network so that interfering transmitters are assigned channels with a given separation and the number of channels used is minimized. Two versions of the channel assignment problem are considered which are equivalent to two specific coloring problems — called L(2, 1) and L (2, 1, 1) — of the graph representing the network topology. In these problems, channels assigned to adjacent vertices must be at least 2 apart, while the same channel can be reused only at vertices whose distance is at least 3 or 4, respectively. Efficient channel assignment algorithms using the minimum number of channels are provided for specific, but realistic, network topologies, including buses, rings, hexagonal grids, bidimensional grids, cellular grids, and complete binary trees.

Mappings for Conflict-Free Access of Paths in Bidimensional Arrays, Circular Lists, and Complete Trees

Since the divergence between the processor speed and the memory access rate is progressively increasing, an efficient partition of the main memory into multibanks is useful to improve the overall system performance. The effectiveness of the multibank partition can be degraded by memory conflicts, that occur when there are many references to the same memory bank while accessing the same memory pattern. Therefore, mapping schemes are needed to distribute data in such a way that data can be retrieved via regular patterns without conflicts. In this paper, the problem of conflict-free access of arbitrary paths in bidimensional arrays, circular lists and complete trees is considered for the first time and reduced to variants of graph-coloring problems. Balanced and fast mappings are proposed which require an optimal number of colors (i.e., memory banks). The solution for bidimensional arrays is based on a particular Latin Square. The functions that map an array node or a circular list node to a memory bank can be calculated in constant time. As for complete trees, the mapping of a tree node to a memory bank takes time that grows logarithmically with the number of nodes of the tree. The problem solved here has further application in minimizing the number of frequencies assigned to the stations of a wireless network so as to avoid interference.

Efficient corona training protocols for sensor networks

Phenomenal advances in nano-technology and packaging have made it possible to develop miniaturized low-power devices that integrate sensing, special-purpose computing, and wireless communications capabilities. It is expected that these small devices, referred to as sensors, will be mass-produced and deployed, making their production cost negligible. Due to their small form factor and modest non-renewable energy budget, individual sensors are not expected to be GPS-enabled. Moreover, in most applications, exact geographic location is not necessary, and all that the individual sensors need is a coarse-grain location awareness. The task of acquiring such a coarse-grain location awareness is referred to as training. In this paper, two scalable energy-efficient training protocols are proposed for massively-deployed sensor networks, where sensors are initially anonymous and unaware of their location. The training protocols are lightweight and simple to implement; they are based on an intuitive coordinate system imposed onto the deployment area which partitions the anonymous sensors into clusters where data can be gathered from the environment and synthesized under local control.

Synchronous black hole search in directed graphs

The paper considers a team of robots which has to explore a graph G, where some nodes can be harmful. Robots are initially located at the so-called home base node. The dangerous nodes are the so-called black hole nodes, and once a robot enters in one of them, it is destroyed. The goal is to find a strategy in order to explore G in such a way that minimum number of robots is wasted. The exploration ends if there is at least one surviving robot which knows all the edges leading to the black holes. As many variations of the problem have been considered so far, the solution and its measure heavily depend on the initial knowledge and the capabilities of the robots. In this paper, we assume that G is a directed graph, the robots are associated with unique identifiers, they know the number of nodes n of G (or at least an upper bound on n), and they know the number of edges @D leading to the black holes. Each node is associated with a whiteboard where robots can read and write information in a mutual exclusive way. A recently posed question [J. Czyzowicz, S. Dobrev, R. Kralovic, S. Miklik, D. Pardubska, Black hole search in directed graphs, in: Proc. of 16th International Colloquium on Structural Information and Communication Complexity, SIROCCO, LNCS, vol. 5869, 2009, pp. 182-194.] is whether some number of robots, expressed as a function of parameter @D only, is sufficient to detect black holes in directed graphs of arbitrarily large order n. We give a positive answer to this question for the synchronous case, i.e., when the robots share a common clock, showing that O(@D@?2^@D) robots are sufficient to solve the problem. This bound is nearly tight, since it is known that at least 2^@D robots are required for some instances. Quite surprisingly, we also show that unlike in the case of undirected graphs, for the directed version of the problem, synchronization can sometimes make a difference: for @D=2, in the synchronous case 4 robots are always sufficient, whereas in the asynchronous case at least 5 robots are sometimes required.

