The Distributed Wireless Gathering Problem

We address the problem of data gathering in a wireless network using multi-hop communication; our main goal is the analysis of simple algorithms suitable for implementation in realistic scenarios. We study the performance of distributed algorithms, which do not use any form of local coordination, and we focus on the objective of minimizing average flow times of data packets. We prove a lower bound of $\Omega(n)$ on the expected competitive ratio of any acknowledgment-based distributed algorithm minimizing the maximum flow time, where $n$ is the number of nodes of the network. Next, we consider a distributed algorithm which sends packets over shortest paths, and we use resource augmentation to analyze its performance when the objective is to minimize the average flow time. If interferences are modeled as in Bar-Yehuda et al. [R. Bar-Yehuda, O. Goldreich, A. Itai, On the time complexity of broadcast in multi-hop radio networks: an exponential gap between determinism and randomization, Journal of Computer and Systems Sciences 45 (1) (1992) 104– 126] we prove that the algorithm is $(1+\epsilon)$-competitive, when the algorithm sends packets a factor $O(\log(\delta/\epsilon) \log \Delta)$ faster than the optimal off-line solution; here $\delta$ is the radius of the network and $\Delta$ the maximum degree. We finally extend this result to a more complex interference model