  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
trasmission. Throughput optimal link scheduling discipline in such a wireless
network is generally an NP-hard problem. In this paper, we develop a poylnomial
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
throughput optimal algorithm can be run in a much less time.
