Gianlorenzo D’Angelo

Recoverable robust timetabling for single delay: Complexity and polynomial algorithms for special cases

In this paper, we study the problem of planning a timetable for passenger trains considering that possible delays might occur due to unpredictable circumstances. If a delay occurs, a timetable could not be able to manage it unless some extra time has been scheduled in advance. Delays might be managed in several ways and the usual objective function considered for such purpose is the minimization of the overall waiting time caused to passengers.We analyze the timetable planning problem in terms of the recoverable robustness model, where a timetable is said to be recoverable robust if it is able to absorb small delays by possibly applying given limited recovery capabilities. The quality of a robust timetable is measured by the price of robustness that is the ratio between the cost of the recoverable robust timetable and that of a non-robust optimal one.We consider the problem of designing recoverable robust timetables subject to bounded delays. We show that finding an optimal solution for this problem is NP-hard. Then, we propose robust algorithms, evaluate their prices of robustness, and show that such algorithms are optimal in some important cases.

Dynamic Multi-level Overlay Graphs for Shortest Paths

Abstract.Multi-level overlay graphs represent a speed-up technique for shortest paths computation which is based on a hierarchical decomposition of a weighted directed graph G. They have been shown to be experimentally efficient, especially when applied to timetable information. However, no theoretical result on the cost of constructing, maintaining and querying multi-level overlay graphs in a dynamic environment is known.In this paper, we show theoretical properties of multi-level overlay graphs that lead us to the definition of a new data structure for the computation and the maintenance of an overlay graph of G while weight decrease or weight increase operations are performed on G. Our solution is theoretically faster than the recomputation from scratch and allows queries that can be performed more efficiently than running Dijkstra’s shortest paths algorithm on G.

Gathering Asynchronous and Oblivious Robots on basic Graph Topologies under the Look-Compute-Move model

Recent and challenging models of robot-based computing systems consider identical, oblivious and mobile robots placed on the nodes of anonymous graphs. Robots operate asynchronously in order to reach a common node and remain with it. This task is known in the literature as the gathering or rendezvous problem. The target node is neither chosen in advance nor marked differently compared to the other nodes. In fact, the graph is anonymous and robots have minimal capabilities. In the context of robot-based computing systems, resources are always limited and precious. Then, the research of the minimal set of assumptions and capabilities required to accomplish the gathering task as well as for other achievements is of main interest. Moreover, the minimality of the assumptions stimulates the investigation of new and challenging techniques that might reveal crucial peculiarities even for other tasks. The model considered in this chapter is known in the literature as the Look-Compute-Move model. Identical robots initially placed at different nodes of an anonymous input graph operate in asynchronous Look-Compute-Move cycles. In each cycle, a robot takes a snapshot of the current global configuration (Look), then, based on the perceived configuration, takes a decision to stay idle or to move to one of its adjacent nodes (Compute), and in the latter case it makes an instantaneous move to this neighbor (Move). Cycles are performed asynchronously for each robot. This means that the time between Look, Compute, and Move operations is finite but unbounded, and it is decided by the adversary for each robot. Hence, robots may move based on significantly outdated perceptions. The only constraint is that moves are instantaneous, and hence any robot performing a Look operation perceives all other robots at nodes of the ring and not on edges. Robots are all identical, anonymous, and execute the same deterministic algorithm. They cannot leave any marks at visited nodes, nor can they send messages to other robots. In this chapter, we aim to survey on recent results obtained for the gathering task over basic graph topologies, that are rings, grids, and trees. Recent achievements to this matter have attracted many researchers, and have provided interesting approaches that might be of main interest to the community that studies robot-based computing systems.

Engineering a New Algorithm for Distributed Shortest Paths on Dynamic Networks

We study the problem of dynamically updating all-pairs shortest paths in a distributed network while edge update operations occur to the network. We consider the practical case of a dynamic network in which an edge update can occur while one or more other edge updates are under processing. A node of the network might be affected by a subset of these changes, thus being involved in the concurrent executions related to such changes.In this paper, we provide a new algorithm for this problem, and experimentally compare its performance with respect to those of the most popular solutions in the literature: the classical distributed Bellman-Ford method, which is still used in real network and implemented in the RIP protocol, and DUAL, the Diffuse Update ALgorithm, which is part of CISCO’s widely used EIGRP protocol. As input to the algorithms, we used both real-world and artificial instances of the problem. The experiments performed show that the space occupancy per node required by the new algorithm is smaller than that required by both Bellman-Ford and DUAL. In terms of messages, the new algorithm outperforms both Bellman-Ford and DUAL on the real-world topologies, while on artificial instances, the new algorithm sends a number of messages that is more than that of DUAL and much smaller than that of Bellman-Ford.

Partially Dynamic Algorithms for Distributed Shortest Paths and their Experimental Evaluation

In this paper, we study the dynamic version of the distributed all-pairs shortest paths problem. Most of the solutions given in the literature for this problem, either (i) work under the assumption that before dealing with an edge operation, the algorithm for the previous operation has to be terminated, that is, they are not able to update shortest paths concurrently, or (ii) concurrently update shortest paths, but their convergence can be very slow (possibly infinite). In this paper we propose a partially dynamic algorithm that overcomes most of these limitations. In particular, it is able to concurrently update shortest paths and in many cases its convergence is quite fast. These properties are highlighted by an experimental study whose aim is to show the effectiveness of the proposed algorithms also in the practical case.

