A New Heuristic Algorithm for the Vertex Separation Problem

Abstract

The Vertex Separation Problem (VSP) belongs to a family of graph layout problems. VSP consists in finding a linear ordering of the vertices of a graph such that the maximum number of vertex separators at each position of the ordering is minimized. This problem has important practical applications in fields such as very large scale integration design, computer language compiler design or natural language processing. VSP has been proven to be NP-hard. In the literature reviewed, we found several heuristic and metaheuristic algorithms designed for solving large instances of VSP. As far as we are aware, these algorithms do not use fuzzy logic. In this chapter, we adapt two fuzzy logic classifiers (FLC) to a constructive algorithm from the literature. More precisely, the first FLC is used to select the vertex to be placed at the first position of the linear ordering according to the adjacency degree. The second FLC is used to select the following vertices according to the number of vertex separators. We have designed five variants of our fuzzy heuristic. The computational experiment indicates that the first four variants have a similar behavior in solution quality and execution time.