Experimental Evaluation of Dynamic Shortest Path Tree Algorithms on Homogeneous Batches

D’Andrea, Annalisa; D’Emidio, Mattia; Frigioni, Daniele; Leucci, Stefano; Proietti, Guido

doi:10.1007/978-3-319-07959-2_24

Cited by 9 publications

(4 citation statements)

References 15 publications

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“…Dynamic SSSP algorithms recompute distances from a source node after a single edge update or a batch of edge updates. Algorithms for the batch problem have been published [24,13,3] and compared in experimental studies [3,10]. The experiments show that the tuned algorithm T-SWSF [3] performs well on many types of graphs and edge updates.…”

Section: Introductionmentioning

confidence: 99%

Approximating Betweenness Centrality in Fully Dynamic Networks

Bergamini

Meyerhenke

2016

Internet Mathematics

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Betweenness is a well-known centrality measure that ranks the nodes of a network according to their participation in shortest paths. Since an exact computation is prohibitive in large networks, several approximation algorithms have been proposed. Besides that, recent years have seen the publication of dynamic algorithms for efficient recomputation of betweenness in networks that change over time.In this paper we propose the first betweenness centrality approximation algorithms with a provable guarantee on the maximum approximation error for dynamic networks. Several new intermediate algorithmic results contribute to the respective approximation algorithms: (i) new upper bounds on the vertex diameter, (ii) the first fully-dynamic algorithm for updating an approximation of the vertex diameter in undirected graphs, and (iii) an algorithm with lower time complexity for updating single-source shortest paths in unweighted graphs after a batch of edge actions.Using approximation, our algorithms are the first to make in-memory computation of betweenness in dynamic networks with millions of edges feasible. Our experiments show that our algorithms can achieve substantial speedups compared to recomputation, up to several orders of magnitude. Moreover, the approximation accuracy is usually significantly better than the theoretical guarantee in terms of absolute error. More importantly, for reasonably small approximation error thresholds, the rank of nodes is well preserved, in particular for nodes with high betweenness.

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Section: Introductionmentioning

confidence: 99%

Approximating Betweenness Centrality in Fully Dynamic Networks

Bergamini

Meyerhenke

2016

Internet Mathematics

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“…Dynamic approaches to update graphs and corresponding (compact) representations of transitive closures have been investigated in the past, in other application domains, due to the effectiveness of such structures for retrieving graph properties [15][16][17][18][19][20][21][22]. However, none of these can be directly employed in the PTL case, where time constraints imposed by the time-expanded graph add a further level of complexity to the involved data structures.…”

Section: Motivationmentioning

confidence: 99%

Journey Planning Algorithms for Massive Delay-Prone Transit Networks

2019

Self Cite

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This paper studies the journey planning problem in the context of transit networks. Given the timetable of a schedule-based transportation system (consisting, e.g., of trains, buses, etc.), the problem seeks journeys optimizing some criteria. Specifically, it seeks to answer natural queries such as, for example, “find a journey starting from a source stop and arriving at a target stop as early as possible”. The fastest approach for answering to these queries, yielding the smallest average query time even on very large networks, is the Public Transit Labeling framework, proposed for the first time in Delling et al., SEA 2015. This method combines three main ingredients: (i) a graph-based representation of the schedule of the transit network; (ii) a labeling of such graph encoding its transitive closure (computed via a time-consuming pre-processing); (iii) an efficient query algorithm exploiting both (i) and (ii) to answer quickly to queries of interest at runtime. Unfortunately, while transit networks’ timetables are inherently dynamic (they are often subject to delays or disruptions), ptl is not natively designed to handle updates in the schedule—even after a single change, precomputed data may become outdated and queries can return incorrect results. This is a major limitation, especially when dealing with massively sized inputs (e.g., metropolitan or continental sized networks), as recomputing the labeling from scratch, after each change, yields unsustainable time overheads that are not compatible with interactive applications. In this work, we introduce a new framework that extends ptl to function in delay-prone transit networks. In particular, we provide a new set of algorithms able to update both the graph and the precomputed labeling whenever a delay affects the network, without performing any recomputation from scratch. We demonstrate the effectiveness of our solution through an extensive experimental evaluation conducted on real-world networks. Our experiments show that: (i) the update time required by the new algorithms is, on average, orders of magnitude smaller than that required by the recomputation from scratch via ptl; (ii) the updated graph and labeling induce both query time performance and space overhead that are equivalent to those that are obtained by the recomputation from scratch via ptl. This suggests that our new solution is an effective approach to handling the journey planning problem in delay-prone transit networks.

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“…Dynamic SSSP algorithms recompute distances from a source node after a single edge update or a batch of edge updates. Algorithms for the batch problem have been published [17,7,2] and compared in experimental studies [2,6]. The experiments show that the tuned algorithm T-SWSF presented in [2] performs well on many types of graphs and edge updates.…”

Section: Batch Dynamic Sssp Algorithmsmentioning

confidence: 99%

Fully-Dynamic Approximation of Betweenness Centrality

Bergamini

Meyerhenke

2015

Algorithms - ESA 2015

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Betweenness is a well-known centrality measure that ranks the nodes of a network according to their participation in shortest paths. Since an exact computation is prohibitive in large networks, several approximation algorithms have been proposed. Besides that, recent years have seen the publication of dynamic algorithms for efficient recomputation of betweenness in evolving networks. In previous work we proposed the first semi-dynamic algorithms that recompute an approximation of betweenness in connected graphs after batches of edge insertions. In this paper we propose the first fully-dynamic approximation algorithms (for weighted and unweighted undirected graphs that need not to be connected) with a provable guarantee on the maximum approximation error. The transfer to fully-dynamic and disconnected graphs implies additional algorithmic problems that could be of independent interest. In particular, we propose a new upper bound on the vertex diameter for weighted undirected graphs. For both weighted and unweighted graphs, we also propose the first fully-dynamic algorithms that keep track of this upper bound. In addition, we extend our former algorithm for semidynamic BFS to batches of both edge insertions and deletions. Using approximation, our algorithms are the first to make in-memory computation of betweenness in fully-dynamic networks with millions of edges feasible. Our experiments show that they can achieve substantial speedups compared to recomputation, up to several orders of magnitude.

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Experimental Evaluation of Dynamic Shortest Path Tree Algorithms on Homogeneous Batches

Cited by 9 publications

References 15 publications

Approximating Betweenness Centrality in Fully Dynamic Networks

Approximating Betweenness Centrality in Fully Dynamic Networks

Journey Planning Algorithms for Massive Delay-Prone Transit Networks

Fully-Dynamic Approximation of Betweenness Centrality

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