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An incremental algorithm for a generalization of the shortest-path problem
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FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
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FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Experimental analysis of dynamic all pairs shortest path algorithms
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
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ACM Transactions on Database Systems (TODS)
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An Efficient Dynamic Algorithm for Maintaining All-Pairs Shortest Paths in Stochastic Networks
IEEE Transactions on Computers
Fully dynamic all pairs shortest paths with real edge weights
Journal of Computer and System Sciences - Special issue on FOCS 2001
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Experimental analysis of dynamic all pairs shortest path algorithms
ACM Transactions on Algorithms (TALG)
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MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
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A Practical Temporal Constraint Management System for Real-Time Applications
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Adaptive algorithms for routing and traffic engineering in stochastic networks
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IEEE/ACM Transactions on Networking (TON)
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Computer Networks: The International Journal of Computer and Telecommunications Networking
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ICICS'09 Proceedings of the 7th international conference on Information, communications and signal processing
Subquadratic algorithm for dynamic shortest distances
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
ASONAM '12 Proceedings of the 2012 International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2012)
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We study novel combinatorial properties of graphs that allow us to devise a completely new approach to dynamic all pairs shortest paths problems. Our approach yields a fully dynamic algorithm for general directed graphs with non-negative real-valued edge weights that supports any sequence of operations in Õ(n2) amortized time per update and unit worst-case time per distance query, where n is the number of vertices. We can also report shortest paths in optimal worst-case time. These bounds improve substantially over previous results and solve a long-standing open problem. Our algorithm is deterministic and uses simple data structures.