Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
Complexity of network synchronization
Journal of the ACM (JACM)
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Introduction to algorithms
On sparse spanners of weighted graphs
Discrete & Computational Geometry
Fast Algorithms for Constructing t-Spanners and Paths with Stretch t
SIAM Journal on Computing
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
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
All pairs shortest paths using bridging sets and rectangular matrix multiplication
Journal of the ACM (JACM)
Sparse distance preservers and additive spanners
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Strong Inapproximability of the Basic k-Spanner Problem
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Exact and Approximate Distances in Graphs - A Survey
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
All Pairs Shortest Paths in Undirected Graphs with Integer Weights
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Approximate distance oracles for unweighted graphs in Õ (n2) time
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
$(1 + \epsilon,\beta)$-Spanner Constructions for General Graphs
SIAM Journal on Computing
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)
New constructions of (α, β)-spanners and purely additive spanners
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Computing almost shortest paths
ACM Transactions on Algorithms (TALG)
Spanners and emulators with sublinear distance errors
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
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
Approximate distance oracles for unweighted graphs in expected O(n2) time
ACM Transactions on Algorithms (TALG)
More algorithms for all-pairs shortest paths in weighted graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
A simple and linear time randomized algorithm for computing sparse spanners in weighted graphs
Random Structures & Algorithms
Distance Oracles for Unweighted Graphs: Breaking the Quadratic Barrier with Constant Additive Error
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
A simple linear time algorithm for computing a (2k - 1)-spanner of o(n1+1/k) size in weighted graphs
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Deterministic constructions of approximate distance oracles and spanners
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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
Approximate distance oracles with improved preprocessing time
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
A compact routing scheme and approximate distance oracle for power-law graphs
ACM Transactions on Algorithms (TALG)
Shortest-path queries in static networks
ACM Computing Surveys (CSUR)
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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.