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: email@example.com 1 Introduction Suppose we have a graph G = (V; E) with n vertices..
To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.