In the frequency allocation problem, we are given a mobile telephone network, whose geographical coverage area is divided into cells, wherein phone calls are serviced by assigning frequencies to them so that no two calls emanating from the same or neighboring cells are assigned the same frequency. The problem is to use the frequencies efficiently, i.e., minimize the span of frequencies used. The frequency allocation problem can be regarded as a multicoloring problem on a weighted hexagonal graph. In this paper, we give a 1-local asymptotic 4/3-competitive distributed algorithm for multicoloring a triangle-free hexagonal graph, which is a special case of hexagonal graph. Based on this result, we then propose a 1-local asymptotic 13/9-competitive algorithm for multicoloring the (general-case) hexagonal graph, thereby improving the previous 1-local 3/2-competitive algorithm.

Orthogonal Variable Spreading Factor (OVSF) code assignment is a fundamental problem in Wideband Code-Division Multiple-Access (W-CDMA) systems, which plays an important role in third generation mobile communications. In the OVSF problem, codes must be assigned to incoming call requests with different data rate requirements, in such a way that they are mutually orthogonal with respect to an OVSF code tree. An OVSF code tree is a complete binary tree in which each node represents a code associated with the combined bandwidths of its two children. To be mutually orthogonal, each leaf-to-root path must contain at most one assigned code. In this paper, we focus on the online version of the OVSF code assignment problem and give a 10-competitive algorithm (where the cost is measured by the total number of assignments and reassignments used). Our algorithm improves the previous O(h)competitive result, where h is the height of the code tree, and also another recent constant-competitive result, where the competitive ratio is only constant under amortized analysis and the constant is not determined. We also improve the lower bound of