Channel assignment problem in cellular network and its reduction to satisfiability using graph k-colorability

In cellular network, the frequency spectrum has become an important resource for communication services; since nowadays numbers of cellular users are rapidly increasing but available frequency spectrum is limited. Therefore, there is need of a proper channel assignment approach by which co-channel interference could be minimized and reusability of channels could be maximized using the limited span of the frequency band while satisfying the communication quality constraints. Since, channel assignment problem has been shown to be an NP-hard problem. Also, it is shown that the channel assignment problem is very similar to the graph k-colorability problem. But Graph k-Colorability (for k ≥ 3) Problem (GCP) is a well known NP-Complete problem. There are many approaches has been proposed to solve graph k-colorability and one of the recent approach is propositional satisfiability (SAT). In this paper, we reduce the channel assignment problem in cellular network to 3-satisfiability (3-CNF-SAT) expression using graph k-colorability and also it is illustrated by a small instance of channel assignment in cellular network. Our reduction formulation generates the 3-CNF-SAT formula corresponding to any channel assignment instance in polynomial time.