Gabriele Di Stefano

A Distributed AOA Based Localization Algorithm for Wireless Sensor Networks

In this paper we propose a distributed algorithm for solving the positioning problem in ad-hoc wireless networks. The method is based on the capability of the nodes to measure the angle of arrival (AOA) of the signals they produce. The main features of the distributed algorithm are simplicity, asynchronous operations (i.e. no global coordination among nodes is required), ability to operate in disconnected networks. Moreover each node can join the computation at any time. Numerical results, obtained by simulating several scenarios, show that the algorithm can reach a good level of convergence even when the number of communications is limited.

Recoverable Robustness in Shunting and Timetabling

In practical optimization problems, disturbances to a given instance are unavoidable due to unpredictable events which can occur when the system is running. In order to face these situations, many approaches have been proposed during the last years in the area of robust optimization. The basic idea of robustness is to provide a solution which is able to keep feasibility even if the input instance is disturbed, at the cost of optimality. However, the notion of robustness in every day life is much broader than that pursued in the area of robust optimization so far. In fact, robustness is not always suitable unless some recovery strategies are introduced. Recovery strategies are some capabilities that can be used when disturbing events occur, in order to keep the feasibility of the pre-computed solution. This suggests to study robustness and recoverability in a unified framework. Recently, a first tentative of unifying the notions of robustness and recoverability into a new integrated notion of recoverable robustness has been done in the context of railway optimization. In this paper, we review the recent algorithmic results achieved within the recoverable robustness model in order to evaluate the effectiveness of this model. To this aim, we concentrate our attention on two problems arising in the area of railway optimization: the shunting problem and the timetabling problem. The former problem regards the reordering of freight train cars over hump yards while the latter one consists in finding passenger train timetables in order to minimize the overall passengers traveling time. We also report on a generalization of recoverable robustness called multi-stage recoverable robustness which aims to extend recoverable robustness when multiple recovery phases are required.

A Graph Theoretical Approach To The Shunting Problem

Abstract In this paper we propose a graph theoretical approach to the problem of train shunting in a railway depot. Especially during the night, the trains have to be parked in a shunting depot in such a way that the operations in the next morning can start as smoothly as possible. The general problem is very difficult and includes many subproblems. We focus on the following subproblem: how to arrange the trains in a “correct” order on the available tracks by avoiding shunting operations for outgoing trains of the morning. We discuss different cases of the problem, and we propose both algorithmic solutions and heuristic approaches.

A fully dynamic algorithm for distributed shortest paths

We propose a fully dynamic distributed algorithm for the all-pairs shortest paths problem on general networks with positive real edge weights. If Δσ is the number of pairs of nodes changing the distance after a single edge modification σ (insert, delete, weight decrease, or weight increase) then the message complexity of the proposed algorithm is O(nΔσ) in the worst case, where n is the number of nodes of the network. If Δσ = o(n2), this is better than recomputing everything from scratch after each edge modification. Up to now only a result of Ramarao and Venkatesan was known, stating that the problem of updating shortest paths in a dynamic distributed environment is as hard as that of computing shortest paths.

Track assignment

We consider a station in which several trains might stop at the same track at the same time. The trains might enter and leave the station from both sides, but the arrival and departure times and directions are fixed according to a given time table. The problem is to assign tracks to the trains such that they can enter and leave the station on time without being blocked by any other train. We consider some variation of the problem on linear time tables as well as on cyclic time tables and show how to solve them as a graph coloring problem on special graph classes. One of these classes are the so called circular arc containment graphs for which we give an optimal O(nlogn) coloring algorithm.

