Tomislav Rudec

A fast work function algorithm for solving the k-server problem

This paper deals with the work function algorithm (WFA) for solving the on-line k-server problem. The paper addresses some practical aspects of the WFA, such as its efficient implementation and its true quality of serving. First, an implementation of the WFA is proposed, which is based on network flows, and which reduces each step of the WFA to only one minimal-cost maximal flow problem instance. Next, it is explained how the proposed implementation can further be simplified if the involved metric space is finite. Also, it is described how actual computing of optimal flows can be speeded up by taking into account special properties of the involved networks. Some experiments based on the proposed implementation and improvements are presented, where actual serving costs of the WFA have been measured on very large problem instances and compared with costs of other algorithms. Finally, suitability of the WFA for solving real-life problems is discussed.

A new approach to solve the k-server problem based on network flows and flow cost reduction

This paper is concerned with two algorithms for solving the k-server problem: the optimal off-line algorithm (OPT) and the on-line work function algorithm (WFA). Both algorithms are usually implemented by network flow techniques including the flow augmentation method. In the paper a new implementation approach is proposed, which is again based on network flows, but uses simpler networks and the cost reduction method. The paper describes in detail the corresponding new implementations of OPT and WFA, respectively. All necessary correctness proofs are given. Also, experiments are presented, which confirm that the new approach assures faster execution of both algorithms.

On the competitiveness of a modified work function algorithm for solving the on-line k-server problem

We study a modification of the well known work function algorithm (WFA) for solving the on-line k-server problem. Our modified WFA is based on a moving window, i.e. on the approximate work function that takes into account only a fixed number of most recent on-line requests. In this paper we prove that, in contrast to the original WFA, the modified WFA is not competitive. Our proof is based on a suitably constructed problem instance showing that the performance of the modified WFA can be an arbitrary number of times worse than optimal.

A fast approximate implementation of the work function algorithm for solving the k-server problem

In this paper we propose an approximate implementation of the work function algorithm (WFA) for solving the

Measuring true performance of the work function algorithm for solving the on-line k-server problem

k

Measuring True Performance of the Work Function Algorithm for Solving the On-line k-Server Problem

k-server problem. Our implementation is based on network flow techniques, a novel network model, and flow cost reduction. Also, it is provided with a parameter that enables tradeoff between accuracy and speed. In the paper we present experiments, showing that the new implementation can mimic perfectly the original WFA and still run at least an order of magnitude faster than any known exact implementation.