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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
The C Programming Language
, 1988
"... The C programming language was devised in the early 1970s as a system implementation language for the nascent Unix operating system. Derived from the typeless language BCPL, it evolved a type structure; created on a tiny machine as a tool to improve a meager programming environment, it has become on ..."
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Cited by 1527 (16 self)
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The C programming language was devised in the early 1970s as a system implementation language for the nascent Unix operating system. Derived from the typeless language BCPL, it evolved a type structure; created on a tiny machine as a tool to improve a meager programming environment, it has become
Duality for mixedinteger linear programs
 The International Journal of Operations Research
, 2007
"... AbstractThe theory of duality for linear programs is welldeveloped and has been successful in advancing both the theory and practice of linear programming. In principle, much of this broad framework can be extended to mixedinteger linear programs, but this has proven difficult, in part because dua ..."
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Cited by 3 (1 self)
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duality theory does not integrate well with current computational practice. This paper surveys what is known about duality for integer programs and offers some minor extensions, with an eye towards developing a more practical framework. KeywordsDuality, Mixedinteger linear programming, Value function
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
 SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
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Cited by 557 (12 self)
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We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized
Financial Intermediation, Loanable Funds, and the Real Sector
 Quarterly Journal of Economics
, 1997
"... We study an incentive model of ®nancial intermediation in which ®rms as well as intermediaries are capital constrained. We analyze how the distribution of wealth across ®rms, intermediaries, and uninformed investors affects investment, interest rates, and the intensity of monitoring. We show that al ..."
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Cited by 494 (5 self)
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We study an incentive model of ®nancial intermediation in which ®rms as well as intermediaries are capital constrained. We analyze how the distribution of wealth across ®rms, intermediaries, and uninformed investors affects investment, interest rates, and the intensity of monitoring. We show that all forms of capital tightening (a credit crunch, a collateral squeeze, or a savings squeeze) hit poorly capitalized ®rms the hardest, but that interest rate effects and the intensity of monitoring will depend on relative changes in the various components of capital. The predictions of the model are broadly consistent with the lending patterns observed during the recent ®nancial crises. I.
Learning the Kernel Matrix with SemiDefinite Programming
, 2002
"... Kernelbased learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information ..."
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Cited by 780 (22 self)
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problems in machine learning. In this paper we show how the kernel matrix can be learned from data via semidefinite programming (SDP) techniques. When applied
Abduction in Logic Programming
"... Abduction in Logic Programming started in the late 80s, early 90s, in an attempt to extend logic programming into a framework suitable for a variety of problems in Artificial Intelligence and other areas of Computer Science. This paper aims to chart out the main developments of the field over th ..."
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Cited by 616 (76 self)
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Abduction in Logic Programming started in the late 80s, early 90s, in an attempt to extend logic programming into a framework suitable for a variety of problems in Artificial Intelligence and other areas of Computer Science. This paper aims to chart out the main developments of the field over
The Semantics Of Constraint Logic Programs
 JOURNAL OF LOGIC PROGRAMMING
, 1996
"... This paper presents for the first time the semantic foundations of CLP in a selfcontained and complete package. The main contributions are threefold. First, we extend the original conference paper by presenting definitions and basic semantic constructs from first principles, giving new and comp ..."
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Cited by 872 (14 self)
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This paper presents for the first time the semantic foundations of CLP in a selfcontained and complete package. The main contributions are threefold. First, we extend the original conference paper by presenting definitions and basic semantic constructs from first principles, giving new and complete proofs for the main lemmas. Importantly, we clarify which theorems depend on conditions such as solution compactness, satisfaction completeness and independence of constraints. Second, we generalize the original results to allow for incompleteness of the constraint solver. This is important since almost all CLP systems use an incomplete solver. Third, we give conditions on the (possibly incomplete) solver which ensure that the operational semantics is confluent, that is, has independence of literal scheduling.
Results 11  20
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502,416