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ABSTRACT

Routing traffic so as to maximize the lifetime of a transmission is a major problem in wireless networks. We address a two-way multicast problem, where a root wishes to transmit data to a subset of nodes, as well as receive data from them. In addition, we consider the anycast problem, wherethere is a subset of nodes that wish to communicate with each other. We consider both a per-hop multi-recipients environment, where over each hop, the transmission is received by all nodes within range, and a per-hop single-recipient environment, where over each hop the transmission is received by a single recipient. For both environments, our work consists of two parts. In the first part we focus on system optimization perspectives of the lifetime maximization problem, while in the second part we investigate the game-theoretic perspective of the respective problems.

We first note that, for the per-hop multi-recipients environment, an optimal solution can be computed in polynomial time. Nevertheless, for the per-hop single-recipient environment, we observe that computing an optimal solution is NP-hard. Accordingly, we provide a polynomial time algorithm that finds a 2-approximate solution for the case of uniform transmission power levels. For different transmission power levels, we provide an O(log² n) approximation algorithm for the general problem, and an O(log n) approximation algorithm for the special case where the set of terminals equals the set of all nodes, whose size equals n.

For each environment, we consider the corresponding noncooperative game scenario, and prove that by following the natural game course users converge to a Nash equilibrium. For the per-hop multi-recipients environment, we show that if the players join the game sequentially, the Nash equilibrium is (networkwide) optimal. For the per-hop single-recipient environment, we show that the price of anarchy is unbounded. On the other hand, we show that for both environments, the price of stability, where the best Nash equilibrium is considered, is 1; hence, optimal (networkwide) performance can be achieved if the initial configuration can be imposed on the players.

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INDEX TERMS

Primary Classification:
  C. Computer Systems Organization
  C.2 COMPUTER-COMMUNICATION NETWORKS
      C.2.1 Network Architecture and Design
          Subjects: Wireless communication

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.2 Nonnumerical Algorithms and Problems
          Subjects: Routing and layout

  K. Computing Milieux
  K.8 PERSONAL COMPUTING
      K.8.0 General
          Subjects: Games

General Terms:
Algorithms, Design, Performance, Theory

Keywords:
anycast game, multicast game, nash equilibrium, price of anarchy, price of stability