Layered graph models and exact algorithms for the generalized hop-constrained minimum spanning tree problem

•New optimization problem generalizing the generalized minimum spanning tree problem and the hop constrained minimum spanning tree problem.•Extended formulations based on layered graph reformulations and strength- ening valid inequalities.•Theoretical and computational comparisons between all formulations.

This paper studies the generalized hop-constrained minimum spanning tree problem (GHMSTP) which has applications in backbone network design subject to quality-of-service constraints that restrict the maximum number of intermediate routers along each communication path. Different possibilities to model the GHMSTP as an integer linear program and strengthening valid inequalities are studied. The obtained formulations are compared theoretically, i.e., by means of their linear programming relaxation. In addition, branch-and-cut approaches based on these formulations are developed and compared in a computational study.