Fully dynamic shortest paths in digraphs with arbitrary arc weights

Frigioni, Daniele; Marchetti-Spaccamela, Alberto; Nanni, Umberto

doi:10.1016/s0196-6774(03)00082-8

Cited by 21 publications

(24 citation statements)

References 11 publications

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“…The approach relies on the existence of a k-bounded accounting function on G, which is a mapping K : E → V such that for each edge (u, v) the node K(u, v) is either u or v and such that for each node n, no more than k edges are n-valued. We use the constructive 2-approximation algorithm described in [10] for finding a k-bounded accounting function on G.…”

Section: Algorithm Of Frigioni Et Almentioning

confidence: 99%

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Batch Dynamic Single-Source Shortest-Path Algorithms: An Experimental Study

Bauer

Wagner

2009

Experimental Algorithms

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Abstract. A dynamic shortest-path algorithm is called a batch algorithm if it is able to handle graph changes that consist of multiple edge updates at a time. In this paper we focus on fully-dynamic batch algorithms for singlesource shortest paths in directed graphs with positive edge weights. We give an extensive experimental study of the existing algorithms for the single-edge and the batch case, including a broad set of test instances. We further present tuned variants of the already existing SWSF-FP-algorithm being up to 15 times faster than SWSF-FP. A surprising outcome of the paper is the astonishing level of data dependency of the algorithms.

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Section: Algorithm Of Frigioni Et Almentioning

confidence: 99%

“…In [6] the algorithm RR is adapted to cope with the existence of negative cycles, in [10] the same is done for the algorithm FMN. In [11] Demetrescu gives some algorithms for that problem.…”

Section: Introductionmentioning

confidence: 99%

Batch Dynamic Single-Source Shortest-Path Algorithms: An Experimental Study

Bauer

Wagner

2009

Experimental Algorithms

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“…The problem of maintaining all-pairs shortest path information under certain classes of graph updates (like increasing or decreasing edge weights) is also an active topic in the algorithms community [1,9,12,21,8,18,23]. Here, solutions usually focus on graphs that fit in main memory.…”

Section: Related Workmentioning

confidence: 99%

Pay-as-you-go maintenance of precomputed nearest neighbors in large graphs

Crecelius

Schenkel

2012

Proceedings of the 21st ACM International Conference on Information and Knowledge Management

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An important building block of many graph applications such as searching in social networks, keyword search in graphs, and retrieval of linked documents is retrieving the transitive neighbors of a node in ascending order of their distances. Since large graphs cannot be kept in memory and graph traversals at query time would be prohibitively expensive, the list of neighbors for each node is usually precomputed and stored in a compact form. While the problem of precomputing all-pairs shortest distances has been well studied for decades, efficiently maintaining this information when the graph changes is not as well understood. This paper presents an algorithm for maintaining nearest neighbor lists in weighted graphs under node insertions and decreasing edge weights. It considers the important case where queries are a lot more frequent than updates, and presents two approaches for transparently performing necessary index updates while executing queries. Extensive experiments with large graphs, including a subset of Twitter's user graph, demonstrate that the overhead for this maintenance is small.

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“…However, unlike the specialized algorithm of Cabello et al, these generic algorithms require the entire graph to be preprocessed anew for each UPDATE. Dynamic data structures supporting UPDATE and DISTANCE operations are also described by Klein [19, Section 6] for directed planar graphs, and by Frigioni et al [9,10] for several families of graphs including graphs of bounded genus. However, at least for our application, these data structures are not as efficient as the structure described in Lemma 2.1.…”

mentioning

confidence: 99%

Computing Replacement Paths in Surface Embedded Graphs

Erickson¹,

Nayyeri²

2011

Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms

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Let s and t be vertices in a directed graph G with non-negative edge weights. The replacement paths problem asks us to compute, for each edge e in G, the length of the shortest path from s to t that does not traverse e. We describe an algorithm that solves the replacement paths problem for directed graphs embedded on a surface of any genus g in O(g n log n) time, generalizing a recent O(n log n)-time algorithm of Wulff-Nilsen for planar graphs [SODA 2010].

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Fully dynamic shortest paths in digraphs with arbitrary arc weights

Cited by 21 publications

References 11 publications

Batch Dynamic Single-Source Shortest-Path Algorithms: An Experimental Study

Batch Dynamic Single-Source Shortest-Path Algorithms: An Experimental Study

Pay-as-you-go maintenance of precomputed nearest neighbors in large graphs

Computing Replacement Paths in Surface Embedded Graphs

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