A 1-Local Asymptotic 13/9-Competitive Algorithm for Multicoloring Hexagonal Graphs

Abstract

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.

Finding influential agent groups in complex multiagent software systems based on citation network analyses

“…In reality, graph theory tools are always used to analyze the topological characteristics of network structures [24]. Citation relations are initially seen in published papers, which denote that some papers cite the results of other papers; therefore, citation ranking is always used to determine the importance of a journal or a scientist [25].…”

Deterministic Online Call Control in Cellular Networks and Triangle-Free Cellular Networks

“…If the duration of each call is infinity and the assigned frequency cannot be changed, the hybrid algorithm gave the best result for online frequency assignment, i.e., a 2-competitive algorithm for the absolute performance and a 1.9126-competitive algorithm for the asymptotic performance. When the background network is triangle-free, a 2-local 5/4-competitive algorithm was given in [9], an inductive proof for the 7/6 ratio was reported in [4], where k-local means when assigning a frequency, the base station only knows the information of its neighboring cells within distance k. In [11], a 1-local 4/3-competitive algorithm was given.…”

“…For example, in linear network, an optimal online algorithm with competitive ratio 3/2 can be achieved [10]. An interesting induced network, triangle-free cellular network, has been studied for many problems including frequency assignment problem [4,9,11].…”

A GNN-Based Variable Partition Framework for DCOPs

“…It has a wide range of applications, such as meeting scheduling, resource allocation, smart homes, sensor networks [1], and many IoT problems [2,3], which has attracted the attention of many researchers. The distributed constraint optimization problems (DCOPs) [4,5] is a distributed implementation for COP, which is a general model to govern the agent's autonomous behavior in a cooperative multi-agent system (MAS). COPs and DCOPs can be often represented graphically using one of the following representations: constraint graphs, factor graphs, or pseudo-trees [6].…”