Fast algorithms for shortest paths in planar graphs, with applications
SIAM Journal on Computing
A data structure for dynamic trees
Journal of Computer and System Sciences
A data structure for dynamically maintaining rooted trees
Journal of Algorithms
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
Undirected single-source shortest paths with positive integer weights in linear time
Journal of the ACM (JACM)
Shortest path queries in planar graphs
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Floats, integers, and single source shortest paths
Journal of Algorithms
Dynamic generators of topologically embedded graphs
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Dynamizing static algorithms, with applications to dynamic trees and history independence
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Bypassing the embedding: algorithms for low dimensional metrics
STOC '04 Proceedings of the thirty-sixth 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)
Multiple-source shortest paths in planar graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Distance estimation and object location via rings of neighbors
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Maintaining information in fully dynamic trees with top trees
ACM Transactions on Algorithms (TALG)
Many distances in planar graphs
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Fast Construction of Nets in Low-Dimensional Metrics and Their Applications
SIAM Journal on Computing
Object location using path separators
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Planar graphs, negative weight edges, shortest paths, and near linear time
Journal of Computer and System Sciences - Special issue on FOCS 2001
Oracles for bounded-length shortest paths in planar graphs
ACM Transactions on Algorithms (TALG)
Multiple source shortest paths in a genus g graph
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
ACM Transactions on Algorithms (TALG)
Distance Oracles for Sparse Graphs
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Fast and compact oracles for approximate distances in planar graphs
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Shortest paths in planar graphs with real lengths in O(n log2n/ log log n) time
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
Distance Oracles beyond the Thorup-Zwick Bound
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Fast, precise and dynamic distance queries
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete 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
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
Structured recursive separator decompositions for planar graphs in linear time
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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
Shortest-path queries in static networks
ACM Computing Surveys (CSUR)
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A (1+ε)-approximate distance oracle for a graph is a data structure that supports approximate point-to-point shortest-path-distance queries. The most relevant measures for a distance-oracle construction are: space, query time, and preprocessing time. There are strong distance-oracle constructions known for planar graphs (Thorup, JACM'04) and, subsequently, minor-excluded graphs (Abraham and Gavoille, PODC'06). However, these require Ω(ε-1n lg n) space for n-node graphs. In this paper, for planar graphs, bounded-genus graphs, and minor-excluded graphs we give distance-oracle constructions that require only O(n) space. The big O hides only a fixed constant, independent of ε and independent of genus or size of an excluded minor. The preprocessing times for our distance oracle are also faster than those for the previously known constructions. For planar graphs, the preprocessing time is O(nlg2 n). However, our constructions have slower query times. For planar graphs, the query time is O(ε-2 lg2 n). For all our linear-space results, we can in fact ensure, for any δ 0, that the space required is only 1 + δ times the space required just to represent the graph itself.