Computing shortest paths with comparisons and additions
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Improved Bounds and New Trade-Offs for Dynamic All Pairs Shortest Paths
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
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)
Multiple-source shortest paths in planar graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Computing the shortest path: A search meets graph theory
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
An O (n log n) algorithm for maximum st-flow in a directed planar graph
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Many distances in planar graphs
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
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
Algorithmic Techniques for Maintaining Shortest Routes in Dynamic Networks
Electronic Notes in Theoretical Computer Science (ENTCS)
A Zero-Space algorithm for Negative Cost Cycle Detection in networks
Journal of Discrete Algorithms
A near-linear time algorithm for computing replacement paths in planar directed graphs
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Point-to-Point Shortest Path Algorithms with Preprocessing
SOFSEM '07 Proceedings of the 33rd conference on Current Trends in Theory and Practice of Computer Science
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
An O(n log n) algorithm for maximum st-flow in a directed planar graph
Journal of the ACM (JACM)
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
Fast and compact oracles for approximate distances in planar graphs
ESA'07 Proceedings of the 15th annual European conference on Algorithms
A near-linear-time algorithm for computing replacement paths in planar directed graphs
ACM Transactions on Algorithms (TALG)
Algorithms and theory of computation handbook
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
Cache-oblivious planar shortest paths
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Finding shortest non-separating and non-contractible cycles for topologically embedded graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Highway hierarchies hasten exact shortest path queries
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Engineering highway hierarchies
Journal of Experimental Algorithmics (JEA)
Search-Space size in contraction hierarchies
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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In this paper, we present an 0(n\log ^3 n) time algorithm for finding shortest paths in a planar graph with real weights.This can be compared to the best previous strongly polynomial time algorithm developed by Lipton, Rose, and Tarjan in 1978 which ran in 0(n^{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}} ) time, and the best polynomial algorithm developed by Henzinger, Klein, Subramanian, and Rao in 1994 which ran in \widetilde0(n^{{4 \mathord{\left/ {\vphantom {4 3}} \right. \kern-\nulldelimiterspace} 3}} ) time.We also present significantly improved algorithms for query and dynamic versions of the shortest path problems.