Memetic algorithm for the antibandwidth maximization problem

The antibandwidth maximization problem (AMP) consists of labeling the vertices of a n-vertex graph G with distinct integers from 1 to n such that the minimum difference of labels of adjacent vertices is maximized. This problem can be formulated as a dual problem to the well known bandwidth problem. Exact results have been proved for some standard graphs like paths, cycles, 2 and 3-dimensional meshes, tori, some special trees etc., however, no algorithm has been proposed for the general graphs. In this paper, we propose a memetic algorithm for the antibandwidth maximization problem, wherein we explore various breadth first search generated level structures of a graph—an imperative feature of our algorithm. We design a new heuristic which exploits these level structures to label the vertices of the graph. The algorithm is able to achieve the exact antibandwidth for the standard graphs as mentioned. Moreover, we conjecture the antibandwidth of some 3-dimensional meshes and complement of power graphs, supported by our experimental results.