Maximum Degree Vertex Central Located Algorithm for Bandwidth Minimization Problem

Abstract

The bandwidth minimization problem (BMP) has been classified as NP-complete because the polynomial time algorithm to find the optimal solution has been unknown yet. This paper suggests polynomial time heuristic algorithm is to find the solution of bandwidth minimization problem. To find the minimum bandwidth O * = min O(G), O(G) = max {│f(ν i )-f(ν i ) : ν i ,ν i ∈E} for given graph G=(V,E) m=│V│,n=│E│ the proposed algorithm sets the maximum degree vertex ν i in graph G into global central point (GCP), and labels the median value?m+1/2? between [1,m] range. The graph G is partitioned into subgroup, the maximum degree vertex in each subgroup is set to local central point(LCP), and we adjust the label of LCP per each subgroup as possible as minimum distance from GCP. The proposed algorithm requires O(mn) time complexity for label to all of vertices. For various twelve graph, the proposed algorithm can be obtains the same result as known optimal solution. For one graph, the proposed algorithm can be improve on known solution.