Computing Maximum Flows in Undirected Planar Networks with Both Edge and Vertex Capacities

Authors:
Xianchao Zhang;Weifa Liang;Guoliang Chen
Affiliations:
School of Software, Dalian University of Technology, Dalian, China 116620;Department of Computer Science, Australian National University Canberra, Australia ACT 0200;Department of Computer, University of Science and Technology of China, Hefei, China 230027
Venue:
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Year:
2008

Citing 9
Cited 0

A new approach to the maximum-flow problem

Journal of the ACM (JACM)
A data structure for dynamic trees

Journal of Computer and System Sciences
Network flows: theory, algorithms, and applications

Network flows: theory, 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
Beyond the flow decomposition barrier

Journal of the ACM (JACM)
Deterministic sorting in O(nlog logn) time and linear space

Journal of Algorithms
Graph Theory With Applications

Graph Theory With Applications
An O (n log n) algorithm for maximum st-flow in a directed planar graph

SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Flow equivalent trees in undirected node-edge-capacitated planar graphs

Information Processing Letters

Quantified Score

Hi-index	0.00

Visualization

Abstract

We study the maximum flow problem in an undirected planar network with both edge and vertex capacities (EVC-network). A previous study reduces the minimum cut problem in an undirected planar EVC-network to the minimum edge-cut problem in another planar network with edge capacity only (EC-network), thus the minimum-cut or the maximum flow value can be computed in O(nlogn) time. Based on this reduction, in this paper we devise an O(nlogn) time algorithm for computing the maximum flow in an undirected general planar EVC-network and an O(n) time algorithm for computing the maximum flow in an undirected (s,t)-planar EVC-network. As a result, the maximum flow problem in undirected planar EVC-networks is as easy as the problem in undirected planar EC-networks in terms of computational complexity.