Separation of partition inequalities with terminals
Discrete Optimization
Separation of partition inequalities for the (1,2)-survivable network design problem
Operations Research Letters
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Given a graphG = ( V,E) with nonnegative weightsx( e) for each edgee, a partition inequality is of the formx(d( S1,...., S p ))= ap+ b. Here d( S1,..., S p ) denotes the multicut defined by a partitionS1,..., S pofV. Partition inequalities arise as valid inequalities for optimization problems related tok-connectivity. We give a polynomial algorithm for the associated separation problem. This is based on an algorithm for finding the minimum ofx(d( S1,..., S p ))-- p that reduces to minimizing a symmetric submodular function. This is handled with the recent algorithm of Queyranne. We also survey some applications of partition inequalities.