TY - GEN

T1 - Budgeted red-blue median and its generalizations

AU - Hajiaghayi, Mohammad Taghi

AU - Khandekar, Rohit

AU - Kortsarz, Guy

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

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U2 - 10.1007/978-3-642-15775-2_27

DO - 10.1007/978-3-642-15775-2_27

M3 - Conference contribution

AN - SCOPUS:78249278457

SN - 3642157742

SN - 9783642157745

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 314

EP - 325

BT - Algorithms, ESA 2010 - 18th Annual European Symposium, Proceedings

T2 - 18th Annual European Symposium on Algorithms, ESA 2010

Y2 - 6 September 2010 through 8 September 2010

ER -