We investigate the problem of computing the top-\(k\) simple shortest paths in weighted digraphs. While the single-pair variant – finding the top-\(k\) simple shortest paths between two specified vertices – has been extensively studied over the past decades, with Yen’s algorithm and its heuristic improvements emerging as the most effective solving strategies, relatively little attention has been devoted to the more general singlesource version, where the goal is determining top-\(k\) simple shortest paths from a source vertex to all other vertices. Motivated by the numerous practical applications of ranked shortest paths, in this paper, we provide new insights and algorithmic contributions to this problem. In particular, we first present a theoretical characterization of the structural properties of its solutions. Then, we introduce the first polynomial-time algorithm specifically designed to handle it. On the one hand, we prove our new algorithm is on par, in terms of time complexity, with the best (and only) polynomial-time approach known in the literature to solve the problem, that is, applying the fastest single-pair algorithm independently to each vertex pair formed by the source and the remaining vertices. On the other hand, through an extensive experimental evaluation on both real-world and synthetic graphs, we demonstrate that our algorithm consistently and significantly outperforms the latter baseline in terms of running time, achieving speed-ups of up to several orders of magnitude. These results establish our new algorithm as the solution to be preferred for computing \(k\) simple shortest paths from a single source in practical settings.

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We study the performance of mildly greedy players in k-coloring games, a relevant subclass of anti-coordination games. A mildly greedy player is a selfish agent who is willing to deviate from a certain strategy profile only if her payoff improves by a factor of more than ε, for some given ε ≥ 0. In presence of mildly greedy players, stability is captured by the concept of (1+ε)-approximate Nash equilibrium. In this paper, we first show that, for any k-coloring game, the (1+ε)-approximate price of anarchy, i.e., the price of anarchy of (1+ε)-approximate pure Nash equilibria, is at least (k-1)/((k-1)ε +k), and that this bound is tight for any ε ≥ 0. Then, we evaluate the approximation ratio of the solutions achieved after a (1 + ε)-approximate one-round walk starting from any initial strategy profile, where a (1 + ε)-approximate one-round walk is a sequence of (1 + ε)-approximate best-responses, one for each player. We provide a lower bound of min{(k-2)/k, (k-1)/((k-1)ε+k)} on this ratio, for any ε ≥ 0 and k ≥ 5; for the cases of k = 3 and k = 4, we give finer bounds depending on ε. Our work generalizes the results known for cut games, the special case of k-coloring games restricted to k = 2.

A beer graph is an edge-weighted graph G = (V,E,ω) with beer vertices B ⊆ V. A beer path between two vertices s and t of a beer graph is a path that connects s and t and visits at least one vertex in B. The beer distance between two vertices is the weight of a shortest beer path, i.e. a beer path having minimum total weight. A graph indexing scheme is a two-phase method that constructs an index data structure by a one-time preprocessing of an input graph and then exploits it to compute (or accelerate the computation of) answers to queries on structures of the graph dataset. In the last decade, such indexing schemes have been designed to perform, effectively, many relevant types of queries, e.g. on reachability, and have gained significant popularity in essentially all data-intensive application domains where large number of queries have to be routinely answered (e.g. journey planners), since they have been shown, through many experimental studies, to offer extremely low query times at the price of limited preprocessing time and space overheads. In this paper, we showcase that an indexing scheme, to efficiently execute queries on beer distances or shortest beer paths for pairs of vertices of a beer graph, can be obtained by adapting the highway labeling, a recently introduced indexing method to accelerate the computation of classical shortest paths. We design a preprocessing algorithm to build a whl index, i.e. a weighted highway labeling of a beer graph, and show how it can be queried to compute beer distances and shortest beer paths. Through extensive experimentation on real networks, we empirically demonstrate its practical effectiveness and superiority, in terms of offered trade-off between preprocessing time, space overhead and query time, with respect to the state-of-the-art.

