Implementation of the iterative relaxation algorithm for the Minimum Bounded-Degree Spanning Tree Problem

Abstract

In the Minimum Bounded-Degree Spanning Tree Problem we want to find a minimum cost spanning tree that satisfies given degree bounds. For this problem a very good quality solution can be found using the iterative relaxation technique of Singh and Lau STOC'07: the cost will not be worse than the cost of the optimal solution, and the degree bounds will be violated by at most one. This paper reports on the experimental comparison of this state-of-art approximation algorithm with standard, although well-tuned meta-heuristics. We have implemented the Iterative Relaxation algorithm of Singh and Lau and speeded it up using several heuristics including row generation and combinatorial LP pivoting. On the other hand, as the heuristic point of reference we have chosen local search techniques in a Simulated Annealing framework, where we allow the violation of degree bounds by one. In such setting there are two natural objectives for comparison: the cost of the solution, and the number of violated degree bounds. If we keep the number of violated constraints fixed in both algorithms then Iterative Rounding usually outperforms Simulated Annealing by several percents. © 2014 Springer International Publishing.