Key points are not available for this paper at this time.
With increasing interest in energy constrained multi-hop wireless networks (Bambos, N. et al., 1991), a fundamental problem is one of determining energy efficient communication strategies over these multi-hop networks. The simplest problem is one where a given source node wants to communicate with a given destination, with a given rate over a multi-hop wireless network, using minimum power. Here the power refers to the total amount of power consumed over the entire network in order to achieve this rate between the source and the destination. There are three decisions that have to be made (jointly) in order to minimize the power requirement. (1) The path(s) that the data has to take between the source and the destination. (Routing). (2) The power with each link transmission is done. (Power Control). (3) Depending on the interference or the MAC characteristics, the time slots in which specific link transmissions have to take place. (Scheduling). (4) To the best of our knowledge, ours is the first attempt to derive a performance guaranteed polynomial time approximation algorithm for jointly solving these three problems. We formulate the overall problem as an optimization problem with non-linear objective function and non-linear constraints. We then derive a polynomial time 3-approximation algorithm to solve this problem. We also present a simple version of the algorithm, with the same performance bound, which involves solving only shortest path problems and which is quite efficient in practice. Our approach readily extends to the case where there are multiple source-destination pairs that have to communicate simultaneously over the multi-hop network.
Bhatia et al. (Tue,) studied this question.