TY - GEN
T1 - Maximum flow in directed planar graphs with vertex capacities
AU - Kaplan, Haim
AU - Nussbaum, Yahav
N1 - Funding Information:
This research was partially supported by the United States - Israel Binational Science Foundation, project number 2006204 and by the Laura Schwarz-Kipp Institute of Computer Networks.
PY - 2009
Y1 - 2009
N2 - In this paper we present an O(nlogn) algorithm for finding a maximum flow in a directed planar graph, where the vertices are subject to capacity constraints, in addition to the arcs. If the source and the sink are on the same face, then our algorithm can be implemented in O(n) time. For general (not planar) graphs, vertex capacities do not make the maximum flow problem more difficult, as there is a simple reduction that eliminates vertex capacities. However, this reduction does not preserve the planarity of the graph. The essence of our algorithm is a different reduction that does preserve the planarity, and can be implemented in linear time. For the special case of undirected planar graph, an algorithm with the same time complexity was recently claimed, but we show that it has a flaw.
AB - In this paper we present an O(nlogn) algorithm for finding a maximum flow in a directed planar graph, where the vertices are subject to capacity constraints, in addition to the arcs. If the source and the sink are on the same face, then our algorithm can be implemented in O(n) time. For general (not planar) graphs, vertex capacities do not make the maximum flow problem more difficult, as there is a simple reduction that eliminates vertex capacities. However, this reduction does not preserve the planarity of the graph. The essence of our algorithm is a different reduction that does preserve the planarity, and can be implemented in linear time. For the special case of undirected planar graph, an algorithm with the same time complexity was recently claimed, but we show that it has a flaw.
UR - http://www.scopus.com/inward/record.url?scp=70350431320&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-04128-0_36
DO - 10.1007/978-3-642-04128-0_36
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AN - SCOPUS:70350431320
SN - 3642041272
SN - 9783642041273
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 397
EP - 407
BT - Algorithms - ESA 2009 - 17th Annual European Symposium, Proceedings
T2 - 17th Annual European Symposium on Algorithms, ESA 2009
Y2 - 7 September 2009 through 9 September 2009
ER -