Minimize the Maximum Duty in Multi-interface Networks

We consider devices equipped with multiple wired or wireless interfaces. By switching of various interfaces, each device might establish several connections. A connection is established when the devices at its endpoints share at least one active interface. Each interface is assumed to require an activation cost. In this paper, we consider two basic networking problems in the field of multi-interface networks. The first one, known as the Coverage problem, requires to establish the connections defined by a network. The second one, known as Connectivity problem, requires to guarantee a connecting path between any pair of nodes of a network. Both are subject to the constraint of keeping as low as possible the maximum cost set of active interfaces at each single node. We study the problems of minimizing the maximum cost set of active interfaces among the nodes of the network in order to cover all the edges in the first case, or to ensure connectivity in the second case. We prove that the Coverage problem is NP-hard for any fixed Δ≥5 and k≥16, with Δ being the maximum degree, and k being the number of different interfaces among the network. We also show that, unless P=NP, the problem cannot be approximated within a factor of ηln Δ, for a certain constant η. We then provide a general approximation algorithm which guarantees a factor of O((1+b)ln Δ), with b being a parameter depending on the topology of the input graph. Interestingly, b can be bounded by a constant for many graph classes. Other approximation and exact algorithms for special cases are presented. Concerning the Connectivity problem, we prove that it is NP-hard for any fixed Δ≥3 and k≥10. Also for this problem, the inapproximability result holds, that is, unless P=NP, the problem cannot be approximated within a factor of ηln Δ, for a certain constant η. We then provide approximation and exact algorithms for the general problem and for special cases, respectively.

A new fully dynamic algorithm for distributed shortest paths and its experimental evaluation

In this paper we study the problem of dynamically update all-pairs shortest paths in a distributed network while edge update operations occur to the network. Most of the previous solutions for this problem suffer of two main limitations: they work under the assumption that before dealing with an edge update operation, the algorithm for each previous operation has to be terminated, that is, they are not able to update shortest paths concurrently; they concurrently update shortest paths, but their convergence can be very slow (possibly infinite) due to the well-known looping and count-to-infinity phenomena; they are not suitable to work in the realistic fully dynamic case, where an arbitrary sequence of edge change operations can occur to the network in an unpredictable way. In this paper, we make a step forward in the area of shortest paths routing, by providing a new fully dynamic solution that overcomes some of the above limitations. In fact, our algorithm is able to concurrently update shortest paths, it heuristically reduces the cases where the looping and count-to-infinity phenomena occur and it is experimentally better than the Bellman-Ford algorithm.

Min-Max Coverage in Multi-interface Networks

We consider devices equipped with multiple wired or wireless interfaces. By switching among interfaces or by combining the available interfaces, each device might establish several connections. A connection is established when the devices at its endpoints share at least one active interface. Each interface is assumed to require an activation cost. In this paper, we consider the problem of establishing the connections defined by a network G = (V, E) while keeping as low as possible the maximum cost set of active interfaces at the single nodes. Nodes V represent the devices, edges E represent the connections that must be established. We study the problem of minimizing the maximum cost set of active interfaces among the nodes of the network in order to cover all the edges. We prove that the problem is NP-hard for any fixed Δ ≥ 5 and k ≥ 16, with Δ being the maximum degree, and k being the number of different interfaces among the network. We also show that the problem cannot be approximated within Ω(ln Δ). We then provide a general approximation algorithm which guarantees a factor of O((1 + b) ln(Δ)), with b being a parameter depending on the topology of the input graph. Interestingly, b can be bounded by a constant for many graph classes. Other approximation and exact algorithms for special cases are presented.

Approximation Bounds for the Minimum k-Storage Problem

Sensor networks are widely used to collect data that are required for future information retrieval. Data might be aggregated in a predefined number \(k\) of special nodes in the network, called storage nodes, which, for replying to external queries, compress the last received raw data and send them towards the sink. We consider the problem of locating such storage nodes in order to minimize the energy consumed for converging the raw data to the storage nodes as well as to converge the aggregated data to the sink. This is known as the minimum k-storage problem. We first prove that it is \(N\!P\)-hard to be approximated within a factor of \(1+\frac{1}{e}\). We then propose a local search algorithm which guarantees a constant approximation factor. We conducted extended experiments to show that the algorithm performs very well in many different scenarios. Further, we prove that the problem is not in APX if we consider directed links, unless \(P=N\!P\).

Distance-Vector Algorithms for Distributed Shortest Paths Computation in Dynamic Networks

Computing and updating distributed shortest paths is a core functionality of today’s communication networks. The solutions known in the literature are classified into two categories, namely Distance-Vector and Link-State algorithms. Distance-Vector algorithms usually require each node of the network to store the distance toward every other node in a data structure called routing table, thus requiring linear storage per node. Such a data structure is used to compute the next hop to be used to forward data toward any destination node of interest. This is usually done by solving very simple equations, thus requiring few computational time per node. The main drawback of Distance-Vector algorithms is that, in dynamic scenarios, they can suffer of the looping and count-to-infinity phenomena, though quite efficient countermeasures for such issues are known. Link-State algorithms, instead, require a node of the network to know and store the entire network topology, to compute its distance and next hop toward any destination. This is usually done by means of a centralized shortest-path algorithm, hence requiring quadratic storage and rather high computational effort per node. The main drawback of Link-State algorithms is that, notwithstanding they do not incur in looping and count-to-infinity problems, they perform quite poorly in dynamic scenarios, since nodes need to receive and store up-to-date information on the entire network topology after each change. In the last years, there has been a renewed interest in devising new light-weight distributed shortest-path solutions for large-scale Ethernet networks, where Distance-Vector algorithms are an attractive alternative to Link-State solutions when scalability and reliability are key issues or when the memory resources of the nodes of the network are limited. In this chapter, we hence focus on Distance-Vector solutions by reviewing classic approaches and recent algorithmic developments in this category.