- A branch and cut algorithm for minimum spanning trees under conflict constraints Phillippe Samer (samerdcc.ufmg.br) Sebastián Urrutia (surrutiadcc.ufmg.br) Abstract: We study approaches for the exact solution of the \NP--hard minimum spanning tree problem under conflict constraints. Given a graph $G(V,E)$ and a set $C \subset E \times E$ of conflicting edge pairs, the problem consists of finding a conflict-free minimum spanning tree, i.e. feasible solutions are allowed to include at most one of the edges from each pair in $C$. The problem was introduced recently in the literature, with several results on its complexity and approximability. Some formulations and both exact and heuristic algorithms were also discussed, but computational results indicate considerably large duality gaps and a lack of optimality certificates for benchmark instances. In this paper, we build on the representation of conflict constraints using an auxiliary conflict graph $\hat{G}(E,C)$, where stable sets correspond to conflict-free subsets of $E$. We introduce a general preprocessing method and a branch and cut algorithm using an IP formulation with exponentially sized classes of valid inequalities for both the spanning tree and the stable set polytopes. Encouraging computational results indicate that the dual bounds of our approach are significantly stronger than those previously available, already in the initial LP relaxation, and we are able to provide new feasibility and optimality certificates. Keywords: Optimal trees, Conflict constraints, Stable set, Branch and cut Category 1: Combinatorial Optimization (Branch and Cut Algorithms ) Category 2: Integer Programming (0-1 Programming ) Category 3: Integer Programming (Cutting Plane Approaches ) Citation: Phillippe Samer, Sebastián Urrutia (2014), "A branch and cut algorithm for minimum spanning trees under conflict constraints". Accepted for publication on Optimization Letters: 10.1007/s11590-014-0750-x Download: [PDF]Entry Submitted: 07/04/2013Entry Accepted: 07/05/2013Entry Last Modified: 06/30/2014Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.