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Optimizing and approximating eigenvectors in max-algebra

Tam, Kin Po (2010)
Ph.D. thesis, University of Birmingham.

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Abstract

This thesis is a reflection of my research in max-algebra. The idea of max-algebra is replacing the conventional pairs of operations (+,x) by (max, +). It has been known for some time that max-algebraic linear systems and eigenvalue-eigenvector problem can be used to describe industrial processes in which a number of processors work interactively and possibly in stages. Solutions to such max-algebraic linear system typically correspond to start time vectors which guarantee that the processes meet given deadlines or will work in a steady regime. The aim of this thesis is to study such problems subjected to additional requirements or constraints. These include minimization and maximization of the time span of completion times or starting times. We will also consider the case of minimization and maximization of the time span when some completion times or starting times are prescribed. The problem of integrality is also studied in this thesis. This is finding completion times or starting times which consists of integer values only. Finally we consider max-algebraic permuted linear systems where we permute a given vector and decide if the permuted vector is a satisfactory completion time or starting time. For some of these problems, we developed exact and efficient methods. Some of them turn out to be hard. For these we have proposed and tested a number of heuristics.

Type of Work:Ph.D. thesis.
School/Faculty:Colleges (2008 onwards) > College of Engineering & Physical Sciences
Department:School of Mathematics
Subjects:QA Mathematics
Institution:University of Birmingham
ID Code:858
This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder.
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