The generalized work function algorithm is competitive for the generalized 2-server problem

TL;DR

This paper proves that the generalized work function algorithm is effectively competitive for the generalized 2-server problem, an online optimization challenge involving two servers with different cost functions in separate metric spaces.

Contribution

It demonstrates the constant competitiveness of the generalized work function algorithm for the generalized 2-server problem, extending prior results to a more general setting.

Findings

The generalized work function algorithm is constant competitive.

The result applies to servers moving in different metric spaces.

It generalizes previous work on the CNN-problem.

Abstract

The generalized 2-server problem is an online optimization problem where a sequence of requests has to be served at minimal cost. Requests arrive one by one and need to be served instantly by at least one of two servers. We consider the general model where the cost function of the two servers may be different. Formally, each server moves in its own metric space and a request consists of one point in each metric space. It is served by moving one of the two servers to its request point. Requests have to be served without knowledge of the future requests. The objective is to minimize the total traveled distance. The special case where both servers move on the real line is known as the CNN-problem. We show that the generalized work function algorithm is constant competitive for the generalized 2-server problem.