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107
Approximation algorithms for combinatorial auctions with complementfree bidders
 In Proceedings of the 37th Annual ACM Symposium on Theory of Computing (STOC
, 2005
"... We exhibit three approximation algorithms for the allocation problem in combinatorial auctions with complement free bidders. The running time of these algorithms is polynomial in the number of items m and in the number of bidders n, even though the “input size ” is exponential in m. The first algori ..."
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Cited by 94 (22 self)
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We exhibit three approximation algorithms for the allocation problem in combinatorial auctions with complement free bidders. The running time of these algorithms is polynomial in the number of items m and in the number of bidders n, even though the “input size ” is exponential in m. The first algorithm provides an O(log m) approximation. The second algorithm provides an O ( √ m) approximation in the weaker model of value oracles. This algorithm is also incentive compatible. The third algorithm provides an improved 2approximation for the more restricted case of “XOS bidders”, a class which strictly contains submodular bidders. We also prove lower bounds on the possible approximations achievable for these classes of bidders. These bounds are not tight and we leave the gaps as open problems. 1
Nearoptimal nonmyopic value of information in graphical models
 In Annual Conference on Uncertainty in Artificial Intelligence
"... A fundamental issue in realworld systems, such as sensor networks, is the selection of observations which most effectively reduce uncertainty. More specifically, we address the long standing problem of nonmyopically selecting the most informative subset of variables in a graphical model. We present ..."
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Cited by 88 (17 self)
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A fundamental issue in realworld systems, such as sensor networks, is the selection of observations which most effectively reduce uncertainty. More specifically, we address the long standing problem of nonmyopically selecting the most informative subset of variables in a graphical model. We present the first efficient randomized algorithm providing a constant factor (1 − 1/e − ε) approximation guarantee for any ε> 0 with high confidence. The algorithm leverages the theory of submodular functions, in combination with a polynomial bound on sample complexity. We furthermore prove that no polynomial time algorithm can provide a constant factor approximation better than (1 − 1/e) unless P = NP. Finally, we provide extensive evidence of the effectiveness of our method on two complex realworld datasets. 1
Algorithms for Facility Location Problems with Outliers (Extended Abstract)
 In Proceedings of the 12th Annual ACMSIAM Symposium on Discrete Algorithms
, 2000
"... ) Moses Charikar Samir Khuller y David M. Mount z Giri Narasimhan x Abstract Facility location problems are traditionally investigated with the assumption that all the clients are to be provided service. A significant shortcoming of this formulation is that a few very distant clients, called outlier ..."
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Cited by 68 (8 self)
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) Moses Charikar Samir Khuller y David M. Mount z Giri Narasimhan x Abstract Facility location problems are traditionally investigated with the assumption that all the clients are to be provided service. A significant shortcoming of this formulation is that a few very distant clients, called outliers, can exert a disproportionately strong influence over the final solution. In this paper we explore a generalization of various facility location problems (Kcenter, Kmedian, uncapacitated facility location etc) to the case when only a specified fraction of the customers are to be served. What makes the problems harder is that we have to also select the subset that should get service. We provide generalizations of various approximation algorithms to deal with this added constraint. 1 Introduction The facility location problem and the related clustering problems, kmedian and kcenter, are widely studied in operations research and computer science [3, 7, 22, 24, 32]. Typically in...
Combination Can Be Hard: Approximability of the Unique Coverage Problem
 In Proceedings of the 17th Annual ACMSIAM Symposium on Discrete Algorithms
, 2006
"... Abstract We prove semilogarithmic inapproximability for a maximization problem called unique coverage:given a collection of sets, find a subcollection that maximizes the number of elements covered exactly once. Specifically, assuming that NP 6 ` BPTIME(2n " ) for an arbitrary "> 0, we pro ..."
