We give a linear-time algorithm for single-source shortest paths in planar graphs with nonnegative edge-lengths. Our algorithm also yields a linear-time algorithm for maximum flow in a planar graph with the source and sink on the same face. For the case where negative edge-lengths are allowed, we give an algorithm requiring O(n
|
6327
|
Introduction to algorithms
– Cormen, Leiserson, et al.
- 1990
|
|
437
|
Fibonacci heaps and their uses in improved network optimization algorithms
– Fredman, Tarjan
- 1987
|
|
307
|
A Separator Theorem for Planar Graphs
– Lipton, Tarjan
- 1979
|
|
205
|
Fast approximation algorithms for fractional packing and covering problems
– Plotkin, Shmoys, et al.
- 1995
|
|
141
|
Trans-dichotomous algorithms for minimum spanning trees and shortest paths
– Fredman, Willard
- 1994
|
|
140
|
Data structures for on-line updating of minimum spanning trees, with applications
– Frederickson
- 1985
|
|
136
|
Generalized nested dissection
– Lipton, Rose, et al.
- 1979
|
|
90
|
Faster Algorithms for the Shortest Path Problem
– Ahuja, Mehlhorn, et al.
- 1990
|
|
88
|
A unified geometric approach to graph separators
– Miller, Teng, et al.
- 1991
|
|
88
|
Faster approximation algorithms for the unit capacity concurrent flow problem with applications to routing and finding sparse cuts
– Klein, Plotkin, et al.
- 1994
|
|
81
|
Fast algorithms for shortest paths in planar graphs, with applications
– Frederickson
- 1987
|
|
78
|
A separator theorem for graphs with an excluded minor and its applications
– Alon, Seymour, et al.
- 1990
|
|
72
|
On RAM priority queues
– Thorup
- 1996
|
|
42
|
Planar separators and parallel polygon triangulation
– Goodrich
- 1995
|
|
42
|
A separator theorem for nonplanar graphs
– Alon, Seymour, et al.
- 1990
|
|
41
|
Scaling algorithms for the shortest paths problem
– Goldberg
- 1995
|
|
28
|
Efficient parallel shortest-paths in digraphs with a separator decomposition
– Cohen
- 1996
|
|
27
|
A parallel algorithm for finding a separator in planar graphs
– GAZIT, MILLER
- 1987
|
|
20
|
Flow in planar graphs with multiple sources and sinks
– Miller, Naor
- 1989
|
|
17
|
Maintaining biconnected components of dynamic planar graphs
– Galil, Italiano
- 1991
|
|
16
|
Fully dynamic planarity testing
– Galil, Italiano, et al.
- 1992
|
|
16
|
Parallel algorithms for minimum cuts and maximum flows in planar networks
– Johnson
- 1987
|
|
15
|
An optimal algorithm for selection in a min-heap
– Frederickson
- 1993
|
|
14
|
Maximum flow in (s; t) planar networks
– Hassin
- 1981
|
|
11
|
Fast and efficient solution of path algebra problems
– Pan, Reif
- 1989
|
|
8
|
Tarjan, "Faster algorithms for the shortest path problem
– Ahuja, Mehlhorn, et al.
- 1990
|
|
8
|
Using divide and conquer to find flows in directed planar networks in O(n 1:5 log n) time
– Johnson, Venkatesan
- 1982
|
|
8
|
The parallel computation of minimum cost paths in graphs by stream contraction
– Pan, Reif
- 1991
|
|
8
|
A fully dynamic data structure for reachability in planar digraphs
– Subramanian
- 1993
|
|
8
|
An O(n log n) algorithm for maximum flow in undirected planar networks
– Hassin, Johnson
- 1985
|
|
5
|
Parallel algorithms with improved work for shortest-paths from multiple sources
– Cohen
- 1993
|
|
5
|
Tarjan, "A separation theorem for graphs of bounded genus
– Gilbert, Hutchinson, et al.
- 1984
|
|
5
|
A fully dynamic approximation scheme for all-pairs shortest paths in planar graphs
– Klein, Subramanian
- 1993
|
|
3
|
Tarjan, "Almost-optimum speed-ups of algorithms for bipartite matching and related problems
– Gabow, E
- 1988
|
|
