Mathematical Programming Models and Their Relaxations for The Minimum Hub Cover Problem

The minimum hub cover is a new NP-hard optimization problem that has been recently introduced to the literature in the context of graph query processing. Although a standard set covering formulation has been given, alternate models have not been studied before. This paper fills in that gap and proposes several new mathematical programming models. We give two binary integer programming formulations as well as a quadratic integer programming formulation. Our relaxation for the quadratic model leads to a semidefinite programming formulation. A solution to the minimum hub cover problem can be obtained by solving the relaxations of the proposed models and then rounding their solutions. We introduce two rounding algorithms after solving the linear programming and semidefinite programming relaxations, respectively. We also implement two well-known rounding algorithms designed for the set covering problem. Computational results demonstrate that our methods outperform those solutions obtained with the standard set covering formulations.