We study digraph k-coloring games where strategic agents are vertices of a digraph and arcs represent agents' mutual unidirectional conflicts/idiosyncrasies. Each agent can select, as strategy, one of k different colors, and her payoff in a given state (a k-coloring) is given by the number of outgoing neighbors with a color different from her one. Such games model lots of strategic real-world scenarios and are related to several fundamental classes of anti-coordination games. Unfortunately, the problem of understanding whether an instance of the game admits a pure Nash equilibrium (NE), i.e., a state where no agent can improve her payoff by changing strategy, is NP-complete. Thus, in this paper, we focus on algorithms to compute an approximate NE: informally, a coloring is an approximate γ-NE, for some γ ≥ 1, if no agent can improve her payoff, by changing strategy, by a multiplicative factor of γ. Our contribution is manifold and of both theoretical and experimental nature. First, we characterize the hardness of finding pure and approximate equilibria in both general and special classes of digraphs. Second, we design and analyze three approximation algorithms with different theoretical guarantees on the approximation ratio, under different conditions; (i) algorithm APPROX-1 which computes, for any k ≥ 3, a Δo-NE for any n vertex graph having a maximum outdegree of Δo, in polynomial time; (ii) algorithm LLL-SPE, a randomized algorithm that, for any constant k ≥ 2, determines a γ-NE for some constant γ but only in digraphs whose minimum outdegree is sufficiently large, in polynomial time in expectation; (iii) algorithm APPROX-3 which, for any ε, computes a (1+ε)-NE by using O(log(n)/ε) colors, for any n-vertex digraph. Note that, the latter shows that a (1+ε)-NE exists and can be computed in polynomial time for k = O(log(n)). Finally, to assess how proposed algorithms behave in the typical case, we complete our study with an extensive experimental evaluation showing that, while newly introduced algorithms achieve bounded worst case behavior, they generally perform poorly in practice. Motivated by such unsatisfactory performance, we shift our attention to the best-response paradigm, successfully applied to other classes of games, and design and experimentally evaluate it a heuristic based on such paradigm. Our experiments provide strong evidences of such approach outperforming, in terms of approximation and computational time, all other methods and hence identify it as the most suited candidate for practical usage. More remarkably, it is also able to compute exact, pure NE in the great majority of cases. This suggests that, while these games are known to not always possess a pure NE, such an equilibrium often exists and can be efficiently computed, even by a distributed uncoordinated interaction of the agents.

Conventional wisdom on model transformations in Model-Driven Engineering (MDE) suggests that they are crucial components in modeling environments to achieve superior automation, whether it be refactoring, simulation, or code generation. While their relevance is well-accepted, model transformations are challenging to design, implement, and verify because of the inherent complexity that they must encode. Thus, defining transformations by chaining existing ones is key to success for enhancing their reusability. This paper proposes an approach, based on well-established algorithms, to support modellers when multiple transformation chains are available to bridge a source metamodel with a target one. The all-important goal of selecting the optimal chain has been based on the quality criteria of coverage and information loss. The feasibility of the approach has been demonstrated by means of experiments operated on chains obtained from transformations borrowed from a publicly available repository.

Multi-objective optimization has demonstrated, in the last few years, to be an effective paradigm to tackle different architectural problems, such as service selection, composition and deployment. In particular, multi-objective approaches for searching architectural configurations that optimize quality properties (such as performance, reliability and cost) have been introduced in the last decade. However, a relevant amount of complexity is introduced in this context when performance are considered, often due to expensive iterative generation of performance models and interpretation of results. In this paper we introduce EASIER (Evolutionary Approach for multi-objective Software archItecturE Refactoring), that is an approach for optimizing architecture refactoring based on performance and on the intensity of changes. We focus on the actionable aspects of architectural optimization, instead of merely searching over a set of alternatives. We also start to investigate on the potential influence of performance antipatterns on such process. We have implemented our approach on AEmilia ADL, so to carry out performance analysis and architecture refactoring within the same environment. We demonstrate the effectiveness and applicability of our approach through its experimentation on a case study.

