Chromatic sets of power graphs and their application to resource placement in multicomputer networks

Authors:
N. Imani;H. Sarbazi-Azad;S. G. Akl;P. Moinzadeh
Affiliations:
IPM School of Computer Science, Tehran, Iran and Department of Computer Engineering, Sharif University of Technology, Tehran, Iran;Department of Computer Engineering, Sharif University of Technology, Tehran, Iran;School of Computing, Queen's University, Kingston, Ontario, Canada;Department of Computer Engineering, Sharif University of Technology, Tehran, Iran and IPM School of Computer Science, Tehran, Iran
Venue:
Computers & Mathematics with Applications
Year:
2009

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Abstract

In this paper, using the chromatic properties of power graphs we propose a new approach for placing resources in symmetric networks. Our novel placement scheme guarantees a perfect placement when such a solution is feasible in the topology, while in general it answers the question of k-resource placement at a distance d where each non-resource node is able to access k resource nodes within at most d hops away. We define a quasi-perfect graph as a graph whose clique number and chromatic number are equal. We derive important properties of quasi-perfect graphs and use them to find a solution for the resource placement problem. We have also applied the proposed method to find a distant resource placement in the popular hypercube network as an example. We have also considered the problem of sparse resource placement.