Planar graphs, negative weight edges, shortest paths, and near linear time

Authors:
Jittat Fakcharoenphol;Satish Rao
Affiliations:
Department of Computer Engineering, Kasetsart University, Bangkok, Thailand and CS Division, University of California, Berkeley;Computer Science Division, University of California, Berkeley, CA
Venue:
Journal of Computer and System Sciences - Special issue on FOCS 2001
Year:
2006

Citing 20
Cited 33

Finding small simple cycle separators for 2-connected planar graphs

Journal of Computer and System Sciences
A new approach to all pairs shortest paths in planar graphs

STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
The discrete geodesic problem

SIAM Journal on Computing
Fast algorithms for shortest paths in planar graphs, with applications

SIAM Journal on Computing
Faster scaling algorithms for network problems

SIAM Journal on Computing
Faster algorithms for finding small edge cuts in planar graphs

STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Using interior-point methods for fast parallel algorithms for bipartite matching and related problems

SIAM Journal on Computing
Dynamic Programming for Detecting, Tracking, and Matching Deformable Contours

IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficient minimum cost matching and transportation using the quadrangle inequality

Journal of Algorithms
Flow in Planar Graphs with Multiple Sources and Sinks

SIAM Journal on Computing
Computational geometry: algorithms and applications

Computational geometry: algorithms and applications
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
Linear and Time Minimum-Cost Matching Algorithms for Quasi-Convex Tours

SIAM Journal on Computing
Efficient Algorithms for Shortest Paths in Sparse Networks

Journal of the ACM (JACM)
Computing Shortest Paths and Distances in Planar Graphs

ICALP '91 Proceedings of the 18th International Colloquium on Automata, Languages and Programming
Planarization of Graphs Embedded on Surfaces

WG '95 Proceedings of the 21st International Workshop on Graph-Theoretic Concepts in Computer Science
A deterministic near-linear time algorithm for finding minimum cuts in planar graphs

SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
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
"Ratio Regions": A Technique for Image Segmentation

ICPR '96 Proceedings of the 13th International Conference on Pattern Recognition - Volume 2

Obnoxious centers in graphs

SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Bounded-leg distance and reachability oracles

Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Shortest paths in directed planar graphs with negative lengths: a linear-space O(n log2 n)-time algorithm

SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Homology flows, cohomology cuts

Proceedings of the forty-first annual ACM symposium on Theory of computing
Minimum cuts and shortest homologous cycles

Proceedings of the twenty-fifth annual symposium on Computational geometry
Engineering Route Planning Algorithms

Algorithmics of Large and Complex Networks
On A☆ search with stopover areas

International Journal of Geographical Information Science
Computing Large Matchings in Planar Graphs with Fixed Minimum Degree

ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Shortest paths in directed planar graphs with negative lengths: A linear-space O(n log2 n)-time algorithm

ACM Transactions on Algorithms (TALG)
Engineering fast route planning algorithms

WEA'07 Proceedings of the 6th international conference on Experimental algorithms
Dynamic highway-node routing

WEA'07 Proceedings of the 6th international conference on Experimental algorithms
Dynamic plane transitive closure

ESA'07 Proceedings of the 15th annual European conference on Algorithms
Finding shortest non-trivial cycles in directed graphs on surfaces

Proceedings of the twenty-sixth annual symposium on Computational geometry
Single source shortest paths in H-minor free graphs

Theoretical Computer Science
Computing large matchings fast

ACM Transactions on Algorithms (TALG)
Maximum flows and parametric shortest paths in planar graphs

SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete 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
Improved algorithms for min cut and max flow in undirected planar graphs

Proceedings of the forty-third annual ACM symposium on Theory of computing
Computing large matchings in planar graphs with fixed minimum degree

Theoretical Computer Science
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
Improved distance queries in planar graphs

WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Min-cuts and shortest cycles in planar graphs in O(n log log n) time

ESA'11 Proceedings of the 19th European conference on Algorithms
Approximate distance queries for weighted polyhedral surfaces

ESA'11 Proceedings of the 19th European conference on Algorithms
Obnoxious Centers in Graphs

SIAM Journal on Discrete Mathematics
Exact distance oracles for planar graphs

Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Submatrix maximum queries in Monge matrices and Monge partial matrices, and their applications

Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Shortest path and distance queries on road networks: an experimental evaluation

Proceedings of the VLDB Endowment
Accelerated bend minimization

GD'11 Proceedings of the 19th international conference on Graph Drawing
Shortest path and distance queries on road networks: towards bridging theory and practice

Proceedings of the 2013 ACM SIGMOD International Conference on Management of Data
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)
Fast shortest-paths algorithms in the presence of few destinations of negative-weight arcs

Journal of Discrete Algorithms

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we present an O(n log3 n) time algorithm for finding shortest paths in an n-node 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 runs in O(n3/2) time, and the best polynomial time algorithm developed by Henzinger, Klein, Subramanian, and Rao in 1994 which runs in Õ(n 4/3) time. We also present significantly improved data structures for reporting distances between pairs of nodes and algorithms for updating the data structures when edge weights change.