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Cited by 61 (3 self)
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Abstract We prove semilogarithmic inapproximability for a maximization problem called unique coverage:given a collection of sets, find a subcollection that maximizes the number of elements covered exactly once. Specifically, assuming that NP 6 ` BPTIME(2n " ) for an arbitrary "> 0, we prove O(1 / logoe n) inapproximability for some constant oe = oe("). We also prove O(1 / log1/3 " n) inapproximability, forany "> 0, assuming that refuting random instances of 3SAT is hard on average; and prove O(1 / log n)inapproximability under a plausible hypothesis concerning the hardness of another problem, balanced bipartite independent set. We establish an \Omega (1 / log n)approximation algorithm, even for a moregeneral (budgeted) setting, and obtain an \Omega (1 / log B)approximation algorithm when every set hasat most B elements. We also show that our inapproximability results extend to envyfree pricing, animportant problem in computational economics. We describe how the (budgeted) unique coverage problem, motivated by realworld applications, has close connections to other theoretical problemsincluding max cut, maximum coverage, and radio broadcasting. 1 Introduction In this paper we consider the approximability of the following natural maximization analog of set cover: Unique Coverage Problem. Given a universe U = {e1,..., en} of elements, and given a collection S = {S1,..., Sm} of subsets of U. Find a subcollection S0 ` S to maximize the number of elements that are uniquely covered, i.e., appear in exactly one set of S 0.
Inferring Networks of Diffusion and Influence
"... Information diffusion and virus propagation are fundamental processes talking place in networks. While it is often possible to directly observe when nodes become infected, observing individual transmissions (i.e., who infects whom or who influences whom) is typically very difficult. Furthermore, in ..."
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Cited by 59 (6 self)
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Information diffusion and virus propagation are fundamental processes talking place in networks. While it is often possible to directly observe when nodes become infected, observing individual transmissions (i.e., who infects whom or who influences whom) is typically very difficult. Furthermore, in many applications, the underlying network over which the diffusions and propagations spread is actually unobserved. We tackle these challenges by developing a method for tracing paths of diffusion and influence through networks and inferring the networks over which contagions propagate. Given the times when nodes adopt pieces of information or become infected, we identify the optimal network that best explains the observed infection times. Since the optimization problem is NPhard to solve exactly, we develop an efficient approximation algorithm that scales to large datasets and in practice gives provably nearoptimal performance. We demonstrate the effectiveness of our approach by tracing information cascades in a set of 170 million blogs and news articles over a one year period to infer how information flows through the online media space. We find that the diffusion network of news tends to have a coreperiphery structure with a small set of core media sites that diffuse information to the rest of the Web. These sites tend to have stable circles of influence with more general news media sites acting as connectors between them.
Learning diverse rankings with multiarmed bandits
 In Proceedings of the 25 th ICML
, 2008
"... Algorithms for learning to rank Web documents usually assume a document’s relevance is independent of other documents. This leads to learned ranking functions that produce rankings with redundant results. In contrast, user studies have shown that diversity at high ranks is often preferred. We presen ..."
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Cited by 56 (4 self)
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Algorithms for learning to rank Web documents usually assume a document’s relevance is independent of other documents. This leads to learned ranking functions that produce rankings with redundant results. In contrast, user studies have shown that diversity at high ranks is often preferred. We present two online learning algorithms that directly learn a diverse ranking of documents based on users ’ clicking behavior. We show that these algorithms minimize abandonment, or alternatively, maximize the probability that a relevant document is found in the top k positions of a ranking. Moreover, one of our algorithms asymptotically achieves optimal worstcase performance even if users’ interests change. 1.
Maximum coverage problem with group budget constraints and applications
 PROC. OF APPROX, SPRINGER LNCS, 72–83
, 2004
"... We study a variant of the maximum coverage problem which we label the maximum coverage problem with group budget constraints (MCG). We are given a collection of sets S = {S1, S2,..., Sm} where each set Si is a subset of a given ground set X. In the maximum coverage problem the goal is to pick k set ..."
