  Topology control algorithms allow each node in a wireless multi-hop network
to adjust the power at which it makes its transmissions and choose the set of
neighbors with which it communicates directly, while preserving global goals
such as connectivity or coverage. This allows each node to conserve energy and
contribute to increasing the lifetime of the network. In this paper, in
contrast to most previous work, we consider (i) both the energy costs of
communication as well as the amount of available energy at each node, (ii) the
realistic situation of varying rates of energy consumption at different nodes,
and (iii) the fact that co-operation between nodes, where some nodes make a
sacrifice by increasing energy consumption to help other nodes reduce their
consumption, can be used to extend network lifetime. This paper introduces a
new distributed topology control algorithm, called the Cooperative Topology
Control with Adaptation (CTCA), based on a game-theoretic approach that maps
the problem of maximizing the network's lifetime into an ordinal potential
game. We prove the existence of a Nash equilibrium for the game. Our simulation
results indicate that the CTCA algorithm extends the life of a network by more
than 50% compared to the best previously-known algorithm. We also study the
performance of the distributed CTCA algorithm in comparison to an optimal
centralized algorithm as a function of the communication ranges of nodes and
node density.
