1-Local 33/24-Competitive Algorithm for Multicoloring Hexagonal Graphs

1-Local 17/12-Competitive Algorithm for Multicoloring Hexagonal Graphs

In the frequency allocation problem we are given a cellular telephone network whose geographical coverage area is divided into cells where phone calls are serviced by frequencies assigned to them, so that none of the pairs of calls emanating from the same or neighboring cells is assigned the same frequency. The problem is to use the frequencies efficiently, i.e. minimize the span of used freque...

A 1-local 4/3-competitive algorithm for multicoloring a subclass of hexagonal graphs

In the frequency allocation problem we are given a cellular telephone network whose geographical coverage area is divided into cells where phone calls are serviced by frequencies assigned to them, so that none of the pairs of calls emanating from the same or neighboring cells is assigned the same frequency. The problem is to use the frequencies efficiently, i.e. minimize the span of used freque...

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

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. Th...

A Distributed 6/5-competitive Algorithm for Multicoloring Triangle-free Hexagonal Graphs

An important optimization problem in the design of cellular networks is to assign sets of frequencies to transmitters to avoid unacceptable interference. A cellular network is generally modeled as a subgraph of the infinite triangular lattice. The distributed frequency assignment problem can be abstracted as a multicoloring problem on a weighted hexagonal graph, where the weight vector represen...

2-local 4/3-competitive Algorithm for Multicoloring Hexagonal Graphs