Routing, frequency channel assignment and clustering are important subjects for multihop wireless networks which packets are relayed. Although various algorithms are proposed, most of them are based on computer simulation and there is almost no theoretical examination. Therefore we consider optimization with graph theory. Moreover we classify hidden terminals into plural patterns and we use it for evaluation function. We first propose the reduction of matrix, the reduction of the list of channel assignment the exclusion of the specific interference pattern during two wireless links. We show that optimal solution can be easily derived using maximum throughput that all wireless stations can receive simultaneously as evaluation function.
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