Exact and heuristic methods for the vertex separator problem

Haeder Althoby (1, 2) , Mohamed Didi Biha (1) , André Sesboüé (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 AL-Qadisiyah University

In this paper, we propose a practical and efficient methods to solve the vertex separator problem (VSP for short), based on branch-and-bound procedure, which uses linear programming, and a greedy algorithm. This problem arises in many areas of applications such as graph algorithms, communication networks, solving systems of equations, finite element and finite difference problems. We show, by computational experiments, that our approach is able to solve in short time large-scale instances of VSP from the literature to optimality or near optimality.

Keywords: Graph partitioning; Vertex separator; Integer programming; Branch-and-Bound; Greedy algorithm

Domains: Mathematics [math]; Optimization and Control [math.OC]; Computer Science [cs]; Discrete Mathematics [cs.DM]

Haeder Althoby, Mohamed Didi Biha, André Sesboüé. Exact and heuristic methods for the vertex separator problem. Computers & Industrial Engineering, 2020, 139, pp.106135. ⟨10.1016/j.cie.2019.106135⟩. ⟨hal-02427906⟩