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The 2005 pascal visual object classes challenge
, 2006
"... Abstract. The PASCAL Visual Object Classes Challenge ran from February to March 2005. The goal of the challenge was to recognize objects from a number of visual object classes in realistic scenes (i.e. not presegmented objects). Four object classes were selected: motorbikes, bicycles, cars and peop ..."
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Cited by 369 (18 self)
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Abstract. The PASCAL Visual Object Classes Challenge ran from February to March 2005. The goal of the challenge was to recognize objects from a number of visual object classes in realistic scenes (i.e. not presegmented objects). Four object classes were selected: motorbikes, bicycles, cars and people. Twelve teams entered the challenge. In this chapter we provide details of the datasets, algorithms used by the teams, evaluation criteria, and results achieved. 1
Primaldual approximation algorithms for metric facility location and kmedian problems
 Journal of the ACM
, 1999
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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 209 (14 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....
Greedy Facility Location Algorithms analyzed using Dual Fitting with FactorRevealing LP
 Journal of the ACM
, 2001
"... We present a natural greedy algorithm for the metric uncapacitated facility location problem and use the method of dual fitting to analyze its approximation ratio, which turns out to be 1.861. The running time of our algorithm is O(m log m), where m is the total number of edges in the underlying c ..."
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Cited by 100 (13 self)
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We present a natural greedy algorithm for the metric uncapacitated facility location problem and use the method of dual fitting to analyze its approximation ratio, which turns out to be 1.861. The running time of our algorithm is O(m log m), where m is the total number of edges in the underlying complete bipartite graph between cities and facilities. We use our algorithm to improve recent results for some variants of the problem, such as the fault tolerant and outlier versions. In addition, we introduce a new variant which can be seen as a special case of the concave cost version of this problem.
Boosted sampling: Approximation algorithms for stochastic optimization problems
 IN: 36TH STOC
, 2004
"... Several combinatorial optimization problems choose elements to minimize the total cost of constructing a feasible solution that satisfies requirements of clients. In the STEINER TREE problem, for example, edges must be chosen to connect terminals (clients); in VERTEX COVER, vertices must be chosen t ..."
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Cited by 90 (22 self)
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Several combinatorial optimization problems choose elements to minimize the total cost of constructing a feasible solution that satisfies requirements of clients. In the STEINER TREE problem, for example, edges must be chosen to connect terminals (clients); in VERTEX COVER, vertices must be chosen to cover edges (clients); in FACILITY LOCATION, facilities must be chosen and demand vertices (clients) connected to these chosen facilities. We consider a stochastic version of such a problem where the solution is constructed in two stages: Before the actual requirements materialize, we can choose elements in a first stage. The actual requirements are then revealed, drawn from a prespecified probability distribution π; thereupon, some more elements may be chosen to obtain a feasible solution for the actual requirements. However, in this second (recourse) stage, choosing an element is costlier by a factor of σ> 1. The goal is to minimize the first stage cost plus the expected second stage cost. We give a general yet simple technique to adapt approximation algorithms for several deterministic problems to their stochastic versions via the following method. • First stage: Draw σ independent sets of clients from the distribution π and apply the approximation algorithm to construct a feasible solution for the union of these sets. • Second stage: Since the actual requirements have now been revealed, augment the firststage solution to be feasible for these requirements.
Better Streaming Algorithms for Clustering Problems
 In Proc. of 35th ACM Symposium on Theory of Computing (STOC
, 2003
"... We study cluster ng pr blems in the str aming model, wher e the goal is to cluster a set of points by making one pass (or a few passes) over the data using a small amount of storSD space.Our mainr esult is a r ndomized algor ithm for kMedian prE lem which p duces a constant factor a ..."
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Cited by 70 (1 self)
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We study cluster ng pr blems in the str aming model, wher e the goal is to cluster a set of points by making one pass (or a few passes) over the data using a small amount of storSD space.Our mainr esult is a r ndomized algor ithm for kMedian prE lem which p duces a constant factor appr oximation in one pass using storR4 space O(kpolylog n). This is a significant imp r vement of the prS ious best algor5 hm which yielded a 2 appr ximation using O(n )space.
Online Facility Location
"... We consider the online variant of facility location, in which demand points arrive one at a time and we must maintain a set of facilities to service these points. We provide a randomized online O(1)competitive algorithm in the case where points arrive in random order. If points are ordered adversar ..."
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Cited by 53 (4 self)
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We consider the online variant of facility location, in which demand points arrive one at a time and we must maintain a set of facilities to service these points. We provide a randomized online O(1)competitive algorithm in the case where points arrive in random order. If points are ordered adversarially, we show that no algorithm can be constantcompetitive, and provide an O(log n)competitive algorithm. Our algorithms are randomized and the analysis depends heavily on the concept of expected waiting time. We also combine our techniques with those of Charikar and Guha to provide a lineartime constant approximation for the offline facility location problem.
Selfish Caching in Distributed Systems: A GameTheoretic Analysis
 in Proc. ACM Symposium on Principles of Distributed Computing (ACM PODC
, 2004
"... We analyze replication of resources by server nodes that act selfishly, using a gametheoretic approach. We refer to this as the selfish caching problem. In our model, nodes incur either cost for replicating resources or cost for access to a remote replica. We show the existence of pure strategy Nas ..."
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Cited by 47 (2 self)
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We analyze replication of resources by server nodes that act selfishly, using a gametheoretic approach. We refer to this as the selfish caching problem. In our model, nodes incur either cost for replicating resources or cost for access to a remote replica. We show the existence of pure strategy Nash equilibria and investigate the price of anarchy, which is the relative cost of the lack of coordination. The price of anarchy can be high due to undersupply problems, but with certain network topologies it has better bounds. With a payment scheme the game can always implement the social optimum in the best case by giving servers incentive to replicate.
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 32 (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
What about Wednesday? approximation algorithms for multistage stochastic optimization
 in APPROX
, 2005
"... Abstract. The field of stochastic optimization studies decision making under uncertainty, when only probabilistic information about the future is available. Finding approximate solutions to wellstudied optimization problems (such as Steiner tree, Vertex Cover, and Facility Location, to name but a f ..."
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Cited by 32 (8 self)
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Abstract. The field of stochastic optimization studies decision making under uncertainty, when only probabilistic information about the future is available. Finding approximate solutions to wellstudied optimization problems (such as Steiner tree, Vertex Cover, and Facility Location, to name but a few) presents new challenges when investigated in this framework, which has promoted much research in approximation algorithms. There has been much interest in optimization problems in the setting of twostage stochastic optimization with recourse, which can be paraphrased as follows: On the first day (Monday), we know a probability distribution π from which client demands will be drawn on Tuesday, and are allowed to make preliminary investments (e.g., installing links, opening facilities) towards meeting this future demand. On Tuesday, the actual requirements are revealed (drawn from the same distribution π) and we must purchase enough additional equipment to satisfy these demands; however, these purchases are now made at an inflated cost. In a recent paper [8], we proposed the Boosted Sampling framework which converted an approximation algorithm A for an optimization problem Π into one for the stochastic version of Π (provided A satisfied certain technical conditions). In this paper, we give two generalizations of this Boosted Sampling framework: Firstly, we show that a natural extension of the framework works in a general kstage setting, where information about the future is gradually revealed in several stages and we are allowed to take (increasingly expensive) corrective actions in each stage. We use these to give approximation