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An O(n log n) algorithm for maximum st-flow in a directed planar graph
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Journal of the ACM (JACM) archive
Volume 56 ,  Issue 2  (April 2009) table of contents
Article No. 9  
Year of Publication: 2009
ISSN:0004-5411
Authors
Glencora Borradaile  Brown University, Providence, Rhode Island
Philip Klein  Brown University, Providence, Rhode Island
Publisher
ACM  New York, NY, USA
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ABSTRACT

We give the first correct O(n log n) algorithm for finding a maximum st-flow in a directed planar graph. After a preprocessing step that consists in finding single-source shortest-path distances in the dual, the algorithm consists of repeatedly saturating the leftmost residual s-to-t path.


REFERENCES

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Dinitz, E. 1970. Algorithm for solution of a problem of maximum flow in networks with power estimation. Sov. Math. Dokl. 11, 1277--1280.
 
5
Edmonds, J. 1960. A combinatorial representation for polyhedral surfaces. Notices AMS 7, 646.
6
 
7
Elias, P., Feinstein, A., and Shannon, C. 1956. A note on the maximum flow through a network. IEEE Trans. Inf. Theory 2, 4, 117--119.
 
8
 
9
 
10
Ford, C., and Fulkerson, D. 1956. Maximal flow through a network. Canad. J. Math. 8, 399--404.
 
11
 
12
13
14
 
15
Harris, T., and Ross, F. 1955. Fundamentals of a method for evaluating rail net capacities. Research Memorandum RM-1573, The RAND Corporation, Santa Monica, CA.
 
16
Hassin, R. 1981. Maximum flow in (s,t) planar networks. Inf. Proc. Lett. 13, 107.
 
17
Hassin, R., and Johnson, D. B. 1985. An O(n log2 n) algorithm for maximum flow in undirected planar networks. SIAM J. Comput. 14, 612--624.
 
18
Heffter, L. 1891. Über das problem der nachbargebiete. Math. Ann. 38, 477--508.
19
 
20
 
21
Itai, A., and Shiloach, Y. 1979. Maximum flow in planar networks. SIAM J. Comput. 8, 135--150.
22
 
23
Johnson, D. B., and Venkatesan, S. 1982. Using divide and conquer to find flows in directed planar networks in O(n3/2 log n) time. In Proceedings of the 20th Annual Allerton Conference on Communication, Control, and Computing. 898--905.
 
24
Khuller, S., and Naor, J. 1994. Flow in planar graphs with vertex capacities. Algorithmica 11, 3, 200--225.
 
25
 
26
 
27
Kotzig, A. 1956. Súvislosť a pravidelná súvislosť konečných grafov. Ph.D. dissertation, Vysoká Škola Ekonomická, Bratislava.
 
28
 
29
Reif, J. 1983. Minimum s-t cut of a planar undirected network in O(n log2 n) time. SIAM Journal on Computing 12, 71--81.
 
30
Ripphausen-Lipa, H., Wagner, D., and Weihe, K. 1995. Efficient algorithms for disjoint paths in planar graphs. In Combinatorial Optimization, W. Cook, L. Lovasz, and P. Seymour, Eds. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 20. AMS, 295--354.
 
31
Schrijver, A. 2002. On the history of the transportation and maximum flow problems. Math. Prog. 91, 3, 437--445.
 
32
 
33
Sommerville, D. 1929. An introduction to the geometry of n dimensions. London.
 
34
 
35
 
36
Whitney, H. 1933. Planar graphs. Fundamenta mathematicae 21, 73--84.
 
37
Youngs, J. 1963. Minimal imbeddings and the genus of a graph. J. Math. Mech. 12, 303--315.


Collaborative Colleagues:
Glencora Borradaile: colleagues
Philip Klein: colleagues