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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 ∆ ≥ 5 and k ≥ 16, with ∆ 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 Ώ(ln ∆). We then provide a general approximation algorithm which guarantees a factor of O((1 + b)ln (∆)), 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. [ABSTRACT FROM AUTHOR]

In heterogeneous networks, devices can communicate by means of 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, and provides a communication bandwidth. In this paper, we consider the problem of activating the cheapest set of interfaces among a network G = (V,E) in order to guarantee a minimum bandwidth B of communication between two specified nodes. Nodes V represent the devices, edges E represent the connections that can be established. In practical cases, a bounded number k of different interfaces among all the devices can be considered. Despite this assumption, the problem turns out to be NP-hard even for small values of k and ∆, where ∆ is the maximum degree of the network. In particular, the problem is NP-hard for any fixed k ≥ 2 and ∆ ≥ 3, while it is polynomially solvable when k = 1, or ∆ ≤ 2 and k = O(1). Moreover, we show that the problem is not approximable within ηlogB or Ώ(loglog|V|) for any fixed k ≥ 3, ∆ ≥ 3, and for a certain constant η, unless ]> . We then provide an approximation algorithm with ratio guarantee of bmax, where bmax is the maximum communication bandwidth allowed among all the available interfaces. Finally, we focus on particular cases by providing complexity results and polynomial algorithms for ∆ ≤ 2. [ABSTRACT FROM AUTHOR]

In modern networks, devices are 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 guarantee the connectivity of 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 can be established. We study the problem of minimizing the maximum cost set of active interfaces among the nodes of the network in order to ensure connectivity. We prove that the problem is NP-hard for any fixed ∆ ≥ 3 and k ≥ 10, with ∆ 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 O(log|V|). We then provide approximation and exact algorithms for the general problem and for special cases, respectively. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In the context of scheduling and timetabling, we study a challenging combinatorial problem which is very interesting for both practical and theoretical points of view. The motivation behind it is to cope with scheduled activities which might be subject to unavoidable disruptions, such as delays, occurring during the operational phase. The idea is to preventively plan some extra time for the scheduled activities in order to be ˵prepared″ if a delay occurs, and absorb it without the necessity of re-scheduling all the activities from scratch. This realizes the concept of designing robust timetables. During the planning phase, one should also consider recovery features that might be applied at runtime if disruptions occur. This leads to the concept of recoverable robust timetables. In this new concept, it is assumed that recovery capabilities are given as input along with the possible disruptions that must be considered. The main objective is the minimization of the overall needed time. We show that finding an optimal solution for this problem is NP-hard even though the topology of the network, which models dependencies among activities, is restricted to trees. However, we manage to design a pseudo-polynomial time algorithm based on dynamic programming. [ABSTRACT FROM AUTHOR]

In the context of scheduling and timetabling, we study a challenging combinatorial problem which is interesting from both a practical and a theoretical point of view. The motivation behind it is to cope with scheduled activities which might be subject to unavoidable disturbances, such as delays, occurring during the operational phase. The idea is to preventively plan some extra time for the scheduled activities in order to be ˵prepared″ if a delay occurs, and to absorb it without the necessity of re-scheduling the activities from scratch. This realizes the concept of designing so called robust timetables. During the planning phase, one has to consider recovery features that might be applied at runtime if delays occur. Such recovery capabilities are given as input along with the possible delays that must be considered. The objective is the minimization of the overall needed time. The quality of a robust timetable is measured by the price of robustness, i.e. the ratio between the cost of the robust timetable and that of a non-robust optimal timetable. The considered problem is known to be NP-hard. We propose a pseudo-polynomial time algorithm and apply it on random networks and real case scenarios provided by Italian railways. We evaluate the effect of robustness on the scheduling of the activities and provide the price of robustness with respect to different scenarios. We experimentally show the practical effectiveness and efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of planning a timetable for passenger trains considering that possible delays might occur due to unpredictable (but bounded) circumstances. Once arrival and departure events are scheduled, if the timetable cannot be respected since an external event has determined a delay to a train, the so called delay management problem occurs. 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 interaction between timetable planning and delay management in terms of the recoverable robustness model, where a timetable is said to be robust if it is able to absorb small delays by possibly applying given recovery capabilities. The quality of a robust timetable is measured by the price of robustness that is the ratio between the cost of the robust timetable and that of a non-robust optimal timetable. We consider the problem of designing robust timetables subject to bounded delays. We show that finding an optimal solution for this problem is NP-hard. Hence, we propose robust algorithms and evaluate their prices of robustness. Moreover, we show that such algorithms are optimal with respect to particular assumptions. [ABSTRACT FROM AUTHOR]