Filtering search: a new approach to query answering
SIAM Journal on Computing
Maintenance of transitive closures and transitive reductions of graphs
Proceedings of the International Workshop WG '87 on Graph-theoretic concepts in computer science
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Mathematics for the Analysis of Algorithms
Mathematics for the Analysis of Algorithms
Fully dynamic biconnectivity and transitive closure
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
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
Fully Dynamic Algorithms for Maintaining All-Pairs Shortest Paths and Transitive Closure in Digraphs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Fully dynamic transitive closure: breaking through the O(n/sup 2/) barrier
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Fully Dynamic All Pairs Shortest Paths with Real Edge Weights
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Maintaining all-pairs approximate shortest paths under deletion of edges
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
A faster and simpler fully dynamic transitive closure
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
A new approach to dynamic all pairs shortest paths
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A new approach to dynamic all pairs shortest paths
Journal of the ACM (JACM)
A dynamic topological sort algorithm for directed acyclic graphs
Journal of Experimental Algorithmics (JEA)
A faster and simpler fully dynamic transitive closure
ACM Transactions on Algorithms (TALG)
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Replacement paths and k simple shortest paths in unweighted directed graphs
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Improved dynamic algorithms for maintaining approximate shortest paths under deletions
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Fully dynamic approximate distance oracles for planar graphs via forbidden-set distance labels
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Replacement paths and k simple shortest paths in unweighted directed graphs
ACM Transactions on Algorithms (TALG)
Pay-as-you-go maintenance of precomputed nearest neighbors in large graphs
Proceedings of the 21st ACM international conference on Information and knowledge management
Maintaining shortest paths under deletions in weighted directed graphs: [extended abstract]
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We present improved algorithms for maintaining transitive closure and all-pairs shortest paths/distances in a digraph under deletion of edges.(MATH) For the problem of transitive closure, the previous best known algorithms, for achieving O(1) query time, require O(\min(m, \frac{n^3}{m}))$ amortized update time, implying an upper bound of O(n^{\frac{3}{2}})$ on update time per edge-deletion. We present an algorithm that achieves $O(1)$ query time and O(n \log^2n + \frac{n^2}{\sqrt{m}}{\sqrt{\log n}})$ update time per edge-deletion, thus improving the upper bound to O(n^{\frac{4}{3}}\sqrt[3]{\log n})$.(MATH) For the problem of maintaining all-pairs shortest distances in unweighted digraph under deletion of edges, we present an algorithm that requires O(\frac{n^3}{m} \log^2 n)$ amortized update time and answers a distance query in O(1) time. This improves the previous best known update bound by a factor of log n. For maintaining all-pairs shortest paths, we present an algorithm that achieves O(\min(n^{\frac{3}{2}} \sqrt{\log n}, \frac{n^3}{m} \log ^2n))$ amortized update time and reports a shortest path in optimal time (proportional to the length of the path). For the latter problem we improve the worst amortized update time bound by a factor of O(\sqrt{\frac{n}{\log n}})$.(MATH) We also present the first decremental algorithm for maintaining all-pairs (1+&egr;) approximate shortest paths/distances, for any &egr; 0, that achieves a sub-quadratic update time of O(n log2n + \frac{n^2}{\sqrt{\epsilon m}}\sqrt{\log n})$ and optimal query time.Our algorithms are randomized and have one-sided error for query (with probability O(1/nc) for any constant c).