Paving the Way Towards Reactive Planar Spanner Construction in Wireless Networks

Abstract

A spanner is a subgraph of a given graph that supports the original graph’s shortest path lengths up to a constant factor. Planar spanners and their distributed construction are of particular interest for geographic routing, which is an efficient localized routing scheme for wireless ad hoc and sensor networks. Planarity of the network graph is a key criterion for guaranteed delivery, while the spanner property supports efficiency in terms of path length. We consider the problem of reactive local spanner construction, where a node’s local topology is determined on demand. Known message-efficient reactive planarization algorithms do not preserve the spanner property, while reactive spanner constructions with a low message overhead have not been described so far. We introduce the concept of direct planarization which may be an enabler of efficient reactive spanner construction. Given an edge, nodes check for all incident intersecting edges a certain geometric criterion and withdraw the edge if this criterion is not satisfied. We use this concept to derive a generic reactive topology control mechanism and consider two geometric criteria. Simulation results show that direct planarization increases the performance of localized geographic routing by providing shorter paths than existing reactive approaches.