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19,272
A Threshold of ln n for Approximating Set Cover
 JOURNAL OF THE ACM
, 1998
"... Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NPhar ..."
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Cited by 776 (5 self)
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Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NP
Algorithms for the Set Covering Problem
 Annals of Operations Research
, 1998
"... The Set Covering Problem (SCP) is a main model for several important applications, including crew scheduling in railway and masstransit companies. ..."
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Cited by 91 (4 self)
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The Set Covering Problem (SCP) is a main model for several important applications, including crew scheduling in railway and masstransit companies.
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
The Online Set Cover Problem
 STOC'03
, 2003
"... Let X = {1, 2,...,n} be a ground set of n elements, and let S be a family of subsets of X, S  = m, with a positive cost cS associated with each S ∈S. Consider the following online version of the set cover problem, described as a game between an algorithm and an adversary. An adversary gives eleme ..."
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Cited by 64 (7 self)
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Let X = {1, 2,...,n} be a ground set of n elements, and let S be a family of subsets of X, S  = m, with a positive cost cS associated with each S ∈S. Consider the following online version of the set cover problem, described as a game between an algorithm and an adversary. An adversary gives
The Set Covering Machine
, 2002
"... We extend the classical algorithms of Valiant and Haussler for learning compact conjunctions and disjunctions of Boolean attributes to allow features that are constructed from the data and to allow a tradeoff between accuracy and complexity. The result is a generalpurpose learning machine, suitabl ..."
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Cited by 36 (8 self)
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, suitable for practical learning tasks, that we call the set covering machine. We present a version of the set covering machine that uses datadependent balls for its set of features and compare its performance with the support vector machine. By extending a technique pioneered by Littlestone and Warmuth
Interactive Submodular Set Cover
, 2010
"... We introduce a natural generalization of submodular set cover and exact active learning with a finite hypothesis class (query learning). We call this new problem interactive submodular set cover. Applications include advertising in social networks with hidden information. We give an approximation gu ..."
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Cited by 17 (4 self)
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We introduce a natural generalization of submodular set cover and exact active learning with a finite hypothesis class (query learning). We call this new problem interactive submodular set cover. Applications include advertising in social networks with hidden information. We give an approximation
The Probabilistic Set Covering Problem
 OPERATIONS RESEARCH
, 2001
"... In a probabilistic set covering problem the right hand side is a random binary vector and the covering constraint has to be satisfied with some prescribed probability. We analyse the structure of the set of probabilistically efficient points of binary random vectors, develop methods for their enu ..."
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Cited by 13 (0 self)
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In a probabilistic set covering problem the right hand side is a random binary vector and the covering constraint has to be satisfied with some prescribed probability. We analyse the structure of the set of probabilistically efficient points of binary random vectors, develop methods
Learning with the Set Covering Machine
 Proc. 18th International Conf. on Machine Learning
, 2001
"... We generalize the classical algorithms of Valiant and Haussler for learning conjunctions and disjunctions of Boolean attributes to the problem of learning these functions over arbitrary sets of features; including features that are constructed from the data. The result is a generalpurposed le ..."
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Cited by 10 (4 self)
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purposed learning machine, suitable for practical learning tasks, that we call the Set Covering Machine. We present a version of the Set Covering Machine that uses generalized balls for its set of datadependent features and compare its performance to the famous Support Vector Machine. By extending a
Hardness of Approximating Set Cover
, 2011
"... This talk describes Feige’s result on the hardness of approximation of set cover. We will start by following (somewhat anachronistically) the footsteps of Lund and Yannakakis, showing an Ω(log n) hardness result. We will improve it, using Feige’s ideas, to (1 − ) log n. For technical reasons, the re ..."
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This talk describes Feige’s result on the hardness of approximation of set cover. We will start by following (somewhat anachronistically) the footsteps of Lund and Yannakakis, showing an Ω(log n) hardness result. We will improve it, using Feige’s ideas, to (1 − ) log n. For technical reasons
The set cover with pairs problem
 IN: PROC. 25TH ANNUAL CONFERENCE ON FOUNDATIONS OF SOFTWARE TECHNOLOGY AND THEORETICAL COMPUTER SCIENCE
, 2005
"... We consider a generalization of the set cover problem, in which elements are covered by pairs of objects, and we are required to find a minimum cost subset of objects that induces a collection of pairs covering all elements. Formally, let U be a ground set of elements and let S be a set of objects ..."
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Cited by 6 (1 self)
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We consider a generalization of the set cover problem, in which elements are covered by pairs of objects, and we are required to find a minimum cost subset of objects that induces a collection of pairs covering all elements. Formally, let U be a ground set of elements and let S be a set
Results 1  10
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19,272