Analysis of Interference in Ad-Hoc Networks

Despite the focused attention to Mobile Ad-Hoc Networks (MANETs) in the past years, models of interference on the abstraction level of graphs are poorly studied. It is often argued that assuring low degree in topologies is sufficient to minimize interference. In this work, several models of interference are defined. A classification of models is developed and relations among different models are investigated. One of the main differences between models is whether they focus on outgoing (Iout) or incoming (Iin) interference. For Iout a greedy algorithm (GLIT) is presented that constructs an interference optimal spanning tree. GLIT can be adapted to construct an interference optimal t-spanner (GLIS). Based on these models, the maximum degree of a network turns out to be merely a lower bound for interference and thus the need for topologies that minimize actual interference instead of node degree becomes obvious. Despite the fact that reducing interference is the main reason for doing topology control at all, widely used topologies as the Minimum Spanning Tree, Relative Neighborhood Graph, Gabriel Graph, Delaunay Triangulation or Yao graph are shown to be prone to bad interference properties, while the introduced algorithms GLIT and GLIS are interference optimal for Iout and provide good heuristics for other measures. Moreover, the MINIMUM INTERFERENCE BROADCAST (MIB) problem and its connected variant (CMIB) are defined. Solutions to CMIB can be used as interference optimal virtual backbones in ad-hoc networks. Although MIB and CMIB are shown to be NP-complete, a constant approximation of both is given. Changing the interference model from Iin to Iout makes MIB and CMIB optimally solvable in polynomial time, which is a very intriguing result concerning the complexity of interference measures.