Comparative Study on Constructive Heuristics for the Vertex Separation Problem

Abstract

The vertex separation problem (VSP) consists of finding a linear ordering of the vertices of an input graph that minimizes the maximum number of vertex separators at each cut-point induced by the ordering. VSP is an NP-hard problem whose efficient solution is relevant in fields such as very large scale integration design, computer language compiler design, graph drawing and bioinformatics. In the literature reviewed, we found several exact algorithms and two metaheuristics based on the variable neighborhood search approach. These metaheuristics are currently the best stochastic algorithms for solving VSP. One of the key points of their efficiency is the usage of heuristics to construct a high-quality initial solution that considerably improves the algorithm performance. In this chapter we augment the literature on VSP by proposing a new set of heuristics. The proposed constructive heuristics are compared with the best ones found in the state-of-the-art and with random solution generator (Rnd). Experimental results demonstrate the importance of constructive algorithms. The best constructive improves Rnd by 89.96 % in solution quality.