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Cited by 44 (3 self)
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We study a variant of the maximum coverage problem which we label the maximum coverage problem with group budget constraints (MCG). We are given a collection of sets S = {S1, S2,..., Sm} where each set Si is a subset of a given ground set X. In the maximum coverage problem the goal is to pick k sets from S to maximize the cardinality of their union. In the MCG problem S is partitioned into groups G1, G2,..., Gℓ. The goal is to pick k sets from S to maximize the cardinality of their union but with the additional restriction that at most one set be picked from each group. We motivate the study of MCG by pointing out a variety of applications. We show that the greedy algorithm gives a 2approximation algorithm for this problem which is tight in the oracle model. We also obtain a constant factor approximation algorithm for the cost version of the problem. We then use MCG to obtain the first constant factor approximation algorithms for the following problems: (i) multiple depot ktraveling repairmen problem with covering constraints and (ii) orienteering problem with time windows when the number of time windows is a constant.
Locating network monitors: Complexity, heuristics and coverage
 in Proceedings of IEEE Infocom
, 2005
"... Abstract — There is increasing interest in concurrent passive monitoring of IP flows at multiple locations within an IP network. The common objective of such a distributed monitoring system is to sample packets belonging to a large fraction of IP flows in a costeffective manner by carefully placing ..."
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Cited by 41 (0 self)
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Abstract — There is increasing interest in concurrent passive monitoring of IP flows at multiple locations within an IP network. The common objective of such a distributed monitoring system is to sample packets belonging to a large fraction of IP flows in a costeffective manner by carefully placing monitors and controlling their sampling rates. In this paper, we consider the problem of where to place monitors within the network and how to control their sampling. To address the tradeoff between monitoring cost and monitoring coverage, we consider minimum cost and maximum coverage problems under various budget constraints. We show that all of the defined problems are NPhard. We propose greedy heuristics, and show that the heuristics provide solutions quite close to the optimal solutions through experiments using synthetic and real network topologies. In addition, our experiments show that a small number of monitors is often enough to monitor most of the traffic in an entire IP network. I.
Approximation Algorithms for Maximum Coverage and Max Cut with Given Sizes of Parts
 Lecture Notes in Computer Science (Proceedings of IPCO'99) 1610
, 1999
"... . In this paper we demonstrate a general method of designing constantfactor approximation algorithms for some discrete optimization problems with cardinality constraints. The core of the method is a simple deterministic ("pipage") procedure of rounding of linear relaxations. By using the method ..."
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Cited by 38 (9 self)
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. In this paper we demonstrate a general method of designing constantfactor approximation algorithms for some discrete optimization problems with cardinality constraints. The core of the method is a simple deterministic ("pipage") procedure of rounding of linear relaxations. By using the method we design a (1 \Gamma (1 \Gamma 1=k) k )approximation algorithm for the maximum coverage problem where k is the maximum size of the subsets that are covered, and a 1=2approximation algorithm for the maximum cut problem with given sizes of parts in the vertex set bipartition. The performance guarantee of the former improves on that of the wellknown (1 \Gamma e \Gamma1 )greedy algorithm due to Cornuejols, Fisher and Nemhauser in each case of bounded k. The latter is, to the best of our knowledge, the first constantfactor algorithm for that version of the maximum cut problem. 1 Introduction It is a fact of the present day that rounding of linear relaxations is one of the mos...
Predicting Diverse Subsets Using Structural SVMs
"... In many retrieval tasks, one important goal involves retrieving a diverse set of results (e.g., documents covering a wide range of topics for a search query). First of all, this reduces redundancy, effectively showing more information with the presented results. Secondly, queries are often ambiguous ..."
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Cited by 36 (7 self)
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In many retrieval tasks, one important goal involves retrieving a diverse set of results (e.g., documents covering a wide range of topics for a search query). First of all, this reduces redundancy, effectively showing more information with the presented results. Secondly, queries are often ambiguous at some level. For example, the query “Jaguar ” can refer to many different topics (such as the car or feline). A set of documents with high topic diversity ensures that fewer users abandon the query because no results are relevant to them. Unlike existing approaches to learning retrieval functions, we present a method that explicitly trains to diversify results. In particular, we formulate the learning problem of predicting diverse subsets and derive a training method based on structural SVMs. 1.