Brief announcement: minimum spanning trees and cone-based topology control

Consider a setting where nodes can vary their transmission power thereby changing the network topology, the goal of topology control is to reduce the transmission power while ensuring the communication graph remains connected. Wattenhofer et al. [6] introduced the distributed cone-based topology control algorithm with parameter (CBTC()) and proved it correct if 2 3 . Li et al. [4] proposed performing asymmetric edge removal or increasing to 5 6 , and proved that when applied separately these optimizations preserve connectivity. Bahramgiri et al. [1] proved that when 2 3 it was possible to extend the algorithm to work in three dimensions and described a variation to preserve kconnectivity. We give a short self-contained proof that when 2 3 the minimum spanning tree is contained in the graph produced by CBTC(). Its interesting to note that by comparison other topology control algorithms are variations of the Gabriel Graph [5], the Relative Neighbor Graph [2] or the Delaunay Tria...

• Type: Conference
• Year: 2009
• Where: PODC
• Authors: Alejandro Cornejo, Nancy A. Lynch
• Keywords: Et Al, Li Et Al, Parallel Computing, PODC 2009, Topology Control Algorithm