Push Less and Pull the Current Highest Demanded Data Item to Decrease the Waiting Time in Asymmetric Communication Environments

A hybrid scheduling that effectively combines broadcasting for very popular data (push data) and dissemination upon-request for less popular data (pull data) in asymmetric communication environments is introduced. In this solution, the server continuously broadcasts one push item and disseminates one pull item. The clients send their requests to the server, which queues-up them for the pull items. At any instant of time, the item to be broadcast is designated applying a pure-push scheduling, while the item to be pulled is the one stored in the pull-queue, which has accumulated, so far, the highest number of pending requests. The value of the average expected waiting time spent by a client in the hybrid system is evaluated analytically, and the cut-off point between push and pull items is chosen so that such a waiting time is minimized. It is found out that by doing so the cut off point decreases to a value, which is much less than the total number of items present in the system, improving upon the average waiting time spent by a client in a pure push system and also on that spent in some of the hybrid systems already proposed in literature.

Cooperative training for high density sensor and actor networks

Exploiting high density features of wireless sensor networks represents a challenging issue. In this context, anonymous, asynchronous and randomly distributed sensors are considered along with few devices, called actors, which are more powerful than sensors in terms of energy and transmission capabilities. The paper proposes a new distributed training protocol for coarse-grain localization purposes in high density environments. The aim is to auto-organize the sensors with respect to a virtual infrastructure centered at actors and constituted of concentric rings divided into sectors. Analytical study as well as experiments on the proposed protocol are provided. The obtained results show under which theoretical and practical settings the training process can be performed in a fast and high quality way with respect to the granularity of the required localization and the energy consumption.

Asynchronous training in wireless sensor networks

A scalable energy-efficient training protocol is proposed for massively-deployed sensor networks, where sensors are initially anonymous and unaware of their location. The protocol is based on an intuitive coordinate system imposed onto the deployment area which partitions the anonymous sensors into clusters. The protocol is asynchronous, in the sense that the sensors wake up for the first time at random, then alternate between sleep and awake periods both of fixed length, and no explicit synchronization is performed between them and the sink. Theoretical properties are stated under which the training of all the sensors is possible. Moreover, a worst-case analysis as well as an experimental evaluation of the performance is presented, showing that the protocol is lightweight and flexible.

A probabilistic push-pull hybrid scheduling algorithm for asymmetric wireless environment

The vision of mobile computing lies in a seamless connectivity with the mobile clients and transmission of data in precise quality of service (QoS) guarantee. In order to endow such mobile applications with advanced data processing capabilities, efficient, dynamic scheduling algorithms are necessary. In this paper, we have introduced a new hybrid scheduling algorithm that probabilistically combines the number of push and pull operations depending on the number of items present in the system and their popularity. The access probabilities of the data items are computed dynamically, without any prior knowledge. The basic elixir of our work lies in the efficiency of the algorithm in obtaining an improved data access-time, even with high system load and items having equivalent degree of access probabilities. The expected waiting time spent by a client is evaluated and compared analytically. Simulation results point out sufficient improvement in average waiting time than pure push systems and some existing hybrid systems.

Localization and scheduling protocols for actor-centric sensor networks

We propose novel localization and routing protocols in an actor-centric wireless sensor network consisting of an actor node and a large number of energy-constrained sensors operating under L different periodic sleep–awake schedules. Specifically, we propose a semidistributed localization algorithm in which a small subset of sensors extracts their positions in polar coordinates based on the messages received from the actor, and subsequently localizes (also in polar coordinates) the remaining sensors. By modeling the deployed sensors as a two-dimensional Poisson point process and applying well-known results from the coupon collectors problem and Chernoff bounds, we analytically derive and also validate, by simulation, the sensor density required to localize all sensors in the network with high probability. The actor-centric network can be modeled by a cluster adjacency graph G with the help of the already localized polar coordinates that logically partition the network into concentric coronas (around the actor), each subdivided in a varying number of clusters (of almost the same area). To avoid intercluster collisions in G, sensors in different clusters transmit on different channels. A lower bound on the number of channels required to schedule the transmissions without collisions is obtained by solving a distance-2 vertex coloring problem on G. Optimal and quasioptimal fully distributed algorithms are provided to determine the channel assigned to each cluster in constant time. Finally, we apply these results to develop a geographic routing protocol: the messages generated from the sensors in a given cluster are routed toward the actor through the unique shortest path of G that starts from the node associated with the cluster and goes up to the corona where the actor resides. In each cluster, to avoid redundant retransmissions toward the actor, we select L leaders, one for each periodic sleep–awake schedule.