Introduction to algorithms
Approximation algorithms for NP-hard problems
Bicriteria network design problems
Journal of Algorithms
Analysis of a cone-based distributed topology control algorithm for wireless multi-hop networks
Proceedings of the twentieth annual ACM symposium on Principles of distributed computing
Algorithmic aspects of topology control problems for ad hoc networks
Proceedings of the 3rd ACM international symposium on Mobile ad hoc networking & computing
Wireless Communications: Principles and Practice
Wireless Communications: Principles and Practice
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Power Consumption in Packet Radio Networks (Extended Abstract)
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
Hardness Results for the Power Range Assignmet Problem in Packet Radio Networks
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
Minimum energy mobile wireless networks
IEEE Journal on Selected Areas in Communications
On approximate optimal dual power assignment for biconnectivity and edge-biconnectivity
Theoretical Computer Science
Wireless network design via 3-decompositions
Information Processing Letters
Topology control in constant rate mobile ad hoc networks
Wireless Networks
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Topology control is the problem of assigning transmission power values to the nodes of an ad hoc network so that the induced graph satisfies some specified property. The most fundamental such property is that the network/graph be connected. For connectivity, prior work on topology control gave a polynomial time algorithm for minimizing the maximum power assigned to any node (such that the induced graph is connected). In this paper we study the problem of minimizing the number of maximum power nodes. After establishing that this minimization problem is NP-complete, we focus on approximation algorithms for graphs with symmetric power thresholds. We first show that the problem is reducible in an approximation preserving manner to the problem of assigning power values so that the sum of the powers is minimized. Using known results for that problem, this provides a family of approximation algorithms for the problem of minimizing the number of maximum power nodes with approximation ratios of 5/3 + ε for every ε 0. Unfortunately, these algorithms, based on solving large linear programming problems, are not practical. The main results of this paper are practical algorithms with approximation ratios of 7/4 and 5/3 (exactly). In addition, we present experimental results, both on randomly generated networks, and on two networks derived from proximity data associated with the TRANSIMS project of Los Alamos National Labs. Finally, based on the reduction to the problem of minimizing the total power, we describe some additional results for minimizing the number of maximum power users, both for graph properties other than connectivity and for graphs with asymmetric power thresholds.