Page 2 Lecture Notes in Computer Science 2865 Edited by G. Goos ...

Topology Control Problems under Symmetricand Asymmetric Power ThresholdsSven O. Krumke 1 , Rui Liu 2 , Errol L. Lloyd 2 , Madhav V. Marathe 3 ,Ram Ramanathan 4 , and S.S. Ravi 51 Konrad-Zuse-Zentrum für Informationstechnik, Berlin (ZIB)Takustraße 7, 14195 Berlin-Dahlem, Germanykrumke@zib.de2 University of Delaware, Newark, DE 19716{ruliu,elloyd}@cis.udel.edu3 Los Alamos National Laboratory, MS M997, Los Alamos, NM 87545marathe@lanl.gov4 Internetwork Research Department, BBN Technologies, Cambridge, MA 02138ramanath@bbn.com5 University at Albany - SUNY, Albany, NY 12222ravi@cs.albany.eduAbstract. We consider topology control problems where the goal is toassign transmission powers to the nodes of an ad hoc network so as toinduce graphs satisfying specific properties. The properties consideredare connectivity, bounded diameter and minimum node degree. The optimizationobjective is to minimize the total power assigned to nodes. Asthese problems are NP-hard in general, our focus is on developing approximationalgorithms with provable performance guarantees. We presentresults under both symmetric and asymmetric power threshold models.1 IntroductionIt is well known that battery power is a precious resource in ad hoc networks.Therefore, techniques for minimizing the energy consumed in ad hoc networkshave assumed importance. Topology control problems arise in that context. Thegoal of such problems is to control the topology of networks through the assignmentof suitable transmission powers to nodes. Formally, such problems arespecified by requiring the induced network to satisfy some graph theoretic propertieswhile minimizing some function of the transmission powers assigned totransceivers (nodes). Previous work in this area has considered properties suchas node and edge connectivity and optimization objectives such as minimizingmaximum power and minimizing total power. A summary of previous results inthis area is presented in Section 3.2.In this paper, we study topology control problems for three graph properties,namely connectedness, bounded diameter and minimum node degree (Preciseformulations of these problems are provided in Section 2.1.). Connectedness isa basic requirement for any network. Ad hoc networks with small diameters areS. Pierre, M. Barbeau, and E. Kranakis (Eds.): ADHOC-NOW 2003, LNCS 2865, pp. 187–198, 2003.c○ Springer-Verlag Berlin Heidelberg 2003