A new approach to dynamic all pairs shortest paths

Demetrescu, Camil; Italiano, Giuseppe F.

doi:10.1145/780542.780567

Cited by 77 publications

(129 citation statements)

References 15 publications

Supporting

Mentioning

128

Contrasting

Unclassified

Order By: Relevance

“…No nontrivial decremental algorithm for either problem was known prior to our work. Our method is a generalization of the decremental algorithm of Demetrescu and Italiano [3] for unique shortest paths, and for graphs with ν * = O(n), we match the bound in [3]. Thus for graphs with a constant number of shortest paths between any pair of vertices, our algorithm maintains APASP and BC scores in amortized time O(n 2 · log n) under decremental updates, regardless of the number of edges in the graph.…”

mentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

“…Our method is a generalization of the method developed by Demetrescu and Italiano [3] (the 'DI' method) for decremental APSP where only one shortest path is needed. The DI decremental algorithm [3] runs in O(n 2 · log n) amortized time per update, for a sufficiently long update sequence. This decremental algorithm is also extended to a fully dynamic algorithm in [3] that runs in O(n 2 · log 3 n) time, and this result was improved to O(n 2 · log 2 n) amortized time by Thorup [14]; both algorithms have within them essentially the same decremental algorithm.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Decremental All-Pairs ALL Shortest Paths and Betweenness Centrality

Nasre

Pontecorvi

Ramachandran

2014

Algorithms and Computation

View full text Add to dashboard Cite

Abstract. We consider the all pairs all shortest paths (APASP) problem, which maintains the shortest path dag rooted at every vertex in a directed graph G = (V, E) with positive edge weights. For this problem we present a decremental algorithm (that supports the deletion of a vertex, or weight increases on edges incident to a vertex). Our algorithm runs in amortized O(ν * 2 · log n) time per update, where n = |V |, and ν * bounds the number of edges that lie on shortest paths through any given vertex. Our APASP algorithm can be used for the decremental computation of betweenness centrality (BC), a graph parameter that is widely used in the analysis of large complex networks. No nontrivial decremental algorithm for either problem was known prior to our work. Our method is a generalization of the decremental algorithm of Demetrescu and Italiano [3] for unique shortest paths, and for graphs with ν * = O(n), we match the bound in [3]. Thus for graphs with a constant number of shortest paths between any pair of vertices, our algorithm maintains APASP and BC scores in amortized time O(n 2 · log n) under decremental updates, regardless of the number of edges in the graph.

show abstract

mentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Decremental All-Pairs ALL Shortest Paths and Betweenness Centrality

Nasre

Pontecorvi

Ramachandran

2014

Algorithms and Computation

View full text Add to dashboard Cite

show abstract

“…The most naive solution consists in recomputing all shortest paths after any update but it is generally quite costly. For instance, the update time of the fastest dynamic algorithms for the all-pairs shortest path takes O(n 2 polylog(n)) [DI04,Tho04]. It turns out that in the failure model, it is not always necessary to recompute all shortest paths.…”

Section: Related Workmentioning

confidence: 99%

The Impact of Edge Deletions on the Number of Errors in Networks

Glacet

Hanusse

Ilcinkas

2011

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. In this paper, we deal with an error model in distributed networks. For a target t, every node is assumed to give an advice, ie.to point to a neighbour that take closer to the destination. Any node giving a bad advice is called a liar . Starting from a situation without any liar, we study the impact of topology changes on the number of liars. More precisely, we establish a relationship between the number of liars and the number of distance changes after one edge deletion. Whenever deleted edges are chosen uniformly at random, for any graph with n nodes, m edges and diameter D, we prove that the expected number of liars and distance changes is O( 2 Dn m ) in the resulting graph. The result is tight for = 1. For some specific topologies, we give more precise bounds.

show abstract

“…Many approaches have been proposed to maintain dynamic APSP data structures. For example, in [12,13], a dynamic algorithm for general directed graphs with non-negative edge weights was proposed with a computational complexity of O(n 2 log 3 n), where n is the number of vertices. However, this time bound is comparable to recomputing all-pairs shortest paths from scratch, which makes the algorithm inefficient for handling changes in graphs.…”

Section: Introductionmentioning

confidence: 99%

Efficient computation of distance labeling for decremental updates in large dynamic graphs

et al. 2016

View full text Add to dashboard Cite

Since today's real-world graphs, such as social network graphs, are evolving all the time, it is of great importance to perform graph computations and analysis in these dynamic graphs. Due to the fact that many applications such as social network link analysis with the existence of inactive users need to handle failed links or nodes, decremental computation and maintenance for graphs is considered a challenging problem. Shortest path computation is one of the most fundamental operations for managing and analyzing large graphs. A number of indexing methods have been proposed to answer distance queries in static graphs. Unfortunately, there is little work on answering such queries for dynamic graphs. In this paper, we focus on the problem of computing the shortest path distance in dynamic graphs, particularly on decremental updates (i.e., edge deletions). We propose maintenance algorithms based on distance labeling, which can handle decremental updates efficiently. By exploiting properties of distance labeling in original graphs, we are able to efficiently maintain distance labeling for new graphs. We experimentally evaluate our algorithms using eleven real-world large graphs and confirm the effectiveness and efficiency of our approach. More specifically, our method can speed up index re-computation by up to an order of magnitude compared with the state-ofthe-art method, Pruned Landmark Labeling (PLL).

show abstract

A new approach to dynamic all pairs shortest paths

Cited by 77 publications

References 15 publications

Decremental All-Pairs ALL Shortest Paths and Betweenness Centrality

Decremental All-Pairs ALL Shortest Paths and Betweenness Centrality

The Impact of Edge Deletions on the Number of Errors in Networks

Efficient computation of distance labeling for decremental updates in large dynamic graphs

Contact Info

Product

Resources

About