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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 778 (5 self)
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hard. We prove that (1 \Gamma o(1)) ln n is a threshold below which set cover cannot be approximated efficiently, unless NP has slightly superpolynomial time algorithms. This closes the gap (up to low order terms) between the ratio of approximation achievable by the greedy algorithm (which is (1 \Gamma
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
Approximate Set Covering in Uniform Hypergraphs
"... The weighted set covering problem, restricted to the class of runiform hypergraphs, is considered. We propose a new approach, based on a recent result of Aharoni, Holzman and Krivelevich about the ratio of integer and fractional covering numbers in kcolorable runiform hypergraphs. This approach, ..."
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Cited by 8 (2 self)
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The weighted set covering problem, restricted to the class of runiform hypergraphs, is considered. We propose a new approach, based on a recent result of Aharoni, Holzman and Krivelevich about the ratio of integer and fractional covering numbers in kcolorable runiform hypergraphs. This approach
LinearWork Greedy Parallel Approximate Set Cover and Variants
"... We present parallel greedy approximation algorithms for set cover and related problems. These algorithms build on an algorithm for solving a graph problem we formulate and study called Maximal Nearly Independent Set (MaNIS)—a graph abstraction of a key component in existing work on parallel set cove ..."
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Cited by 5 (0 self)
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We present parallel greedy approximation algorithms for set cover and related problems. These algorithms build on an algorithm for solving a graph problem we formulate and study called Maximal Nearly Independent Set (MaNIS)—a graph abstraction of a key component in existing work on parallel set
A threshold of inn for approximating set cover (Preliminary version)
"... We prove that (] – o(]))lnn is a threshold below which set, cover cannot be approximated efficiently, unless NP has slightly superpolynornial time algorithms. This closes tlw gap (up to low order terms) between the ratio of approx&ation achievable by the greedy algorithm (which is (1 – O ( 1) ..."
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We prove that (] – o(]))lnn is a threshold below which set, cover cannot be approximated efficiently, unless NP has slightly superpolynornial time algorithms. This closes tlw gap (up to low order terms) between the ratio of approx&ation achievable by the greedy algorithm (which is (1 – O ( 1
Property Testing and its connection to Learning and Approximation
"... We study the question of determining whether an unknown function has a particular property or is fflfar from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the fun ..."
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Cited by 498 (68 self)
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w.r.t the vertex set). Our graph property testing algorithms are probabilistic and make assertions which are correct with high probability, utilizing only poly(1=ffl) edgequeries into the graph, where ffl is the distance parameter. Moreover, the property testing algorithms can be used
Greedy Function Approximation: A Gradient Boosting Machine
 Annals of Statistics
, 2000
"... Function approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest{descent minimization. A general gradient{descent \boosting" paradigm is developed for additi ..."
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Cited by 951 (12 self)
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Function approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest{descent minimization. A general gradient{descent \boosting" paradigm is developed
A Guided Tour to Approximate String Matching
 ACM COMPUTING SURVEYS
, 1999
"... We survey the current techniques to cope with the problem of string matching allowing errors. This is becoming a more and more relevant issue for many fast growing areas such as information retrieval and computational biology. We focus on online searching and mostly on edit distance, explaining t ..."
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Cited by 584 (38 self)
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We survey the current techniques to cope with the problem of string matching allowing errors. This is becoming a more and more relevant issue for many fast growing areas such as information retrieval and computational biology. We focus on online searching and mostly on edit distance, explaining the problem and its relevance, its statistical behavior, its history and current developments, and the central ideas of the algorithms and their complexities. We present a number of experiments to compare the performance of the different algorithms and show which are the best choices according to each case. We conclude with some future work directions and open problems.
Approximate Signal Processing
, 1997
"... It is increasingly important to structure signal processing algorithms and systems to allow for trading off between the accuracy of results and the utilization of resources in their implementation. In any particular context, there are typically a variety of heuristic approaches to managing these tra ..."
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Cited by 516 (2 self)
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these tradeoffs. One of the objectives of this paper is to suggest that there is the potential for developing a more formal approach, including utilizing current research in Computer Science on Approximate Processing and one of its central concepts, Incremental Refinement. Toward this end, we first summarize a
Results 1  10
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