NDLI: The Online Median Problem

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The Online Median Problem

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Plaxton, C. Greg Mettu, Ramgopal R.
Copyright Year	2003
Abstract	We introduce a natural variant of the (metric uncapacitated) k-median problem that we call the online median problem. Whereas the k-median problem involves optimizing the simultaneous placement of k facilities, the online median problem imposes the following additional constraints: the facilities are placed one at a time, a facility cannot be moved once it is placed, and the total number of facilities to be placed, k, is not known in advance. The objective of an online median algorithm is to minimize the competitive ratio, that is, the worst-case ratio of the cost of an online placement to that of an optimal offline placement. Our main result is a constant-competitive algorithm for the online median problem running in time that is linear in the input size. In addition, we present a related, though substantially simpler, constant-factor approximation algorithm for the (metric uncapacitated) facility location problem that runs in time linear in the input size. The latter algorithm is similar in spirit to the recent primal-dual-based facility location algorithm of Jain and Vazirani, but our approach is more elementary and yields an improved running time. While our primary focus is on problems which ask us to minimize the weighted average service distance to facilities, we also show that our results can be generalized to hold, to within constant factors, for more general objective functions. For example, we show that all of our approximation results hold, to within constant factors, for the k-means objective function.
Starting Page	816
Ending Page	832
Page Count	17
File Format	PDF
ISSN	00975397
DOI	10.1137/S0097539701383443
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	3
Volume Number	32
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2003-01-01
Access Restriction	Subscribed
Subject Keyword	discrete location theory Computational difficulty of problems Analysis of algorithms and problem complexity k-median k-means Approximation algorithms clustering approximation algorithms Analysis of algorithms facility location
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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