Abstract

ESTEFANO, Viteri,  and  RAMIRO, Torres,. An Exact Approach for the Graph Equipartitioning Problem in Connected Components. Rev Politéc. (Quito) [online]. 2023, vol.51, n.1, pp.103-116. ISSN 2477-8990.  https://doi.org/10.33333/rp.vol51n1.09.

Abstract: In the present work, the graph equipartitioning problem in connected components is studied. The problem consists of partitioning an undirected graph with cost on the edges into a fixed number of connected components, such that the number of nodes in each component differs in at most one unit and the total cost of the edges with end-nodes in the same connected component is minimized. Several integer linear programming models using different approaches (maximizing the edges in the cut or minimizing the edges in the connected components) are presented and the results are compared. Moreover, several families of valid inequalities associated to the polytope of these formulations, together with a Branch & Cut algorithm are exposed. Finally, computational results based on simulated instances of different sizes are reported.

Keywords : Graph equipartitioning; Integer programming; Branch & Cut.

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