Competitive algorithms for on-line problems and their application to mobile agents

Abstract

Most traditional optimization theories deal with finding an optimal solution to a problem with initial conditions that are known and fixed. If the initial conditions change, most solutions found using these algorithms will not remain optimal. Researchers investigating competitive algorithms for on-line problems are exploring strategies for producing solutions that are proportional to the optimal solution (within a certain range), even in the worst cases. In contrast to the conventional (model-based) on-line approaches and the existing off-line strategies for optimization, we propose several new on-line competitive algorithms. These algorithms apply competitive analysis to on-line performance evaluation. In these proposed algorithms, we focus on several on-line problems, which include: (1) the on-line k-truck problem, (2) the on-line k-sever problem with twin-request, and (3) the on-line number of snacks problem. For each of these problems, several research steps are involved: (1) to establish and describe a model of the problem; (2) to construct a relevant on-line algorithm to solve the problem; (3) to derive a competitive ratio, which is an important measure of an on-line algorithm; (4) to provide a report on performance analysis and preliminary results; (5) to describe future work on the application of the proposed algorithm to task scheduling for systems based on mobile agents. With rapid growth in the use of on-line systems, on-line algorithms are playing an increasingly important role in decision-making for higher performance. A general on-line problem requires an optimized solution to either maximize the benefit or minimize the cost based on the existing information associated with the system. There are three key issues to consider: (1) the identification/specification of an on-line problem, (2) the decision strategy of an on-line algorithm, and (3) the performance measurement used for optimization. In this thesis, three new kinds of on-line problems are proposed, and several competitive algorithms (with good competitive ratios) are provided to solve these problems. Application of these algorithms to systems with mobile agents is also discussed. Based on the existing results concerning on-line problems and competitive algorithms, we first propose the on-line k-truck problem, which is an extension of the famous k-server problem. With the help of the Position Maintaining Strategy (PMS), we give different competitive algorithms according to the different cases of the k-truck problem. Next, we extend the k-server problem. Traditionally, the k-server problem assumes that at any given time there is only one request occurring, and no new request can occur until the previous request has been satisfied. Based on this observation, we propose the concept of a k-sever problem with multi-request. Specifically, we focus on the k-server problem with twin-request and employ the work function algorithm to obtain some minor results. We also give a lower bound for the k-server problem with twin-request, but it needs further improvement. Next, the on-line number of snacks problem is proposed, which is a realistic noshery management problem. We discuss four versions of this problem, and also provide relevant competitive algorithms. This is followed by analysis and evaluation of the algorithms for the on-line number of snacks problem. Next, we employ the theory of on-line problems and competitive algorithms to handle the dynamic allocation of mobile agents in an on-line task-scheduling problem. A new approach is presented to solve this problem for high performance in Internet computing. Of course, there are many unsolved problems concerning on-line problems and competitive algorithms. How to combine the existing theories with more realistic problems is still a challenging question. Finally, we discuss future work and further research directions. Keywords: on-line problem, competitive algorithm, k-server problem, k-truck problem, on-line number of snacks problem, on-line k-server problem with twin-request, dynamic allocation of mobile agents.