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76
Improved Combinatorial Algorithms for the Facility Location and kMedian Problems
 In Proceedings of the 40th Annual IEEE Symposium on Foundations of Computer Science
, 1999
"... We present improved combinatorial approximation algorithms for the uncapacitated facility location and kmedian problems. Two central ideas in most of our results are cost scaling and greedy improvement. We present a simple greedy local search algorithm which achieves an approximation ratio of 2:414 ..."
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Cited by 204 (13 self)
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We present improved combinatorial approximation algorithms for the uncapacitated facility location and kmedian problems. Two central ideas in most of our results are cost scaling and greedy improvement. We present a simple greedy local search algorithm which achieves an approximation ratio of 2:414 + in ~ O(n 2 =) time. This also yields a bicriteria approximation tradeoff of (1 +; 1+ 2=) for facility cost versus service cost which is better than previously known tradeoffs and close to the best possible. Combining greedy improvement and cost scaling with a recent primal dual algorithm for facility location due to Jain and Vazirani, we get an approximation ratio of 1.853 in ~ O(n 3 ) time. This is already very close to the approximation guarantee of the best known algorithm which is LPbased. Further, combined with the best known LPbased algorithm for facility location, we get a very slight improvement in the approximation factor for facility location, achieving 1.728....
A new greedy approach for facility location problems
"... We present a simple and natural greedy algorithm for the metric uncapacitated facility location problem achieving an approximation guarantee of 1.61 whereas the best previously known was 1.73. Furthermore, we will show that our algorithm has a property which allows us to apply the technique of Lagra ..."
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Cited by 116 (9 self)
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We present a simple and natural greedy algorithm for the metric uncapacitated facility location problem achieving an approximation guarantee of 1.61 whereas the best previously known was 1.73. Furthermore, we will show that our algorithm has a property which allows us to apply the technique of Lagrangian relaxation. Using this property, we can nd better approximation algorithms for many variants of the facility location problem, such as the capacitated facility location problem with soft capacities and a common generalization of the kmedian and facility location problem. We will also prove a lower bound on the approximability of the kmedian problem.
Improved Approximation Algorithms for Metric Facility Location Problems
 In Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
, 2002
"... In this paper we present a 1.52approximation algorithm for the metric uncapacitated facility location problem, and a 2approximation algorithm for the metric capacitated facility location problem with soft capacities. Both these algorithms improve the best previously known approximation factor for ..."
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Cited by 111 (11 self)
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In this paper we present a 1.52approximation algorithm for the metric uncapacitated facility location problem, and a 2approximation algorithm for the metric capacitated facility location problem with soft capacities. Both these algorithms improve the best previously known approximation factor for the corresponding problem, and our softcapacitated facility location algorithm achieves the integrality gap of the standard LP relaxation of the problem. Furthermore, we will show, using a result of Thorup, that our algorithms can be implemented in quasilinear time.
Adwords and generalized online matching
 In FOCS ’05: Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
, 2005
"... How does a search engine company decide what ads to display with each query so as to maximize its revenue? This turns out to be a generalization of the online bipartite matching problem. We introduce the notion of a tradeoff revealing LP and use it to derive two optimal algorithms achieving competit ..."
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Cited by 98 (5 self)
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How does a search engine company decide what ads to display with each query so as to maximize its revenue? This turns out to be a generalization of the online bipartite matching problem. We introduce the notion of a tradeoff revealing LP and use it to derive two optimal algorithms achieving competitive ratios of 1 − 1/e for this problem. 1
Approximation Algorithms for Data Placement in Arbitrary Networks
 in Proceedings of the 12th Annual ACMSIAM Symposium on Discrete Algorithms
, 2001
"... Abstract We develop approximation algorithms for the problem of placing replicated data in arbitrary networks, where the nodes may both issue requests for data objects and have capacity for storing data objects, so as to minimize the average dataaccess cost. We introduce the data placement problem ..."
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Cited by 59 (2 self)
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Abstract We develop approximation algorithms for the problem of placing replicated data in arbitrary networks, where the nodes may both issue requests for data objects and have capacity for storing data objects, so as to minimize the average dataaccess cost. We introduce the data placement problem tomodel this problem. We have a set of caches F, a set of clients D, and a set of data objects O. Each cache i can store at most ui data objects. Each client j 2 D has demand dj for a specific data object o(j) 2 O and has to be assigned to a cache that stores that object. Storing an object o in cache i incurs astorage cost of f oi, and assigning client j to cache i incurs an access cost of djcij. The goal is to find aplacement of the data objects to caches respecting the capacity constraints, and an assignment of clients
The effectiveness of lloydtype methods for the kmeans problem
 In FOCS
, 2006
"... We investigate variants of Lloyd’s heuristic for clustering high dimensional data in an attempt to explain its popularity (a half century after its introduction) among practitioners, and in order to suggest improvements in its application. We propose and justify a clusterability criterion for data s ..."
