Finding small simple cycle separators for 2-connected planar graphs
Journal of Computer and System Sciences
Fast algorithms for shortest paths in planar graphs, with applications
SIAM Journal on Computing
Planar graph decomposition and all pairs shortest paths
Journal of the ACM (JACM)
Faster shortest-path algorithms for planar graphs
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
Shortest path queries in planar graphs
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Approximating the Stretch Factor of Euclidean Graphs
SIAM Journal on Computing
On-Line Algorithms for Shortest Path Problems on Planar Digraphs
WG '96 Proceedings of the 22nd International Workshop on Graph-Theoretic Concepts in Computer Science
Planar Spanners and Approximate Shortest Path Queries among Obstacles in the Plane
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Short path queries in planar graphs in constant time
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Planar Graphs, Negative Weight Edges, Shortest Paths, and Near Linear Time
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Compact oracles for reachability and approximate distances in planar digraphs
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
Finding shortest non-separating and non-contractible cycles for topologically embedded graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
All-pairs shortest paths with real weights in O(n3/ log n) time
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
Splitting (complicated) surfaces is hard
Proceedings of the twenty-second annual symposium on Computational geometry
Splitting (complicated) surfaces is hard
Computational Geometry: Theory and Applications
Testing contractibility in planar rips complexes
Proceedings of the twenty-fourth annual symposium on Computational geometry
Finding shortest contractible and shortest separating cycles in embedded graphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Minimum cuts and shortest homologous cycles
Proceedings of the twenty-fifth annual symposium on Computational geometry
Finding shortest contractible and shortest separating cycles in embedded graphs
ACM Transactions on Algorithms (TALG)
Shortest non-trivial cycles in directed surface graphs
Proceedings of the twenty-seventh annual symposium on Computational geometry
Linear-space approximate distance oracles for planar, bounded-genus and minor-free graphs
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Approximate distance queries for weighted polyhedral surfaces
ESA'11 Proceedings of the 19th European conference on Algorithms
Delineating imprecise regions via shortest-path graphs
Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Exact distance oracles for planar graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Minimum cuts and shortest non-separating cycles via homology covers
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Linear-time algorithms for max flow and multiple-source shortest paths in unit-weight planar graphs
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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Let G be a planar graph with n vertices and non-negative edge-lengths. Given a set of k pairs of vertices, we are interested in computing the distance in G between those k pairs of vertices. We describe how this can be achieved in O(n2/3k2/3 log n + n4/3log1/3 n) time, improving previous results for a large range of k. As possible applications, we show how this result speeds up previous algorithms for finding shortest non-contractible cycles for graphs on a bounded-genus surface or for computing the dilation of a geometric planar graph.