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145
An Improved Approximation Algorithm for the Metric Uncapacitated Facility Location Problem
, 2002
"... We design new approximation algorithm for the metric uncapacitated facility location problem. This algorithm is of LP rounding type and is based on a rounding technique developed in [57]. ..."
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Cited by 40 (2 self)
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We design new approximation algorithm for the metric uncapacitated facility location problem. This algorithm is of LP rounding type and is based on a rounding technique developed in [57].
The pipelined set cover problem
, 2003
"... A classical problem in query optimization is to find the optimal ordering of a set of possibly correlated selections. We provide an abstraction of this problem as a generalization of set cover called pipelined set cover, where the sets are applied sequentially to the elements to be covered and the ..."
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Cited by 37 (7 self)
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A classical problem in query optimization is to find the optimal ordering of a set of possibly correlated selections. We provide an abstraction of this problem as a generalization of set cover called pipelined set cover, where the sets are applied sequentially to the elements to be covered and the elements covered at each stage are discarded. We show that several natural heuristics for this NPhard problem, such as the greedy setcover heuristic and a localsearch heuristic, can be analyzed using a linearprogramming framework. These heuristics lead to efficient algorithms for pipelined set cover that can be applied to order possibly correlated selections in conventional database systems as well as datastream processing systems. We use our linearprogramming framework to show that the greedy and localsearch algorithms are 4approximations for pipelined set cover. We extend our analysis to minimize the lpnorm of the costs paid by the sets, where p ≥ 2 is an integer, to examine the improvement in performance when the total cost has increasing contribution from initial sets in the pipeline. Finally, we consider the online version of pipelined set cover and present a competitive algorithm with a logarithmic performance guarantee. Our analysis framework may be applicable to other problems in query optimization where it is important to account for correlations.
Optimal Time Bounds for Approximate Clustering
, 2002
"... Clusteringisafundamentalprobleminunsupervised learning, andhasbeenstudiedwidelyboth asaproblemoflearningmixture modelsandasanoptimizationproblem. Inthispaper, we studyclusteringwithrespectthe kmedian objectivefunction, anaturalformulationofclusteringin whichweattempttominimize the average distance ..."
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Cited by 36 (2 self)
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Clusteringisafundamentalprobleminunsupervised learning, andhasbeenstudiedwidelyboth asaproblemoflearningmixture modelsandasanoptimizationproblem. Inthispaper, we studyclusteringwithrespectthe kmedian objectivefunction, anaturalformulationofclusteringin whichweattempttominimize the average distancetoclustercenters. Oneofthe maincontributionsofthispaperisasimplebutpowerful samplingtechniquethatwecall successivesampling thatcouldbeofindependentinterest. Weshowthatoursamplingprocedurecan rapidlyidentify asmallsetofpoints(ofsizejust O(k log n/k))thatsummarizetheinputpoints forthepurposeofclustering. Usingsuccessive sampling, we develop analgorithmforthe kmedianproblemthatrunsin O(nk) timeforawiderangeof valuesof k andisguaranteed, with high probability, to return a solution with cost at most a constant factor times optimal. We also establish a lower bound of \Omega ( nk) onanyrandomizedconstantfactorapproximation algorithm for the kmedian problem that succeeds with even a negligible (say
A MultiExchange Local Search Algorithm for the Capacitated Facility Location Problem
 Mathematics of Operations Research
, 2004
"... We present a multiexchange local search algorithm for approximating the capacitated facility location problem (CFLP), where a new local improvement operation is introduced that possibly exchanges multiple facilities simultaneously. We give a tight analysis for our algorithm and show that the per ..."
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Cited by 35 (0 self)
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We present a multiexchange local search algorithm for approximating the capacitated facility location problem (CFLP), where a new local improvement operation is introduced that possibly exchanges multiple facilities simultaneously. We give a tight analysis for our algorithm and show that the performance guarantee of the algorithm is between 3+ 2 # 2 # and 3+ 2 # 2+ # for any given constant # > 0. Previously known best approximation ratio for the CFLP is 7.88, due to Mahdian and Pal (2003), based on the operations proposed by Pal, Tardos and Wexler (2001).
Approximating kmedian via pseudoapproximation
 In Proceedings of the Fortyfifth Annual ACM Symposium on Theory of Computing, STOC ’13
, 2013
"... We present a novel approximation algorithm for kmedian that achieves an approximation guarantee of 1 + 3 + , improving upon the decadeold ratio of 3 + . Our approach is based on two components, each of which, we believe, is of independent interest. First, we show that in order to give an αapproxi ..."
