On Computing the Diameter of (Weighted) Link Streams

Q2 Mathematics Journal of Experimental Algorithmics Pub Date : 2022-10-28 DOI:10.1145/3569168
M. Calamai, P. Crescenzi, Andrea Marino
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引用次数: 4

Abstract

A weighted link stream is a pair (V, 𝔼) comprising V, the set of nodes, and 𝔼, the list of temporal edges (u,v,t,λ) , where u,v are two nodes in V, t is the starting time of the temporal edge, and λ is its travel time. By making use of this model, different notions of diameter can be defined, which refer to the following distances: earliest arrival time, latest departure time, fastest time, and shortest time. After proving that any of these diameters cannot be computed in time sub-quadratic with respect to the number of temporal edges, we propose different algorithms (inspired by the approach used for computing the diameter of graphs) that allow us to compute, in practice very efficiently, the diameter of quite large real-world weighted link stream for several definitions of the diameter. In the case of the fastest time distance and of the shortest time distance, we introduce the notion of pivot-diameter, to deal with the fact that temporal paths cannot be concatenated in general. The pivot-diameter is the diameter restricted to the set of pair of nodes connected by a path that passes through a pivot (that is, a node at a given time instant). We prove that the problem of finding an optimal set of pivots, in terms of the number of pairs connected, is NP-hard, and we propose and experimentally evaluate several simple and fast heuristics for computing “good” pivot sets. All the proposed algorithms (for computing either the diameter or the pivot-diameter) require very often a very low number of single source (or target) best path computations. We verify the effectiveness of our approaches by means of an extensive set of experiments on real-world link streams. We also experimentally prove that the temporal version of the well-known 2-sweep technique, for computing a lower bound on the diameter of a graph, is quite effective in the case of weighted link stream, by returning very often tight bounds.
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关于计算(加权)链路流的直径
加权链路流是由节点集V和时间边列表(u, V, t,λ)组成的一对(V,),其中u, V是V中的两个节点,t是时间边的起始时间,λ是其行进时间。利用该模型,可以定义不同的直径概念,即最早到达时间、最晚出发时间、最快时间和最短时间。在证明了这些直径中的任何一个都不能在时间边数量的时间次二次中计算出来之后,我们提出了不同的算法(受到用于计算图直径的方法的启发),这些算法允许我们在实践中非常有效地计算相当大的现实世界加权链接流的直径,用于几种直径定义。在最快时间距离和最短时间距离的情况下,我们引入了枢轴直径的概念,以处理一般情况下时间路径不能连接的事实。枢轴直径是由通过枢轴(即给定时刻的节点)的路径连接的一组节点的直径。我们证明了找到一个最优的枢轴集的问题,根据连接对的数量,是np困难的,我们提出并实验评估了几个简单而快速的启发式方法来计算“好”枢轴集。所有提出的算法(用于计算直径或枢轴直径)通常只需要非常少的单源(或目标)最佳路径计算。我们通过在现实世界的链接流上进行大量的实验来验证我们方法的有效性。我们还通过实验证明了众所周知的2-sweep技术的时间版本,用于计算图直径的下界,在加权链接流的情况下非常有效,通过返回非常紧密的边界。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Journal of Experimental Algorithmics
Journal of Experimental Algorithmics Mathematics-Theoretical Computer Science
CiteScore
3.10
自引率
0.00%
发文量
29
期刊介绍: The ACM JEA is a high-quality, refereed, archival journal devoted to the study of discrete algorithms and data structures through a combination of experimentation and classical analysis and design techniques. It focuses on the following areas in algorithms and data structures: ■combinatorial optimization ■computational biology ■computational geometry ■graph manipulation ■graphics ■heuristics ■network design ■parallel processing ■routing and scheduling ■searching and sorting ■VLSI design
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