Graph applications on frequency assignment problems and map colouring

Pao Yue-kong Library Electronic Theses Database

Graph applications on frequency assignment problems and map colouring

 

Author: Lau, Chai-fat
Title: Graph applications on frequency assignment problems and map colouring
Degree: M.Sc.
Year: 2000
Subject: Mobile communication systems
Hong Kong Polytechnic University -- Dissertations
Department: Multi-disciplinary Studies
Dept. of Applied Mathematics
Pages: vi, 224 leaves : ill., col. maps ; 30 cm
Language: English
InnoPac Record: http://library.polyu.edu.hk/record=b1523571
URI: http://theses.lib.polyu.edu.hk/handle/200/2665
Abstract: Frequency Assignment Problems (FAP), or called Channel Assignment Problems (CAP) is a kind of assignment problems. The problems are tackled by setting a constraint model, which represents the minimum channel-separations between network stations in matrix form. Then it is to find a feasible channel assignment as a solution subject to the given constraints. Two traditional Heuristic End-Packing, Heuristic Ordering-Packing and a new developed Heuristic Graph-Approach methods have been studied through written programs. The most important discovery in this project is the theoretical background for the five assignment techniques of which the Graph-Approach technique is to solve a feasible solution set rather than using a traditional low-efficiency trial-and-error method in Ordering-Packing, End-Packing or Test-and-Assign methods. The traditional methods can be represented in Graph-Approach method and they are just some particular types derived from the method. Optimization for channel assignments has also been studied such as on the search for the possible minimum number of channels, and the selection of the best assignment through the performance analysis of the found feasible solutions for the channel assignment in a network system. Moreover, we can have optimization on the network system itself by the consideration of the effect of the channel separation constraints. Both Simplex Channel Assignments and Fixed Channel Assignments in a Complex Duplex Network System, taking account of the existing assigned channels in some network stations, have been studied. Since the Fixed Channel Assignment has similar requirements as the Dynamic Channel Assignment, and the Heuristic Graph-Approach method has been found to be very suitable for this type of assignment, it is believed that the Heuristic Graph-Approach method can be applied to Dynamic Channel Assignment efficiently. Finally, the assignment techniques subject to the given constraints are modelled for the finding of colouring of maps for South America and Africa continents that the minimum number of four colours can be used according to the Four-colour Theorem.

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