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485,324
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 NP
Feature selection based on mutual information: Criteria of maxdepe ndency, maxrelevance, and minredundancy
 IEEE Trans. Pattern Analysis and Machine Intelligence
"... Abstract—Feature selection is an important problem for pattern classification systems. We study how to select good features according to the maximal statistical dependency criterion based on mutual information. Because of the difficulty in directly implementing the maximal dependency condition, we f ..."
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Cited by 533 (7 self)
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Abstract—Feature selection is an important problem for pattern classification systems. We study how to select good features according to the maximal statistical dependency criterion based on mutual information. Because of the difficulty in directly implementing the maximal dependency condition, we first derive an equivalent form, called minimalredundancymaximalrelevance criterion (mRMR), for firstorder incremental feature selection. Then, we present a twostage feature selection algorithm by combining mRMR and other more sophisticated feature selectors (e.g., wrappers). This allows us to select a compact set of superior features at very low cost. We perform extensive experimental comparison of our algorithm and other methods using three different classifiers (naive Bayes, support vector machine, and linear discriminate analysis) and four different data sets (handwritten digits, arrhythmia, NCI cancer cell lines, and lymphoma tissues). The results confirm that mRMR leads to promising improvement on feature selection and classification accuracy.
MaxProp: Routing for VehicleBased DisruptionTolerant Networks
 In Proc. IEEE INFOCOM
, 2006
"... Abstract — Disruptiontolerant networks (DTNs) attempt to route network messages via intermittently connected nodes. Routing in such environments is difficult because peers have little information about the state of the partitioned network and transfer opportunities between peers are of limited dura ..."
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Cited by 476 (12 self)
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duration. In this paper, we propose MaxProp, a protocol for effective routing of DTN messages. MaxProp is based on prioritizing both the schedule of packets transmitted to other peers and the schedule of packets to be dropped. These priorities are based on the path likelihoods to peers according
THE COMPLEXITY OF THE MINIMUM kCOVER PROBLEM
, 2005
"... We consider the problem of determining the minimum cardinality collection of substrings, each of given length k ≥ 2, that “cover” a given string x of length n. We show first, by reduction from 3SAT, that this minimum kcover problem is NPcomplete. Then we propose further two greedy algorithms that ..."
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Cited by 1 (0 self)
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We consider the problem of determining the minimum cardinality collection of substrings, each of given length k ≥ 2, that “cover” a given string x of length n. We show first, by reduction from 3SAT, that this minimum kcover problem is NPcomplete. Then we propose further two greedy algorithms
Some optimal inapproximability results
, 2002
"... We prove optimal, up to an arbitrary ffl? 0, inapproximability results for MaxEkSat for k * 3, maximizing the number of satisfied linear equations in an overdetermined system of linear equations modulo a prime p and Set Splitting. As a consequence of these results we get improved lower bounds for ..."
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Cited by 782 (12 self)
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We prove optimal, up to an arbitrary ffl? 0, inapproximability results for MaxEkSat for k * 3, maximizing the number of satisfied linear equations in an overdetermined system of linear equations modulo a prime p and Set Splitting. As a consequence of these results we get improved lower bounds
Set KCover Algorithms for Energy Efficient Monitoring in Wireless Sensor Networks
 In Proceedings of IPSN’04
, 2004
"... Wireless sensor networks (WSNs) are emerging as an e#ective means for environment monitoring. This paper investigates a strategy for energy e#cient monitoring in WSNs that partitions the sensors into covers, and then activates the covers iteratively in a roundrobin fashion. This approach takes adva ..."
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Cited by 129 (0 self)
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advantage of the overlap created when many sensors monitor a single area. Our work builds upon previous work in [13], where the model is first formulated. We have designed three approximation algorithms for a variation of the SET KCOVER problem, where the objective is to partition the sensors into covers
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
The irreducibility of the space of curves of given genus
 Publ. Math. IHES
, 1969
"... Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k ~ ..."
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Cited by 512 (2 self)
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Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k
Hierarchical Models of Object Recognition in Cortex
, 1999
"... The classical model of visual processing in cortex is a hierarchy of increasingly sophisticated representations, extending in a natural way the model of simple to complex cells of Hubel and Wiesel. Somewhat surprisingly, little quantitative modeling has been done in the last 15 years to explore th ..."
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Cited by 817 (84 self)
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predictions. The model is based on a novel MAXlike operation on the inputs to certain cortical neurons which may have a general role in cortical function.
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 800 (26 self)
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likelihoods, marginal probabilities and most probable configurations. We describe how a wide varietyof algorithms — among them sumproduct, cluster variational methods, expectationpropagation, mean field methods, maxproduct and linear programming relaxation, as well as conic programming relaxations — can
Results 1  10
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485,324