Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
All-Pairs Almost Shortest Paths
SIAM Journal on Computing
Journal of Algorithms
(1 + &egr;&Bgr;)-spanner constructions for general graphs
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Computing almost shortest paths
Proceedings of the twentieth annual ACM symposium on Principles of distributed computing
Approximation algorithms
All Pairs Shortest Paths in weighted directed graphs ? exact and almost exact algorithms
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
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
Efficient algorithms for constructing (1+,ε, β)-spanners in the distributed and streaming models
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
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
Approximate distance oracles for graphs with dense clusters
Computational Geometry: Theory and Applications
A simple and linear time randomized algorithm for computing sparse spanners in weighted graphs
Random Structures & Algorithms
Dynamic algorithms for graph spanners
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Approximate distance oracles for geometric spanners
ACM Transactions on Algorithms (TALG)
Fast deterministic distributed algorithms for sparse spanners
Theoretical Computer Science
All-pairs nearly 2-approximate shortest paths in O(n2polylogn) time
Theoretical Computer Science
Approximating Shortest Paths in Graphs
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Additive spanners in nearly quadratic time
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Fast distributed graph partition and application
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
Fast deterministic distributed algorithms for sparse spanners
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
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
Deterministic distributed construction of linear stretch spanners in polylogarithmic time
DISC'07 Proceedings of the 21st international conference on Distributed Computing
Approximate shortest paths guided by a small index
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Small stretch pairwise spanners
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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Let G(V, E) be an undirected weighted graph with |V| = n, |E| = m. Recently Thorup and Zwick introduced a remarkable data-structure that stores all pairs approximate distance information implicitly in o(n2) space, and yet answers any approximate distance query in constant time. They named this data-structure approximate distance oracle because of this feature. Given an integer k O(kn1+1/k) space and answers a (2k-1)-approximate distance query in O(k) time. Thorup and Zwick showed that a (2k - 1)-approximate distance oracle can be computed in O(kmn1/k) time, and posed the following question : Can (2k - 1)-approximate distance oracle be computed in Õ(n2) time?In this paper, we answer their question in affirmative for unweighted graphs. We present an algorithm that computes (2k -1)-approximate distance oracle for a given unweighted graph in Õ(n2) time. One of the new ideas used in the improved algorithm also leads to the first linear time algorithm for computing an optimal size (2, 1)-spanner of an unweighted graph.