Serafino Cicerone

Cardinal directions between spatial objects: the pairwise-consistency problem

The paper formalizes an open-problem (called by the authors the pairwise-consistency problem) which is relevant in the context of cardinal directions among extended objects, proposes an efficient algorithmic solution for it, discusses the implementation of the algorithm and briefly reports the numerical results obtained by running the code.

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 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.

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.

On the extension of bipartite to parity graphs

Abstract Parity graphs form a superclass of bipartite and distance-hereditary graphs. Since their introduction, all the algorithms proposed as solutions to the recognition problem and other combinatorial problems exploit the structural property of these graphs described by Burlet and Uhry (Berge and Chvatal (Eds.), Topics on Perfect Graphs, Ann. Discrete Math., vol. 21, North-Holland, Amsterdam, 1984, pp. 253–277). This paper introduces a different structural property of parity graphs: split decomposition returns exactly, as building blocks of parity graphs, cliques and bipartite graphs. This characterization, together with the observation that the split decomposition process can be performed in linear time, allows us to provide optimum algorithms for both the recognition problem and the maximum weighted clique. Moreover, it can also be used to show that the maximum weighted independent set problem can be solved by an algorithm whose worst complexity occurs when the parity graph considered is bipartite. A remarkable consequence of this work is that the extension of bipartite graphs to parity graphs does not increase the complexity of the basic problems we have considered, since the worst case occurs when the parity graph under consideration is an undecomposable bipartite graph.

Graph classes between parity and distance-hereditary graphs☆

Several graph problems (e.g., steiner tree, connected domination, hamiltonian path, and isomorphism problem), which can be solved in polynomial time for distance-hereditary graphs, are NP-complete or open for parity graphs. Moreover, the metric characterizations of these two graph classes suggest an excessive gap between them. We introduce a family of classes forming an infinite lattice with respect to inclusion, whose bottom and top elements are the class of the distance-hereditary graphs and the class of the parity graphs, respectively. We propose this family as a reference framework for studying the computational complexity of fundamental graph problems. For this purpose we characterize these classes using Cunningham decomposition and then use the devised structural characterization in order to show efficient algorithms for the recognition and isomorphism problems. As far as the isomorphism graph problem is concerned we find efficient algorithms for an infinite number of different classes (forming a chain with respect to the inclusion relation) in the family.

Graphs with Bounded Induced Distance

In this work we introduce graphs with bounded induced distance of order k (BID(k) for short). In any graph belonging to BID(k), the length of every induced path between every pair of nodes is at most k times the distance between the same nodes. In communication networks modeled by these graphs any message can be always delivered through a path whose length is at most k times the best possible one, even if some nodes fail.

Partially dynamic efficient algorithms for distributed shortest paths

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) due to the looping and counting infinity phenomena. In this paper, we propose partially dynamic algorithms that are able to concurrently update shortest paths. We experimentally analyze the effectiveness and efficiency of our algorithms by comparing them against several implementations of the well-known Bellman-Ford algorithm.

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.

Cardinal relations between regions with a broad boundary

Despite the innovative relevance of the results about spatial relations today available, the expressiveness of spatial query languages needs to be pushed further significantly in order to cope with the complexity of spatial entities. In particular, more research is necessary in order to support queries against data with uncertainty. In connection with cardinal directions, the best method today available is the Boolean, 3 × 3 direction-relation matrix proposed very recently by Goyal and Egenhofer. Our paper extends such a method to the case of regions with a broad boundary by introducing a 4-value, 5 × 5 direction-relation matrix. Furthermore, the present contribution studies the notion of consistency for a direction-relation matrix and proposes a set of conditions which are necessary and sufficient for assessing consistency.