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202,951
0 Integrality Gap of the Hypergraphic Relaxation of Steiner Trees: a short proof of a 1.55 upper bound
, 2010
"... ar ..."
Matroids and integrality gaps for hypergraphic steiner tree relaxations
 In Proceedings of the Fortyfourth Annual ACM Symposium on Theory of Computing, STOC ’12
, 2012
"... Until recently, LP relaxations have only played a very limited role in the design of approximation algorithms for the Steiner tree problem. In particular, no (efficiently solvable) Steiner tree relaxation was known to have an integrality gap bounded away from 2, before Byrka et al. [3] showed an upp ..."
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Cited by 6 (1 self)
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an upper bound of ≈ 1.55 of a hypergraphic LP relaxation and presented a ln(4) + ≈ 1.39 approximation based on this relaxation. Interestingly, even though their approach is LP based, they do not compare the solution produced against the LP value. We take a fresh look at hypergraphic LP relaxations
Hypergraphic LP Relaxations for Steiner Trees
"... Abstract. We investigate hypergraphic LP relaxations for the Steiner tree problem, primarily the partition LP relaxation introduced by Könemann et al. [Math. Programming, 2009]. Specifically, we are interested in proving upper bounds on the integrality gap of this LP, and studying its relation to ot ..."
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Cited by 7 (3 self)
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Abstract. We investigate hypergraphic LP relaxations for the Steiner tree problem, primarily the partition LP relaxation introduced by Könemann et al. [Math. Programming, 2009]. Specifically, we are interested in proving upper bounds on the integrality gap of this LP, and studying its relation
On the Equivalence of the Bidirected and Hypergraphic Relaxations for Steiner Tree
"... The bottleneck of the currently best (ln(4)+ε)approximation algorithm for the NPhard Steiner tree problem is the solution of its large, so called hypergraphic, linear programming relaxation (HYP). Hypergraphic LPs are NPhard to solve exactly, and it is a formidable computational task to even appr ..."
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The bottleneck of the currently best (ln(4)+ε)approximation algorithm for the NPhard Steiner tree problem is the solution of its large, so called hypergraphic, linear programming relaxation (HYP). Hypergraphic LPs are NPhard to solve exactly, and it is a formidable computational task to even
Just Relax: Convex Programming Methods for Identifying Sparse Signals in Noise
, 2006
"... This paper studies a difficult and fundamental problem that arises throughout electrical engineering, applied mathematics, and statistics. Suppose that one forms a short linear combination of elementary signals drawn from a large, fixed collection. Given an observation of the linear combination that ..."
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Cited by 496 (2 self)
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This paper studies a difficult and fundamental problem that arises throughout electrical engineering, applied mathematics, and statistics. Suppose that one forms a short linear combination of elementary signals drawn from a large, fixed collection. Given an observation of the linear combination
Mining Frequent Patterns without Candidate Generation: A FrequentPattern Tree Approach
 DATA MINING AND KNOWLEDGE DISCOVERY
, 2004
"... Mining frequent patterns in transaction databases, timeseries databases, and many other kinds of databases has been studied popularly in data mining research. Most of the previous studies adopt an Apriorilike candidate set generationandtest approach. However, candidate set generation is still co ..."
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Cited by 1700 (64 self)
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based mining method, FPgrowth, for mining the complete set of frequent patterns by pattern fragment growth.
Efficiency of mining is achieved with three techniques: (1) a large database is compressed into a condensed,
smaller data structure, FPtree which avoids costly, repeated database scans, (2) our
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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the solution to a nonlinear programming relaxation. This relaxation can be interpreted both as a semidefinite program and as an eigenvalue minimization problem. The best previously known approximation algorithms for these problems had performance guarantees of ...
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
The strength of weak learnability
 Machine Learning
, 1990
"... Abstract. This paper addresses the problem of improving the accuracy of an hypothesis output by a learning algorithm in the distributionfree (PAC) learning model. A concept class is learnable (or strongly learnable) if, given access to a Source of examples of the unknown concept, the learner with h ..."
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Cited by 861 (24 self)
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well. In addition, the construction has some interesting theoretical consequences, including a set of general upper bounds on the complexity of any strong learning algorithm as a function of the allowed error e.
A scheduling model for reduced CPU energy
 ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE
, 1995
"... The energy usage of computer systems is becoming an important consideration, especially for batteryoperated systems. Various methods for reducing energy consumption have been investigated, both at the circuit level and at the operating systems level. In this paper, we propose a simple model of job s ..."
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Cited by 550 (3 self)
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times the minimum energy required. The analysis involves bounding the largest eigenvalue in matrices of a special type.
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