Particionamiento Balanceado de Hipergrafos en un Número Fijo de Componentes.

Abstract

In this paper, the partitioning hypergraph problem in a fixed number of components is studied. Hypergraphs are the generalization of graphs where, unlike edges, each hyperedge can connect two or more vertices. Given a hypergraph H = (V,E), where V is the vertices set and E the hyperedges set, we seek to partition its vertex set into k disjoint components such that each vertex is covered by hyperedges completely contained in some component, while minimizing the total cost of these hyperedges. Several Integer Programming formulations are proposed for the k-way equipartitioning, minimum size partitioning, balanced partitioning, and k-way equipartitioning in linear hyper-trees. Moreover, some types of valid inequalities are demonstrated and implemented for the different formulations. Finally, the computational experiments performed on the different formulations for different instances are discussed.