Affiliation:
1. The University of Tokyo, Tokyo, Japan
Abstract
In this article, we develop an
O
((
m
log
k
)MSF(
n,m
,1))-time algorithm to find a half-integral node-capacitated multiflow of the maximum total flow-value in a network with
n
nodes,
m
edges, and
k
terminals, where MSF(
n
′
,
m
′
,γ) denotes the time complexity of solving the maximum submodular flow problem in a network with
n
′
nodes,
m
′
edges, and the complexity γ of computing the exchange capacity of the submodular function describing the problem. By using Fujishige-Zhang algorithm for submodular flow, we can find a maximum half-integral multiflow in
O
(
m n
3
log
k
) time. This is the first combinatorial strongly polynomial time algorithm for this problem. Our algorithm is built on a developing theory of discrete convex functions on certain graph structures. Applications include “ellipsoid-free” combinatorial implementations of a 2-approximation algorithm for the minimum node-multiway cut problem by Garg, Vazirani, and Yannakakis.
Publisher
Association for Computing Machinery (ACM)
Subject
Mathematics (miscellaneous)
Cited by
1 articles.
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