Quadratic Integer Programming with Application to the Chaotic Mappings of Complete Multipartite Graphs

H. L. Fu, C. L. Shiue, X. Cheng, D. Z. Du and J. M. Kim

Journal of Optimization Theory and Applications, 2001, vol. 110, issue 3, No 4, 545-556

Abstract: Abstract Let α be a permutation of the vertex set V(G) of a connected graph G. Define the total relative displacement of α in G by be $$\delta _\alpha (G) = \mathop \Sigma \limits_{x,y \in V(G)} |d_G (x,y) - d_G (\alpha (x),\alpha (y))|,$$ where dG(x, y) is the length of the shortest path between x and y in G. Let π* (G) be the maximum value of δα (G) among all permutations of V(G). The permutation which realizes π* (G) is called a chaotic mapping of G. In this paper, we study the chaotic mappings of complete multipartite graphs. The problem is reduced to a quadratic integer programming problem. We characterize its optimal solution and present an algorithm running in $$O(n^5 \log n)$$ time, where n is the total number of vertices in a complete multipartite graph.

Keywords: Chaotic mapping; complete multipartite graph; quadratic integer programming; optimal solution (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (4)

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DOI: 10.1023/A:1017584227417

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