A layered graph model and an adaptive layers framework to solve delay-constrained minimum tree problems

Abstract

We present a layered graph model for delay-constrained minimum tree problems with a polynomial number of constraints which can be solved well for instances with low- to medium-sized sets of achievable delay values and not too high bounds. Layered graph models have been recently shown to frequently yield tight bounds in the context of hop- or delay-constrained network design problems. However, since the size of the layered graph heavily depends on the size of the set of achievable delay values and the corresponding delay bound the practical applicability of these models is limited. To overcome this problem we introduce an iterative strategy in which an initially small layered graph is successively extended in order to tighten lower and upper bounds until convergence to the optimal solution. Computational results show the synergetic effectiveness of both approaches outperforming existing models in nearly all cases. © 2011 Springer-Verlag.