Bounded-hops power assignment in ad hoc wireless networks

  • Authors:

  • G. Calinescu;S. Kapoor;M. Sarwat

  • Affiliations:

  • Department of Computer Science, Illinois Institute of Technology, Stuart Building, 10 West 31st Street, Chicago, IL 60616, USA;Department of Computer Science, Illinois Institute of Technology, Stuart Building, 10 West 31st Street, Chicago, IL 60616, USA;Department of Computer Science, Illinois Institute of Technology, Stuart Building, 10 West 31st Street, Chicago, IL 60616, USA

  • Venue:
  • Discrete Applied Mathematics - Special issue: 2nd cologne/twente workshop on graphs and combinatorial optimization (CTW 2003)
  • Year:
  • 2006

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Abstract

Motivated by topology control in ad hoc wireless networks, Power Assignment is a family of problems, each defined by a certain connectivity constraint (such as strong connectivity). The input consists of a directed complete weighted digraph G=(V,c) (that is, c:VxV-R^+). The power of a vertex u in a directed spanning subgraph H is given by p"H(u)=max"u"v"@?"E"("H")c(uv), and corresponds to the energy consumption required for node u to transmit to all nodes v with uv@?E(H). The power of H is given by p(H)=@?"u"@?"Vp"H(u). Power Assignment seeks to minimize p(H) while H satisfies the given connectivity constraint. Min-Power Bounded-Hops Broadcast is a power assignment problem which has as additional input a positive integer d and a r@?V. The output H must be a r-rooted outgoing arborescence of depth at most d. We give an (O(logn),O(logn)) bicriteria approximation algorithm for Min-Power Bounded-Hops Broadcast: that is, our output has depth at most O(dlogn) and power at most O(logn) times the optimum solution. For the Euclidean case, when c(u,v)=c(v,u)=@?u,v@?^@k (here @?u,v@? is the Euclidean distance and @k is a constant between 2 and 5), the output of our algorithm can be modified to give a O((logn)^@k) approximation ratio. Previous results for Min-Power Bounded-Hops Broadcast are only exact algorithms based on dynamic programming for the case when the nodes lie on the line and c(u,v)=c(v,u)=@?u,v@?^@k. Our bicriteria results extend to Min-Power Bounded-Hops Strong Connectivity, where H must have a path of at most d edges in between any two nodes. Previous work for Min-Power Bounded-Hops Strong Connectivity consists only of constant or better approximation for special cases of the Euclidean case.