Chromatic number in random scaled sector graphs

Abstract

In this paper, we introduce a new model of random graph that we call random sector graph. This model aims to provide a tool for studying communication problems in networks of sensors using laser communication such as the ones addressed in the Smart Dust project. Current technology allows steering the laser cannon along a contigous sector, providing undirectional communication. Thus, random sector graphs are a generalization of random geometric graphs, in which this restricted communication is taken into account. We provide tight estimations of the maximum and minimum degree and show that random sector graphs are connected for an adequate selection of the sector radius. We also propose and analyze decentralized protocols to solve two basic issues in networks of sensors.