Geodesic
Centdian Computation in Cactus Graphs
Journal of Graph Algorithms and Applications, Tome 16 (2012) no. 2, pp. 199-224.

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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.
DOI : 10.7155/jgaa.00255
Keywords: Distributed Algorithm, Cactus Graph, Centdian Node, Sensor Network 
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Boaz Ben-Moshe; Amit Dvir; Michael Segal; Arie Tamir. Centdian Computation in Cactus Graphs. Journal of Graph Algorithms and Applications, Tome 16 (2012) no. 2, pp. 199-224. doi : 10.7155/jgaa.00255. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00255/

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