The Generalized Work Function Algorithm Is Competitive for the Generalized 2-Server Problem

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...

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Vydané v:SIAM journal on computing Ročník 43; číslo 1; s. 96 - 125
Hlavný autor: Sitters, René
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Philadelphia Society for Industrial and Applied Mathematics 01.01.2014
Predmet:
Algorithms
Competition
Cost engineering
Metric space
On-line systems
Online
Optimization
Servers
Work functions
ISSN:0097-5397, 1095-7111
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Shrnutí: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 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, $\mathrm{WFA}_{\lambda}$, is constant competitive for the generalized 2-server problem. Further, we give an outline for a possible extension to $k\geqslant2$ servers and discuss the applicability of our techniques and of the work function algorithm in general. We conclude with a discussion on several open problems in online optimization. [PUBLICATION ABSTRACT]
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ISSN:0097-5397
1095-7111
DOI:10.1137/120885309