Computing 2-hop neighborhoods in ad hoc wireless networks

Abstract

We present efficient distributed algorithms for computing 2-hop neighborhoods in Ad Hoc Wireless Networks. The knowledge of the 2-hop neighborhood is assumed in many protocols and algorithms for routing, clustering, and distributed channel assignment, but no efficient distributed algorithms for computing the 2-hop neighborhoods were previously published. The problem is nontrivial, as the graphs induced by ad-hoc wireless networks can be dense. We employ the broadcast nature of the wireless networks to obtain a distributed algorithm in which every node gains knowledge of its 2-hop neighborhood using a total of O(n) messages, where n is the total number of nodes in the network, and each message has O(log n) bits, which we assume is enough to encode the ID and the geographic position of a node. Our algorithm operates in an asynchronous environment, and makes use of the geographic position of the nodes. A more complicated algorithm achieves the same communication bounds when geographical positions are not available, but nodes are capable of evaluating the distance to neighboring nodes or the angle of signal arrival. We also discuss updating the knowledge of 2-hop neighborhoods when nodes join or leave the network. © Springer-Verlag Berlin Heidelberg 2003.