The distributed setting of computational mobile entities, called robots, thathave to perform tasks without global coordination has been extensively studied in the literature. A well-known scenario is that in which robots operate in Look-Compute-Move (LCM) cycles. During each cycle, a robot acquires asnapshot of the surrounding environment (Look phase), then executes an appropriate algorithm by using the obtained snapshot as input (Computephase), and finally moves toward a desired destination, if any (Movephase). Look-Compute-Move cycles might be subject to different temporal constraints dictated by the considered schedule. The classic models for theactivation and synchronization of mobile robots are the well-known fully-synchronous, semi-synchronous, and asynchronous models. A first comprehensive evaluation of the computational power of robots operating in the LCM model and moving within the Euclidean plane, under different levels of synchronization, has been proposed in [Das et al., Int.'l Conf. on Distributed Computing Systems, 2012]. In detail, the authors provide a series of results that prove relations between classic models and variations of them, which consider the possibility that robots are endowed with a visible light, i.e. they are luminous, or with the capability to store some past snapshots, or combinations of them. In this paper, we are interested in similar settings but for robots moving on graphs. In particular, we propose a characterization of the computational power of mobile robots on graphs as follows. First, we show the relations among the three classic activation and synchronization models. Second, we compare the models where robots are endowed with lights against the models without lights. Third, we highlight the relations among the different models concerning luminous robots. Finally, we provide a detailed comparison of the proposed results with the case of robots moving in the Euclidean plane.

Many efforts have been done in the last years to model public transport timetables in order to find optimal routes. The proposed models can be classified into two types: those representing the timetable as an array, and those representing it as a graph. The array-based models have been shown to be very effective in terms of query time, while the graph-based models usually answer queries by computing shortest paths, and hence they are suitable to be used in combination with speed-up techniques developed for road networks. In this paper, we focus on the dynamic behavior of graph-based models considering the case where transportation systems are subject to delays with respect to the given timetable. We make three contributions: (i) we give a simplified and optimized update routine for the well-known time-expanded model along with an engineered query algorithm; (ii) we propose a new graph-based model tailored for handling dynamic updates; (iii) we assess the effectiveness of the proposed models and algorithms by an experimental study, which shows that both models require negligible update time and a query time which is comparable to that required by some array-based models.

Best connections in real networks are usually found by applying Dijkstra's shortest paths algorithm. Unfortunately, networks deriving from real-world applications are huge, yielding unsustainable times to compute shortest paths. Therefore, considerable research has been conducted in recent years to accelerate Dijkstra's algorithm on typical instances of transportation and communication networks, such as road networks. These efforts have led to the development of many so called speed-up techniques, as for example Arc-Flags. The main drawback of many of these techniques, including Arc-Flags, is that they do not work well in the realistic dynamic scenarios where the networks change over time. In this article, we introduce a new data structure, named Road-Signs, which is used to update the Arc-Flags of a graph in fully dynamic scenarios. Road-Signs can be used to compute Arc-Flags, can be efficiently updated and does not require large space consumption for sparse networks. We develop a fully dynamic algorithm for updating Arc-Flags, by updating Road-Signs, each time that a modification occurs on an edge of the network. We show that this algorithm is better than recomputation from scratch of Arc-Flags in terms of the affected parameters of the input, which makes this solution suitable to be efficient in practice. However, it is not better than recomputation from scratch in the worst case. We also propose an experimental study to evaluate the practical performance of the new dynamic algorithm. To this aim, we use real-world road networks subject to sequences of weight change operations. Our experiments show a significant speed-up in the updating phase with respect to the recomputation from scratch of Arc-Flags.Copyright © 2014 Wiley Periodicals, Inc. NETWORKS, Vol. 63(3), 243–259 2014