Journal of Graph Algorithms and Applications
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Centdian Computation in Cactus Graphs
Vol. 16, no. 2, pp. 199-224, 2012. Regular paper.
Abstract This paper focuses on the centdian problem in a cactus network where a cactus network is a connected undirected graph, and any two simple cycles in the graph have at most one node in common. The cactus network has important applications for wireless sensor networks when a tree topology might not be applicable and for extensions to the ring architecture. The centdian criterion represents a convex combination of two QoS requirements: transport and delay. To the best of our knowledge, no efficient algorithm has yet been developed for constructing a centdian node in a cactus graph, either sequential or distributed. We first investigate the properties of the centdian node in a cycle graph, and then explore the behavior of the centdian node in a cactus graph. Finally, we present new efficient sequential and distributed algorithms for finding all centdian nodes in a cycle graph and a cactus graph.
Submitted: July 2010.
Reviewed: February 2011.
Revised: June 2011.
Reviewed: December 2011.
Revised: December 2011.
Accepted: December 2011.
Final: January 2012.
Published: January 2012.
Communicated by Gerhard J. Woeginger