The Maximum Degree & Diameter-Bounded Subgraph and its Applications

Authors:
Anthony Dekker;Hebert Pérez-Rosés;Guillermo Pineda-Villavicencio;Paul Watters
Affiliations:
Center for Informatics and Applied Optimization, University of Ballarat, Ballarat, Australia;Department of Computer Science, The University of Newcastle, Newcastle, Australia;Center for Informatics and Applied Optimization, University of Ballarat, Ballarat, Australia;Center for Informatics and Applied Optimization, University of Ballarat, Ballarat, Australia
Venue:
Journal of Mathematical Modelling and Algorithms
Year:
2012

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Abstract

We introduce the problem of finding the largest subgraph of a given weighted undirected graph (host graph), subject to constraints on the maximum degree and the diameter. We discuss some applications in security, network design and parallel processing, and in connection with the latter we derive some bounds for the order of the largest subgraph in host graphs of practical interest: the mesh and the hypercube. We also present a heuristic strategy to solve the problem, and we prove an approximation ratio for the algorithm. Finally, we provide some experimental results with a variety of host networks, which show that the algorithm performs better in practice than the prediction provided by our theoretical approximation ratio.