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Cited by 31 (2 self)
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We present a novel approximation algorithm for kmedian that achieves an approximation guarantee of 1 + 3 + , improving upon the decadeold ratio of 3 + . Our approach is based on two components, each of which, we believe, is of independent interest. First, we show that in order to give an αapproximation algorithm for kmedian, it is sufficient to give a pseudoapproximation algorithm that finds an αapproximate solution by opening k + O(1) facilities. This is a rather surprising result as there exist instances for which opening k + 1 facilities may lead to a significant smaller cost than if only k facilities were opened. Second, we give such a pseudoapproximation algorithm with α = 1 + 3 + . Prior to our work, it was not even known whether opening k + o(k) facilities would help improve the approximation ratio. 1
The Facility Location Problem with General Cost Functions
 Networks
, 2002
"... In this paper we introduce a generalized version of the facility location problem in which the facility cost is a function of the number of clients assigned to the facility. We focus on the case of concave facility cost functions. We observe that this problem can be reduced to the uncapacitated faci ..."
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Cited by 31 (4 self)
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In this paper we introduce a generalized version of the facility location problem in which the facility cost is a function of the number of clients assigned to the facility. We focus on the case of concave facility cost functions. We observe that this problem can be reduced to the uncapacitated facility location problem. We analyze a natural greedy algorithm for this problem and show that its approximation factor is at most 1.861. We also consider several generalizations and variants of this problem.
On Optimal Service Selection
, 2005
"... While many works have been devoted to service matchmaking and modeling nonfunctional properties, the problem of matching service requests to o#ers in an optimal way has not yet been extensively studied. In this paper we formalize three kinds of optimal service selection problems, based on di#erent c ..."
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Cited by 29 (0 self)
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While many works have been devoted to service matchmaking and modeling nonfunctional properties, the problem of matching service requests to o#ers in an optimal way has not yet been extensively studied. In this paper we formalize three kinds of optimal service selection problems, based on di#erent criteria. Then we study their complexity and implement solutions. We prove that onetime costs make the optimal selection problem computationally hard; in the absence of these costs the problem can be solved in polynomial time. We designed and implemented both exact and heuristic (suboptimal) algorithms for the hard case, and carried out a preliminary experimental evaluation with interesting results.
Faulttolerant facility location
 in Proceedings of the 14th Annual ACMSIAM Symposium on Discrete Algorithms
, 2003
"... We study a faulttolerant generalization of the classical uncapacitated facility location problem. We want to open a subset of facilities from a given set F and assign each client j in a given set D to rj ≥ 1 distinct open facilities so as to minimize the sum of the facility opening costs and the cl ..."
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Cited by 29 (4 self)
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We study a faulttolerant generalization of the classical uncapacitated facility location problem. We want to open a subset of facilities from a given set F and assign each client j in a given set D to rj ≥ 1 distinct open facilities so as to minimize the sum of the facility opening costs and the client assignment costs. We also consider the faulttolerant kmedian problem where instead of facility costs we are given a number k of facilities that may be opened, and the objective is to minimize only the assignment cost. Multiple facilities provide a safeguard against failures. If the facility closest to a client ‘fails’, the other facilities assigned to it could be used to serve it, e.g., in designing a network involving the placement of caches or routers, one would like to connect a client to multiple caches or routers so as to be resistant under node or link failures. We consider the case where the distances, cij, formametric.
Further improvements in competitive guarantees for QoS buffering
 In Proc. 31st International Colloquium on Automata, Languages, and Programming (ICALP
, 2004
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Designing overlay multicast networks for streaming
 In Proceedings of ACM Symposium on Parallel Algorithms and Architectures
, 2003
"... In this paper we present a polynomial time approximation algorithm for designing a multicast overlay network. The algorithm finds a solution that satisfies capacity and reliability constraints to within a constant factor of optimal, and cost to within a logarithmic factor. The class of networks that ..."
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Cited by 25 (6 self)
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In this paper we present a polynomial time approximation algorithm for designing a multicast overlay network. The algorithm finds a solution that satisfies capacity and reliability constraints to within a constant factor of optimal, and cost to within a logarithmic factor. The class of networks that our algorithm applies to includes the one used by Akamai Technologies to deliver live media streams over the Internet. In particular, we analyze networks consisting of three stages of nodes. The nodes in the first stage are the sources where live streams originate. A source forwards each of its streams to one or more nodes in the second stage, which are called reflectors. A reflector can split an incoming stream into multiple identical outgoing streams, which are then sent on to nodes in the third and final stage, which are called the sinks. As the packets in a stream travel from one stage to the next, some of them may be lost. The job of a sink is to combine the packets from multiple instances of the same stream (by reordering packets and discarding duplicates) to form a single instance of the stream with minimal loss. We assume that the loss rate between any pair of nodes in the network is known, and that losses between different pairs are independent, but discuss extensions in which some losses may be correlated.