Budgeted red-blue median and its generalizations

Mohammad Taghi Hajiaghayi, Rohit Khandekar, Guy Kortsarz

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


In a Content Distribution Network application, we have a set of servers and a set of clients to be connected to the servers. Often there are a few server types and a hard budget constraint on the number of deployed servers of each type. The simplest goal here is to deploy a set of servers subject to these budget constraints in order to minimize the sum of client connection costs. These connection costs often satisfy metricity, since they are typically proportional to the distance between a client and a server within a single autonomous system. A special case of the problem where there is only one server type is the well-studied k-median problem. In this paper, we consider the problem with two server types and call it the budgeted red-blue median problem. We show, somewhat surprisingly, that running a single-swap local search for each server type simultaneously, yields a constant factor approximation for this case. Its analysis is however quite non-trivial compared to that of the k-median problem (Arya et al., 2004; Gupta and Tangwongsan, 2008). Later we show that the same algorithm yields a constant approximation for the prize-collecting version of the budgeted red-blue median problem where each client can potentially be served with an alternative cost via a different vendor. In the process, we also improve the approximation factor for the prize-collecting k -median problem from 4 (Charikar et al., 2001) to 3 + ε, which matches the current best approximation factor for the k-median problem.

Original languageEnglish
Title of host publicationAlgorithms, ESA 2010 - 18th Annual European Symposium, Proceedings
Number of pages12
EditionPART 1
StatePublished - 2010
Externally publishedYes
Event18th Annual European Symposium on Algorithms, ESA 2010 - Liverpool, United Kingdom
Duration: 6 Sep 20108 Sep 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume6346 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference18th Annual European Symposium on Algorithms, ESA 2010
Country/TerritoryUnited Kingdom


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