On some variants of the bandwidth minimization problem
SIAM Journal on Computing
Hamiltonian powers in threshold and arborescent comparability graphs
Discrete Mathematics
A survey of graph layout problems
ACM Computing Surveys (CSUR)
The Obnoxious Center Problem on a Tree
SIAM Journal on Discrete Mathematics
A Survey on Obnoxious Facility Location Problems
A Survey on Obnoxious Facility Location Problems
Powers of Hamiltonian paths in interval graphs
Journal of Graph Theory
Note: On explicit formulas for bandwidth and antibandwidth of hypercubes
Discrete Applied Mathematics
Variable neighborhood search with ejection chains for the antibandwidth problem
Journal of Heuristics
An improved memetic algorithm for the antibandwidth problem
EA'11 Proceedings of the 10th international conference on Artificial Evolution
Antibandwidth and cyclic antibandwidth of Hamming graphs
Discrete Applied Mathematics
A hybrid metaheuristic for the cyclic antibandwidth problem
Knowledge-Based Systems
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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.