A generalization of line graphs via link scheduling in wireless networks

In single channel wireless networks, concurrent transmission at different links may interfere with each other. To improve system throughput, a scheduling algorithm is necessary to choose a subset of links at each time slot for data transmission. Throughput optimal link scheduling discipline in such a wireless network is generally an NPhard problem. In this paper, we develop a polynomial time algorithm for link scheduling problem provided that network conflict graph is line multigraph. (i.e., line graph for which its root graph is multigraph). This result can be a guideline for network designers to plan the topology of a stationary wireless network such that the required conditions hold and then the throughout optimal algorithm can be run in a much less time.