Phase transition in the bandwidth minimization problem

Abstract

It is known that some NP-Complete problems exhibit sharp phase transitions with respect to some order parameter. Moreover, a correlation between that critical behavior and the hardness of finding a solution exists in some of these problems. This paper shows experimental evidence about the existence of a critical behavior in the computational cost of solving the bandwidth minimization problem for graphs (BMPG). The experimental design involved the density of a graph as order parameter, 200000 random connected graphs of size 16 to 25 nodes, and a branch and bound algorithm taken from the literature. The results reveal a bimodal phase transition in the computational cost of solving the BMPG instances. This behavior was confirmed with the results obtained by metaheuristics that solve a known BMPG benchmark. © 2009 Springer-Verlag Berlin Heidelberg.