Maximizing number of satisfiable routing requests in static ad hoc networks

We study an energy-efficient routing problem in static ad hoc networks. The problem, referred to as maxR, is to maximize the number of routing requests that can be satisfied in the network, under the constraint that each node has finite battery power. The online version of the problem, where the sequence of messages that has to be routed over the network is not known ahead of time, has been studied extensively. In this paper, we study the offline version of the problem where the sequence of requests is pre-known. As far as we know, the offline maxR problem, its hardness and approximability have not been well studied. We show that after appropriate transformation, offline maxR is equivalent to the well-known maximum disjoint path problem, which is NP-hard. We propose a greedy algorithm called GDP that has a constant approximation ratio to the optimal algorithm. GDP can be used as a benchmark to evaluate the performance of online algorithms as it is known that the best offline algorithm performs better than any online algorithm. We then put forward a new online algorithm called MECBE to solve the online maxR problem. Simulation results show that GDP outperforms MECBE, which outperforms the state-of-the-art online algorithm OML, in terms of the number of satisfiable requests, the average energy consumption per request, and the number of energy-depleted nodes.