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Optimal approximation by piecewise smooth functions and associated variational problems
 Commun. Pure Applied Mathematics
, 1989
"... (Article begins on next page) The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. Citation Mumford, David Bryant, and Jayant Shah. 1989. Optimal approximations by piecewise smooth functions and associated variational problems. ..."
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Cited by 1294 (14 self)
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(Article begins on next page) The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. Citation Mumford, David Bryant, and Jayant Shah. 1989. Optimal approximations by piecewise smooth functions and associated variational problems
Greed is Good: Algorithmic Results for Sparse Approximation
, 2004
"... This article presents new results on using a greedy algorithm, orthogonal matching pursuit (OMP), to solve the sparse approximation problem over redundant dictionaries. It provides a sufficient condition under which both OMP and Donoho’s basis pursuit (BP) paradigm can recover the optimal representa ..."
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Cited by 916 (9 self)
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This article presents new results on using a greedy algorithm, orthogonal matching pursuit (OMP), to solve the sparse approximation problem over redundant dictionaries. It provides a sufficient condition under which both OMP and Donoho’s basis pursuit (BP) paradigm can recover the optimal
An Optimal Algorithm for Approximate Nearest Neighbor Searching in Fixed Dimensions
 ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS
, 1994
"... Consider a set S of n data points in real ddimensional space, R d , where distances are measured using any Minkowski metric. In nearest neighbor searching we preprocess S into a data structure, so that given any query point q 2 R d , the closest point of S to q can be reported quickly. Given any po ..."
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Cited by 984 (32 self)
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positive real ffl, a data point p is a (1 + ffl)approximate nearest neighbor of q if its distance from q is within a factor of (1 + ffl) of the distance to the true nearest neighbor. We show that it is possible to preprocess a set of n points in R d in O(dn log n) time and O(dn) space, so that given a
SubOptimality Approximation
 In CP05
, 2005
"... Abstract. The suboptimality approximation problem considers an optimization problem O, its optimal solution σ ∗ , and a variable x with domain {d1,..., dm} and returns approximations to O[x ← d1],..., O[x ← dm], where O[x ← d1] denotes the problem O with x assigned to di. The suboptimality approxi ..."
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Cited by 5 (3 self)
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Abstract. The suboptimality approximation problem considers an optimization problem O, its optimal solution σ ∗ , and a variable x with domain {d1,..., dm} and returns approximations to O[x ← d1],..., O[x ← dm], where O[x ← d1] denotes the problem O with x assigned to di. The suboptimality
Approximating discrete probability distributions with dependence trees
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1968
"... A method is presented to approximate optimally an ndimensional discrete probability distribution by a product of secondorder distributions, or the distribution of the firstorder tree dependence. The problem is to find an optimum set of n1 first order dependence relationship among the n variables ..."
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Cited by 881 (0 self)
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A method is presented to approximate optimally an ndimensional discrete probability distribution by a product of secondorder distributions, or the distribution of the firstorder tree dependence. The problem is to find an optimum set of n1 first order dependence relationship among the n
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 1000 (13 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
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 751 (11 self)
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for the efficient approximability of many optimization problems studied previously. In particular, for MaxE2Sat, MaxCut, MaxdiCut, and Vertex cover. Warning: Essentially this paper has been published in JACM and is subject to copyright restrictions. In particular it is for personal use only.
Optimal Aggregation Algorithms for Middleware
 IN PODS
, 2001
"... Assume that each object in a database has m grades, or scores, one for each of m attributes. For example, an object can have a color grade, that tells how red it is, and a shape grade, that tells how round it is. For each attribute, there is a sorted list, which lists each object and its grade under ..."
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Cited by 717 (4 self)
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must access every object in the database, to find its grade under each attribute. Fagin has given an algorithm (“Fagin’s Algorithm”, or FA) that is much more efficient. For some monotone aggregation functions, FA is optimal with high probability in the worst case. We analyze an elegant and remarkably
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 1211 (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
Results 1  10
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