Worst-case update times for fully-dynamic all-pairs shortest paths
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Computing almost shortest paths
ACM Transactions on Algorithms (TALG)
Fully dynamic algorithm for graph spanners with poly-logarithmic update time
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the forty-second ACM symposium on Theory of computing
Streaming and fully dynamic centralized algorithms for constructing and maintaining sparse spanners
ACM Transactions on Algorithms (TALG)
Replacement paths and k simple shortest paths in unweighted directed graphs
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Small stretch spanners on dynamic graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Fast, precise and dynamic distance queries
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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)
Fully dynamic randomized algorithms for graph spanners
ACM Transactions on Algorithms (TALG)
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 obtain three new dynamic algorithms for the approximate all-pairs shortest paths problem in unweighted undirected graphs: 1. For any fixed 驴 0, a decremental algorithm with an expected total running time of 脮(mn), where m is the number of edges and n is the number of vertices in the initial graph. Each distance query is answered in 0(1) worst-case time, and the stretch of the returned distances is at most 1 + 驴 The algorithm uses 驴(n虏) space. 2. For any fixed integer k 驴 1, a decremental algorithm with an expected total running time of 脮(mn). Each query is answered in 0(1) worst-case time, and the stretch of the returned distances is at most 2k - 1. This algorithm uses, however, only 0(m + n^{1 + {1 \mathord{\left/ {\vphantom {1 k}} \right. \kern-\nulldelimiterspace} k}} ) space. It is obtained by dynamizing techniques of Thorup and Zwick. In addition to being more space efficient, this algorithm is also one of the building blocks used to obtain the first algorithm. 3. For any fixed 驴, 驴 0 and every t \leqslant m^{{1 \mathord{\left/ {\vphantom {1 {2 - \delta }}} \right. \kern-\nulldelimiterspace} {2 - \delta }}}, a fully dynamic algorithm with an expected amortized update time of 脮(mn/t) and worst-case query time of 0(t). The stretch of the returned distances is at most 1 + 驴. All algorithms can also be made to work on undirected graphs with small integer edge weights. If the largest edge weight is b, then all bounds on the running times are multiplied by b.