Centdian Computation in Cactus Graphs

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 Article type: Regular paper Communicated by: G. J. Woeginger This work was done while the second author was graduate student in the Department of Communication System, Ben-Gurion University of the Negev, Israel. Amit has also been supported by the Marie Curie Mobility Grant, OTKA-HUMAN-MB08-B 81654. Work of Michael Segal has been partially Supported by EPSRC grant EP/H018816/1, US Air Force European Office of Aerospace Research and Development, grant FA8655-09-1-3016, Deutsche Telecom, France Telecom, European project FLAVIA and Israeli Ministry of Industry, Trade and Labor (consortium CORNET). E-mail addresses: [email protected] (Boaz Ben-Moshe) [email protected] (Amit Dvir) [email protected] (Michael Segal) [email protected] (Arie Tamir) 200 B. Ben-Moshe et al. Centdian in cactus graphs