On selection problem in radio networks

Abstract

A selection problem is among the basic communication primitives in networks. In this problem at most k participating stations have to broadcast successfully their messages. This problem is especially important in packet radio networks, where simultaneous transmissions of many neighbors result in interference among delivered messages. This work focuses on a single-hop radio networks with n-stations, also called a multiple access channel, and considers both static and dynamic versions of the selection problem. We construct a family of efficient oblivious deterministic protocols based on selectors, one of them with selection time cO(klog(n/k)), and the second explicit construction with selection time cO(k polylog n). The first construction matches the lower bound Ω(klog(n/k)) on deterministic oblivious selection, while the second one is the first known explicit construction better than Θ(k2). In the dynamic case we introduce the model of dynamic requests, called k-streams, which generalizes the static model and the dynamic requests with at most k participants. We prove that each oblivious deterministic protocol has latency Ω(k2/log k), and on the other hand we prove the existence of the oblivious deterministic protocol with latency cO(k2log n). In view of the existence of the randomized oblivious protocol with expected latency cO(klog(n/k)), this shows that randomization is substantially better than determinism for dynamic setting. Selection problem can be applied to implement other communication primitives --- we demonstrate it in the example of broadcast problem in multi-hop ad-hoc radio networks. In particular, we design an adaptive deterministic protocol broadcasting in time cO(nlog D) in every D-hop radio network of n-stations.