Gathering of robots on anonymous grids without multiplicity detection

The paper studies the gathering problem on grid networks. A team of robots placed at different nodes of a grid, have to meet at some node and remain there. Robots operate in Look-Compute-Move cycles; in one cycle, a robot perceives the current configuration in terms of occupied nodes (Look), decides whether to move towards one of its neighbors (Compute), and in the positive case makes the computed move instantaneously (Move). Cycles are performed asynchronously for each robot. The problem has been deeply studied for the case of ring networks. However, the known techniques used on rings cannot be directly extended to grids. Moreover, on rings, another assumption concerning the so-called multiplicity detection capability was required in order to accomplish the gathering task. That is, a robot is able to detect during its Look operation whether a node is empty, or occupied by one robot, or occupied by an undefined number of robots greater than one. In this paper, we provide a full characterization about gatherable configurations for grids. In particular, we show that in this case, the multiplicity detection is not required. Very interestingly, sometimes the problem appears trivial, as it is for the case of grids with both odd sides, while sometimes the involved techniques require new insights with respect to the well-studied ring case. Moreover, our results reveal the importance of a structure like the grid that allows to overcome the multiplicity detection with respect to the ring case.

Gathering of six robots on anonymous symmetric rings

The paper deals with a recent model of robot-based computing which makes use of identical, memoryless mobile robots placed on nodes of anonymous graphs. The robots operate in Look-Compute-Move cycles; in one cycle, a robot takes a snapshot of the current configuration (Look), takes a decision whether to stay idle or to move to one of its adjacent nodes (Compute), and in the latter case makes an instantaneous move to this neighbor (Move). Cycles are performed asynchronously for each robot. In particular, we consider the case of only six robots placed on the nodes of an anonymous ring in such a way they constitute a symmetric placement with respect to one single axis of symmetry, and we ask whether there exists a strategy that allows the robots to gather at one single node. This is in fact the first case left open after a series of papers [1,2,3,4] dealing with the gathering of oblivious robots on anonymous rings. As long as the gathering is feasible, we provide a new distributed approach that guarantees a positive answer to the posed question. Despite the very special case considered, the provided strategy turns out to be very interesting as it neither completely falls into symmetry-breaking nor into symmetry-preserving techniques.

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.

Gathering on rings under the Look---Compute---Move model

A set of robots arbitrarily placed on different nodes of an anonymous ring have to meet at one common node and there remain. This problem is known in the literature as the gathering. Anonymous and oblivious robots operate in Look–Compute–Move cycles; in one cycle, a robot takes a snapshot of the current configuration (Look), decides whether to stay idle or to move to one of its neighbors (Compute), and in the latter case makes the computed move instantaneously (Move). Cycles are asynchronous among robots. Moreover, each robot is empowered by the so called multiplicity detection capability, that is, it is able to detect during its Look operation whether a node is empty, or occupied by one robot, or occupied by an undefined number of robots greater than one. The described problem has been extensively studied during the last years. However, the known solutions work only for specific initial configurations and leave some open cases. In this paper, we provide an algorithm which solves the general problem but for few marginal and specific cases, and is able to detect all the ungatherable configurations. It is worth noting that our new algorithm makes use of some previous techniques and unifies them with new strategies in order to deal with any initial configuration, even those left open by previous works.

How to gather asynchronous oblivious robots on anonymous rings

A set of robots arbitrarily placed on different nodes of an anonymous ring have to meet at one common node and remain in there. This problem is known in the literature as the gathering. Anonymous and oblivious robots operate in Look-Compute-Move cycles; in one cycle, a robot takes a snapshot of the current configuration (Look), decides whether to stay idle or to move to one of its neighbors (Compute), and in the latter case makes the computed move instantaneously (Move). Cycles are asynchronous among robots. Moreover, each robot is empowered by the so called multiplicity detection capability, that is, it is able to detect during its Look operation whether a node is empty, or occupied by one robot, or occupied by an undefined number of robots greater than one. The described problem has been extensively studied during the last years. However, the known solutions work only for specific initial configurations and leave some open cases. In this paper, we provide an algorithm which solves the general problem, and is able to detect all the ungatherable configurations. It is worth noting that our new algorithm makes use of a unified and general strategy for any initial configuration, even those left open by previous works.