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The gamma-Connected Assignment Problem

By Marcus Poggi de Aragão and Eduardo Uchoa

Abstract

Given a graph and costs of assigning to each vertex one of k different colors, we want to find a minimum cost assignment such that no color q induces a subgraph with more than a given number (fl q ) of connected components. This problem arised in the context of contiguity-constrained clustering, but also has a number of other possible applications. We show the problem to be NP-hard. Nevertheless, we derive a dynamic programming algorithm that proves the case where the underlying graph is a tree to be solvable in polynomial time. Next, we propose mixed-integer programming formulations for this problem that lead to branch-and-cut and branch-and-price algorithms. Finally, we introduce a new class of valid inequalities to obtain an enhanced branch-and-cut. Extensive computational experiments are reported. Keywords:Assignment, Clustering, Cutting, Pricing, Integer Programming Current e-mail: uchoa@inf.puc-rio.br 1 Introduction Suppose we have a graph G = (V; E) with n vertices..

Topics: Assignment, Clustering, Cutting, Pricing, Integer Programming
Year: 1998
OAI identifier: oai:CiteSeerX.psu:10.1.1.41.1497
Provided by: CiteSeerX
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