Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
A polynomial-time approximation scheme for weighted planar graph TSP
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of 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
Fast Algorithms for Maintaining Shortest Paths in Outerplanar and Planar Digraphs
FCT '95 Proceedings of the 10th International Symposium on Fundamentals of Computation Theory
Compact Oracles for Reachability and Approximate Distances in Planar Digraphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Well-separated pair decomposition for the unit-disk graph metric and its applications
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Compact oracles for reachability and approximate distances in planar digraphs
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Computing the shortest path: A search meets graph theory
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
A subset spanner for Planar graphs,: with application to subset TSP
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Oracles for bounded-length shortest paths in planar graphs
ACM Transactions on Algorithms (TALG)
Bounded-leg distance and reachability oracles
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
Compact oracles for approximate distances around obstacles in the plane
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Fast and compact oracles for approximate distances in planar graphs
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Approximate distance queries for weighted polyhedral surfaces
ESA'11 Proceedings of the 19th European conference on Algorithms
Exact distance oracles for planar graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Fast, precise and dynamic distance queries
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
Approximating the diameter of planar graphs in near linear time
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Shortest-path queries in static networks
ACM Computing Surveys (CSUR)
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We describe a method for preprocessing a weighted planar undirected graph and representing the results of the preprocessing so as to facilitate subsequent approximate distance queries. For any 0 O(ε-1) time, principally consisting of about 15ε-1 additions. The representation requires storage of 7.2ε-1n log2 n distances. By using compressed representation of the distances, the number of bytes required is about .5nε-1(9 + 3 log ε-1)log2 n (at the expense of a small increase in query time).