A Probabilistic Greedy Algorithm with Forced Assignment and Compression for Fast Frequency Assignment in Cellular Network

This paper presents a probabilistic greedy algorithm for solving the channel assignment problem (CAP) in cellular networks. We took each call as a vertex of a complete edge weighed graph, termed as CAP graph, where an edge weight represents the minimum frequency separation needed between the calls represented by the terminal vertices of that edge. Our objective is to assign non-negative integers representing colors or frequencies to the vertices of the CAP graph such that the required span (maximum frequency - minimum frequency) is minimized while satisfying the frequency separation constraints represented by the edge weights. We begin with a probabilistic ordering of the vertices and apply frequency exhaustive strategy to color them. During the coloring, when color of a vertex exceeds the maximum color of previously allocated vertices, we apply a forced assignment phase to reduce the so far obtained span. Finally we propose an iterative compression phase to further reduce the span obtained from applying the frequency exhaustive strategy with forced assignment phase. The proposed polynomial time algorithm is then applied over the well-known benchmark instances and the obtained spans are measured. The obtained results show that the proposed algorithm performs better that the existing assignment strategies with respect to deviation from optimality and computation time. The time taken by our algorithm is less than 1.77 seconds (HP Z400 Workstation) even for the most difficult benchmark instances and thus is very much suitable where fast channel assignment is of primary importance while a marginal deviation from optimality may be tolerated.