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Cited by 51 (4 self)
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We investigate variants of Lloyd’s heuristic for clustering high dimensional data in an attempt to explain its popularity (a half century after its introduction) among practitioners, and in order to suggest improvements in its application. We propose and justify a clusterability criterion for data sets. We present variants of Lloyd’s heuristic that quickly lead to provably nearoptimal clustering solutions when applied to wellclusterable instances. This is the first performance guarantee for a variant of Lloyd’s heuristic. The provision of a guarantee on output quality does not come at the expense of speed: some of our algorithms are candidates for being faster in practice than currently used variants of Lloyd’s method. In addition, our other algorithms are faster on wellclusterable instances than recently proposed approximation algorithms, while maintaining similar guarantees on clustering quality. Our main algorithmic contribution is a novel probabilistic seeding process for the starting configuration of a Lloydtype iteration. 1
Strategyproof Costsharing Mechanisms for Set Cover and Facility Location Games
, 2003
"... this paper, we obtain strategyproof cost allocations for two fundamental games whose underlying optimization problems are NPhard, the set cover game and the facility location game. For the latter game, this is made possible by new approximation algorithms for the underlying optimization problem usi ..."
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Cited by 44 (0 self)
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this paper, we obtain strategyproof cost allocations for two fundamental games whose underlying optimization problems are NPhard, the set cover game and the facility location game. For the latter game, this is made possible by new approximation algorithms for the underlying optimization problem using the technique of dual fitting [7]. In retrospect, the natural greedy algorithm for the set cover problem (see [17]) can also analyzed using this technique  we utilize this viewpoint for handling the set cover game. The facility location game was studied in [9, 4], who left the open problem of obtaining a group strategyproof mechanism based on a constant factor approximation algorithm. Our paper partially answers this question. We give a strategyproof mechanism, but cannot achieve group strategyproofness. More recently, Pal and Tardos [15] have announced a 3approximately budget balanced crossmonotonic costsharing method for the facility location problem. This gives a group strategyproof mechanism for the facility location game that recovers 3 rd of the cost
Allocating online advertisement space with unreliable estimates
 In Proceedings of the 8th ACM Conference on Electronic Commerce (EC
, 2007
"... We study the problem of optimally allocating online advertisement space to budgetconstrained advertisers. This problem was defined and studied from the perspective of worstcase online competitive analysis by Mehta et al. Our objective is to find an algorithm that takes advantage of the given estim ..."
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Cited by 44 (6 self)
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We study the problem of optimally allocating online advertisement space to budgetconstrained advertisers. This problem was defined and studied from the perspective of worstcase online competitive analysis by Mehta et al. Our objective is to find an algorithm that takes advantage of the given estimates of the frequencies of keywords to compute a near optimal solution when the estimates are accurate, while at the same time maintaining a good worstcase competitive ratio in case the estimates are totally incorrect. This is motivated by realworld situations where search engines have stochastic information that provide reasonably accurate estimates of the frequency of search queries except in certain highly unpredictable yet economically valuable spikes in the search pattern. Our approach is a blackbox approach: we assume we have access to an oracle that uses the given estimates to recommend an advertiser every time a query arrives. We use this oracle to design an algorithm that provides two performance guarantees: the performance guarantee in the case that the oracle gives an accurate estimate, and its worstcase performance guarantee. Our algorithm can be fine tuned by adjusting a parameter α, giving a tradeoff curve between the two performance measures with the best competitive ratio for the worstcase scenario at one end of the curve and the optimal solution for the scenario where estimates are accurate at the other end. Finally, we demonstrate the applicability of our framework by applying it to two classical online problems, namely the lost cow and the ski rental problems.
Budget optimization in searchbased advertising auctions. AMEC07
, 2007
"... Internet search companies sell advertisement slots based on users ’ search queries via an auction. While there has been a lot of attention on the auction process and its gametheoretic aspects, our focus is on the advertisers. In particular, the advertisers have to solve a complex optimization probl ..."
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Cited by 33 (10 self)
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Internet search companies sell advertisement slots based on users ’ search queries via an auction. While there has been a lot of attention on the auction process and its gametheoretic aspects, our focus is on the advertisers. In particular, the advertisers have to solve a complex optimization problem of how to place bids on the keywords of their interest so that they can maximize their return (the number of user clicks on their ads) for a given budget. We model the entire process and study this budget optimization problem. While most variants are NP hard, we show, perhaps surprisingly, that simply randomizing between two uniform strategies that bid equally on all the keywords works well. More precisely, this strategy gets at least 1 − 1/e fraction of the maximum clicks possible. Such uniform strategies are likely to be practical. We also present inapproximability results, and optimal algorithms for variants of the budget optimization problem. 1
Facility location: distributed approximation
 In Proceedings of the twentyfourth annual ACM symposium on Principles of distributed computing
, 2005
"... In this paper, we initiate the study of the approximability of the facility location problem in a distributed setting. In particular, we explore a tradeoff between the amount of communication and the resulting approximation ratio. We give a distributed algorithm that, for every constant k, achieves ..."
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Cited by 27 (1 self)
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In this paper, we initiate the study of the approximability of the facility location problem in a distributed setting. In particular, we explore a tradeoff between the amount of communication and the resulting approximation ratio. We give a distributed algorithm that, for every constant k, achieves an O ( √ k(mρ) 1/ √ k log (m + n)) approximation in O(k) communication rounds where message size is bounded to O(log n) bits. The number of facilities and clients are m and n, respectively, and ρ is a coefficient that depends on the cost values of the instance. Our technique is based on a distributed primaldual approach for approximating a linear program, that does not form a covering or packing program.