Randomized algorithms
Fast Algorithms for Constructing t-Spanners and Paths with Stretch t
SIAM Journal on Computing
Near-Linear Time Construction of Sparse Neighborhood Covers
SIAM Journal on Computing
Fast rectangular matrix multiplication and applications
Journal of Complexity
Fast Estimation of Diameter and Shortest Paths (Without Matrix Multiplication)
SIAM Journal on Computing
All-Pairs Almost Shortest Paths
SIAM Journal on Computing
Journal of Algorithms
All pairs shortest paths using bridging sets and rectangular matrix multiplication
Journal of the ACM (JACM)
A new approach to all-pairs shortest paths on real-weighted graphs
Theoretical Computer Science - Special issue on automata, languages and programming
Journal of the ACM (JACM)
Computing almost shortest paths
ACM Transactions on Algorithms (TALG)
Faster Algorithms for Approximate Distance Oracles and All-Pairs Small Stretch Paths
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
More algorithms for all-pairs shortest paths in weighted graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Faster algorithms for all-pairs small stretch distances in weighted graphs
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
All-pairs nearly 2-approximate shortest-paths in O(n2 polylog n) time
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Faster algorithms for all-pairs small stretch distances in weighted graphs
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
f-sensitivity distance Oracles and routing schemes
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Efficient distributed source detection with limited bandwidth
Proceedings of the 2013 ACM symposium on Principles of distributed computing
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Let G = (V,E) be a weighted undirected graph, with nonnegative edge weights. We consider the problem of efficiently computing approximate distances between all pairs of vertices in G. While many efficient algorithms are known for this problem in unweighted graphs, not many results are known for this problem in weighted graphs. Zwick [15] showed that for any fixed Ɛ 0, stretch (1+Ɛ) distances between all pairs of vertices in a weighted directed graph on n vertices can be computed in Õ (nω) time assuming that edge weights in G are not too large, where ω n is the number of vertices in G. It is known that finding distances of stretch less than 2 between all pairs of vertices in G is at least as hard as Boolean matrix multiplication of two n×n matrices. It is also known that all-pairs stretch 3 distances can be computed in Õ(n2) time and all-pairs stretch 7/3 distances can be computed in Õ(n7/3) time. Here we consider efficient algorithms for the problem of computing all-pairs stretch (2+Ɛ) distances in G, for any 0 We show that all pairs stretch (2+Ɛ) distances for any fixed Ɛ 0 in G can be computed in expected time O(n9/4) assuming that edge weights in G are not too large. This algorithm uses a fast rectangular matrix multiplication subroutine. We also present a combinatorial algorithm (that is, it does not use fast matrix multiplication) with expected running time O(n9/4) for computing all-pairs stretch 5/2 distances in G.