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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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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 NPhard
KodairaSpencer theory of gravity and exact results for quantum string amplitudes
 Commun. Math. Phys
, 1994
"... We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particu ..."
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Cited by 545 (60 self)
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We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a
Learning Bayesian Networks is NPHard
, 1994
"... Algorithms for learning Bayesian networks from data have two components: a scoring metric and a search procedure. The scoring metric computes a score reflecting the goodnessoffit of the structure to the data. The search procedure tries to identify network structures with high scores. Heckerman et ..."
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Cited by 191 (2 self)
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there is a Bayesian networkamong those where each node has at most k parentsthat has a relative posterior probability greater than a given constant is NPcomplete, when the BDe metric is used. 1 Introduction Recently, many researchers have begun to investigate methods for learning Bayesian networks
Tcl and the Tk Toolkit
, 1994
"... This book is about two packages called Tcl and Tk. Together they provide a programming system for developing and using graphical user interface (GUI) applications. Tcl stands for "tool command language" and is pronounced "tickle"; is a simple scripting language for controlling an ..."
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Cited by 1335 (4 self)
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and extending applications. It provides generic programming facilities that are useful for a variety of applications, such as variables and loops and procedures. Furthermore, Tcl is embeddable: its interpreter is implemented as a library of C procedures that can easily be incorporated into applications
Where the REALLY Hard Problems Are
 IN J. MYLOPOULOS AND R. REITER (EDS.), PROCEEDINGS OF 12TH INTERNATIONAL JOINT CONFERENCE ON AI (IJCAI91),VOLUME 1
, 1991
"... It is well known that for many NPcomplete problems, such as KSat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NPcomplete problems can be summarized by at least one "order parameter", and that the hard p ..."
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Cited by 681 (1 self)
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It is well known that for many NPcomplete problems, such as KSat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NPcomplete problems can be summarized by at least one "order parameter", and that the hard
Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming
 Journal of the ACM
, 1995
"... We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution ..."
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Cited by 1231 (13 self)
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We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds
Three Generative, Lexicalised Models for Statistical Parsing
, 1997
"... In this paper we first propose a new statistical parsing model, which is a generative model of lexicalised contextfree gram mar. We then extend the model to in clude a probabilistic treatment of both subcategorisation and wh~movement. Results on Wall Street Journal text show that the parse ..."
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Cited by 567 (8 self)
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that the parser performs at 88.1/87.5% constituent precision/recall, an average improvement of 2.3% over (Collins 96).
Concurrent Constraint Programming
, 1993
"... This paper presents a new and very rich class of (concurrent) programming languages, based on the notion of comput.ing with parhal information, and the concommitant notions of consistency and entailment. ’ In this framework, computation emerges from the interaction of concurrently executing agent ..."
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Cited by 502 (16 self)
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This paper presents a new and very rich class of (concurrent) programming languages, based on the notion of comput.ing with parhal information, and the concommitant notions of consistency and entailment. ’ In this framework, computation emerges from the interaction of concurrently executing
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