Application of Line Graph for Link Scheduling in Wireless Networks under M-hop Interference Model

In this paper, we study the link scheduling problem in wireless networks under M-hop interference model. In wireless networks, a scheduling algorithm is required to choose a subset of links at each time slot such that the packets do not corrupt due to interference. To deal with the interference in such a radio network different models have been introduced in the literature. In M-hop interference model two links are said to be conflicting links if they are within distance M of each other. It has been proven that for M > 1 the problems are generally NP-Hard. But for M=1, this problem becomes the classical matching problem, that can be solved in polynomial time and is a well studied subject. Having motivated to solve the above NP-hard problem, we utilize the concept of line graph from graph theory and incorporate it with the notion of conflict graph to simplify the development of link scheduling algorithms under M-hop interference model for a large class of graphs. We show that it is possible to achieve a low complexity discipline for link selection under M-hop interference model by applying a well known matching algorithm to the root graph of the conflict graph, provided that the conflict graph does not include claw, 6-Wheel and 4-Polyiamond as induced subgraphs.