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 shortest paths using bridging sets and rectangular matrix multiplication
TL;DR: Two new algorithms for solving the All Pairs Shortest Paths (APSP) problem for weighted directed graphs using fast matrix multiplication algorithms are presented.
Journal ArticleDOI
All-Pairs Almost Shortest Paths
TL;DR: A simple argument shows that computing all distances in G with an additive one-sided error of at most 1 is as hard as Boolean matrix multiplication, and describes an APASP2 algorithm, which is simple, easy to implement, and faster than the fastest known matrix-multiplication algorithm.
Journal Article
All Pairs Shortest Paths using Bridging Sets and Rectangular Matrix Multiplication
TL;DR: In this paper, the APSP problem for weighted directed graphs was solved in O(n2+μ) time, where μ satisfies the equation ω(1, μ, 1) = 1 + 2μ and ω is the exponent of the multiplication of an n × nμ matrix by an nμ × n matrix.
Proceedings ArticleDOI
More algorithms for all-pairs shortest paths in weighted graphs
TL;DR: A new algorithm with running time approaching O(n3/log2n), which improves all known algorithms for general real-weighted dense graphs and is perhaps close to the best result possible without using fast matrix multiplication, modulo a few log log n factors.