Separation of Partition Inequalities

Given a graph $G=(V,E)$ with nonnegative weights $x(e)$ for each edge $e$, a partition inequality is of the form $x\big(\delta(S_1,...,S_p)\big)\ge a p + b$. Here $\delta(S_1,...,S_p)$ denotes the multicut defined by a partition $S_1,...,S_p$ of $V$. We give a polynomial algorithm for the associated separation problem. This is based on an algorithm for finding the minimum of $x\big(\delta(S_1,...,S_p)\big)-p$ that reduces to minimizing a symmetric submodular function. This is handled with the recent algorithm of Queyranne.

By: Mourad Baiou, Francisco Barahona and Ali Ridha Mahjoub

Published in: RC20539 in 1996

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