Abstract
In single channel wireless networks, concurrent transmissions at different links may interfere with each other. To improve system throughput, a scheduling algorithm is necessary to choose a subset of links for data transmission. Throughput optimal link scheduling discipline is generally an NP-hard problem. In this paper, we utilise the concept of line graph and extend it to line multigraph to cope with the complexity issue of the maximum weight scheduling (MWS) algorithm. The necessary and sufficient conditions for reducing the complexity of MWS in terms of network topology are derived. We prove that the complexity of eLehot is polynomial time provided that conflict graph does not contain seven derived forbidden graphs as induced subgraphs. We also propose eLehot algorithm for detecting whether a graph is line multigraph and output its root graph. The results of this paper introduce a new approach in wireless topology control where the target is complexity reduction.
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