Book ChapterDOI
Approximating Shortest Paths in Graphs
Sandeep Sen
- pp 32-43
TLDR
Some of the fundamental developments like spanners and distance oracles, their underlying constructions, as well as their applications to the approximate all-pairs shortest paths are traced.Abstract:
Computing all-pairs distances in a graph is a fundamental problem of computer science but there has been a status quo with respect to the general problem of weighted directed graphs. In contrast, there has been a growing interest in the area of algorithms for approximate shortest paths leading to many interesting variations of the original problem.
In this article, we trace some of the fundamental developments like spanners and distance oracles, their underlying constructions, as well as their applications to the approximate all-pairs shortest paths.read more
Citations
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Journal ArticleDOI
Shortest-path queries in static networks
TL;DR: This survey reviews selected approaches, algorithms, and results on shortest-path queries from these fields, with the main focus lying on the tradeoff between the index size and the query time.
Posted Content
A Survey of Shortest-Path Algorithms.
TL;DR: This survey studies and classifies shortest-path algorithms according to the proposed taxonomy and presents the challenges and proposed solutions associated with each category in the taxonomy.
Proceedings ArticleDOI
Approximate distance oracles with improved preprocessing time
TL;DR: In this article, a (2k − 1)-approximate distance oracle for G of size O(kn 1+1/k) can be constructed in [EQUATION] time and answer queries in O(k) time.
Proceedings ArticleDOI
Approximate distance oracles with improved query time
TL;DR: In this paper, a (2k − 1)-approximate distance oracle with O(log k) query time was constructed in O(min{kmn1/k, √km + kn1+c/√k}) time for some constant c.
Dissertation
Approximate shortest path and distance queries in networks
TL;DR: This thesis investigates the problem of efficiently computing exact and approximate shortest paths in graphs, with the main focus being on shortest path query processing and proves that exploiting well-connected nodes yields efficient distance oracles for scale-free graphs.
References
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Journal ArticleDOI
All-Pairs Small-Stretch Paths
Edith Cohen,Uri Zwick +1 more
TL;DR: Three algorithms for finding small-stretch paths between all pairs of vertices in a weighted graph with n vertices and m edges are described.
Proceedings ArticleDOI
New constructions of (α, β)-spanners and purely additive spanners
TL;DR: The construction algorithm can be understood as an economical agent that assigns costs and values to paths in the graph, purchasing affordable paths and ignoring expensive ones, which are intuitively well-approximated by paths already purchased.
Proceedings ArticleDOI
Sparse distance preservers and additive spanners
TL;DR: This paper introduces the notion of distance preserver, and shows that for any graph or digraph there exists a diSteiner D-preserver with at most n2/D) edges (resp., arcs), and there are graphs and digraphs for which any diSteiners can be improved.
Book ChapterDOI
Distance Oracles for Unweighted Graphs: Breaking the Quadratic Barrier with Constant Additive Error
TL;DR: This paper is able to break this quadratic barrier at the expense of introducing a (small) constant additive error forunweighted graphs, and has been able to topreserve the optimal size-stretch trade offs of the oracles.
Proceedings ArticleDOI
Approximate distance oracles for unweighted graphs in Õ (n2) time
Surender Baswana,Sandeep Sen +1 more
TL;DR: An algorithm is presented that computes the first linear time algorithm for computing an optimal size (2, 1)-spanner of an unweighted graph in Õ(n2) time.