Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
A separator theorem for graphs of bounded genus
Journal of Algorithms
Graph minors. V. Excluding a planar graph
Journal of Combinatorial Theory Series B
Fast algorithms for shortest paths in planar graphs, with applications
SIAM Journal on Computing
The C programming language
Computing shortest paths and distances in planar graphs
Proceedings of the 18th international colloquium on Automata, languages and programming
Dynamic reachability in planar digraphs with one source and one sink
Theoretical Computer Science
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
Sublinear time algorithms for metric space problems
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
On the all-pairs Euclidean short path problem
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
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
SODA '01 Proceedings of the twelfth 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
Journal of Algorithms
Preprocessing an undirected planar network to enable fast approximate distance queries
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
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
A Fully Dynamic Data Structure for Reachability in Planar Digraphs
ESA '93 Proceedings of the First Annual European Symposium on Algorithms
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
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
Traveling with a Pez Dispenser (Or, Routing Issues in MPLS)
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Graph minors. XVI. excluding a non-planar graph
Journal of Combinatorial Theory Series B
Proximity-preserving labeling schemes
Journal of Graph Theory
Many distances in planar graphs
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A subset spanner for Planar graphs,: with application to subset TSP
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Object location using path separators
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
On space-stretch trade-offs: upper bounds
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
Planar graphs, negative weight edges, shortest paths, and near linear time
Journal of Computer and System Sciences - Special issue on FOCS 2001
Strong-diameter decompositions of minor free graphs
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Improved sparse covers for graphs excluding a fixed minor
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Optimal scale-free compact routing schemes in networks of low doubling dimension
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Labeling schemes for weighted dynamic trees
Information and Computation
Approximate distance oracles for geometric spanners
ACM Transactions on Algorithms (TALG)
A near-linear time algorithm for computing replacement paths in planar directed graphs
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Bounded-leg distance and reachability oracles
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
On Compact Representations of All-Pairs-Shortest-Path-Distance Matrices
CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Note: A note on models for graph representations
Theoretical Computer Science
Compact Routing Schemes for Dynamic Trees in the Fixed Port Model
ICDCN '09 Proceedings of the 10th International Conference on Distributed Computing and Networking
On A☆ search with stopover areas
International Journal of Geographical Information Science
An Optimal Labeling for Node Connectivity
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Labeling schemes for vertex connectivity
ACM Transactions on Algorithms (TALG)
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
Compact oracles for approximate distances around obstacles in the plane
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Dynamic plane transitive closure
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
An optimal ancestry scheme and small universal posets
Proceedings of the forty-second ACM symposium on Theory of computing
Algorithms for sensor and ad hoc networks: advanced lectures
Algorithms for sensor and ad hoc networks: advanced lectures
A near-linear-time algorithm for computing replacement paths in planar directed graphs
ACM Transactions on Algorithms (TALG)
Note: On compact representations of All-Pairs-Shortest-Path-Distance matrices
Theoretical Computer Science
Forbidden-set distance labels for graphs of bounded doubling dimension
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Decomposition, approximation, and coloring of odd-minor-free graphs
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Compact ancestry labeling schemes for XML trees
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
Improved Compact Routing Tables for Planar Networks via Orderly Spanning Trees
SIAM Journal on Discrete Mathematics
Approximate shortest path queries using Voronoi duals
Transactions on computational science IX
Approximate shortest path queries using Voronoi duals
Transactions on computational science IX
Sparse spanners vs. compact routing
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
Join-reachability problems in directed graphs
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
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
Navigating in a Graph by Aid of Its Spanning Tree Metric
SIAM Journal on Discrete Mathematics
Exact distance oracles for planar graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Single source distance oracle for planar digraphs avoiding a failed node or link
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Distance labeling in hyperbolic graphs
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Fast, precise and dynamic distance queries
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
General compact labeling schemes for dynamic trees
DISC'05 Proceedings of the 19th international conference on Distributed Computing
Constructing labeling schemes through universal matrices
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Distributed computing of efficient routing schemes in generalized chordal graphs
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
Compact representation of posets
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
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
Distributed computing of efficient routing schemes in generalized chordal graphs
Theoretical Computer Science
Labeling schemes for vertex connectivity
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Maintaining shortest paths under deletions in weighted directed graphs: [extended abstract]
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Search-Space size in contraction hierarchies
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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)
Simple, fast, and scalable reachability oracle
Proceedings of the VLDB Endowment
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It is shown that a planar digraph can be preprocessed in near-linear time, producing a near-linear space oracle that can answer reachability queries in constant time. The oracle can be distributed as an O(log n) space label for each vertex and then we can determine if one vertex can reach another considering their two labels only.The approach generalizes to give a near-linear space approximate distances oracle for a weighted planar digraph. With weights drawn from {0, …, N}, it approximates distances within a factor (1 + ϵ) in O(log log (nN) + 1/ϵ) time. Our scheme can be extended to find and route along correspondingly short dipaths.