Page 2 Lecture Notes in Computer Science 2865 Edited by G. Goos ...

Computing 2-Hop Neighborhoodsin Ad Hoc Wireless NetworksGruia CalinescuDepartment of Computer Science, Illinois Institute of Technology, Chicago, IL 60616calinesc@iit.eduAbstract. We present efficient distributed algorithms for computing 2-hop neighborhoods in Ad Hoc Wireless Networks. The knowledge of the2-hop neighborhood is assumed in many protocols and algorithms forrouting, clustering, and distributed channel assignment, but no efficientdistributed algorithms for computing the 2-hop neighborhoods were previouslypublished.The problem is nontrivial, as the graphs induced by ad-hoc wireless networkscan be dense. We employ the broadcast nature of the wirelessnetworks to obtain a distributed algorithm in which every node gainsknowledge 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 messagehas O(log n) bits, which we assume is enough to encode the ID andthe geographic position of a node. Our algorithm operates in an asynchronousenvironment, and makes use of the geographic position of thenodes.A more complicated algorithm achieves the same communication boundswhen geographical positions are not available, but nodes are capable ofevaluating the distance to neighboring nodes or the angle of signal arrival.We also discuss updating the knowledge of 2-hop neighborhoods whennodes join or leave the network.1 IntroductionWireless ad hoc networks can be flexibly and quickly deployed for many applicationssuch as automated battlefield, search and rescue, and disaster relief.Unlike wired networks or cellular networks, no physical backbone infrastructureis installed in wireless ad hoc networks. A communication session is achievedeither through a single-hop radio transmission if the communication parties areclose enough, or through relaying by intermediate nodes otherwise.In this paper, we assume that all nodes in a wireless ad hoc network aredistributed in a two-dimensional plane and have an equal maximum transmissionrange of one unit. The topology of such wireless ad hoc network can be modeledas a unit-disk graph, or UDG (see [11] for many interesting properties of unitdiskgraphs), a geometric graph in which there is a link between two nodes ifand only if their distance is at most one.The 1-hop neighborhood of a node v (denoted by N 1 (v)) is simply the setof nodes adjacent to it in the UDG. We use N 2 (v) to denote the set of nodesS. Pierre, M. Barbeau, and E. Kranakis (Eds.): ADHOC-NOW 2003, LNCS 2865, pp. 175–186, 2003.c○ Springer-Verlag Berlin Heidelberg 2003