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A greedy algorithm for aligning DNA sequences

by Zheng Zhang, Scott Schwartz, Lukas Wagner, Webb Miller - J. COMPUT. BIOL , 2000
"... For aligning DNA sequences that differ only by sequencing errors, or by equivalent errors from other sources, a greedy algorithm can be much faster than traditional dynamic programming approaches and yet produce an alignment that is guaranteed to be theoretically optimal. We introduce a new greedy a ..."
Abstract - Cited by 585 (16 self) - Add to MetaCart
For aligning DNA sequences that differ only by sequencing errors, or by equivalent errors from other sources, a greedy algorithm can be much faster than traditional dynamic programming approaches and yet produce an alignment that is guaranteed to be theoretically optimal. We introduce a new greedy

Greedy Algorithm:

by unknown authors
"... A dominating set of a graph G = (V, E) is a subset S ⊆ V of the nodes such that for all nodes v ∈ V, either v ∈ S or a neighbor u of v is in S. There are many distributed applications where computing a small dominating set of the network graph is important. It is well-known that computing a dominati ..."
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dominating set of minimal size is NP-hard. We therefore look for approximation algorithms, that is, algorithms which produce solutions which are optimal up to a certain factor. 10.1 Sequential Greedy Algorithm In order to understand the problem, we start with a very simple sequential algorithm. We start

Approximation and learning by greedy algorithms

by Andrew Barron, Albert Cohen, Wolfgang Dahmen, Ronald Devore - Ann. Statist , 2008
"... We consider the problem of approximating a given element f from a Hilbert space H by means of greedy algorithms and the application of such procedures to the regression problem in statistical learning theory. We improve on the existing theory of convergence rates for both the orthogonal greedy algor ..."
Abstract - Cited by 56 (9 self) - Add to MetaCart
We consider the problem of approximating a given element f from a Hilbert space H by means of greedy algorithms and the application of such procedures to the regression problem in statistical learning theory. We improve on the existing theory of convergence rates for both the orthogonal greedy

Vector Greedy Algorithms

by Adam Lutoborski, et al.
"... Our objective is to study nonlinear approximation with regard to redundant systems. Redundancy on the one hand offers much promise for greater efficiency in terms of approximation rate, but on the other hand gives rise to highly nontrivial theoretical and practical problems. Greedy type approximati ..."
Abstract - Cited by 67 (11 self) - Add to MetaCart
approximations proved to be convenient and efficient ways of constructing m-term approximants. We introduce and study vector greedy algorithms that are designed with aim of constructing mth greedy approximants simultaneously for a given finite number of elements. We prove convergence theorems and obtain some

Approximate weak greedy algorithms

by R. Gribonval, M. Nielsen - Advances in Computational Mathematics , 2001
"... We present a generalization of V. Temlyakov’s weak greedy algorithm, and give a sufficient condition for norm convergence of the algorithm for an arbitrary dictionary in a Hilbert space. We provide two counter-examples to show that the condition cannot be relaxed for general dictionaries. For a clas ..."
Abstract - Cited by 5 (3 self) - Add to MetaCart
We present a generalization of V. Temlyakov’s weak greedy algorithm, and give a sufficient condition for norm convergence of the algorithm for an arbitrary dictionary in a Hilbert space. We provide two counter-examples to show that the condition cannot be relaxed for general dictionaries. For a

The Greedy Algorithm for the Symmetric TSP

by Gregory Gutin, Anders Yeo
"... We corrected proofs of two results on the greedy algorithm for the Symmetric TSP and answered a question in Gutin and Yeo, Oper. Res. Lett. 30 (2002), 97–99. ..."
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We corrected proofs of two results on the greedy algorithm for the Symmetric TSP and answered a question in Gutin and Yeo, Oper. Res. Lett. 30 (2002), 97–99.

Simultaneous approximation by greedy algorithms

by D. Leviatan, V. N. Temlyakov , 2003
"... Abstract. We study nonlinear m-term approximation with regard to a redundant dictionary D in a Hilbert space H. It is known that the Pure Greedy Algorithm (or, more generally, the Weak Greedy Algorithm) provides for each f ∈ H and any dictionary D an expansion into a series f = cj(f)ϕj(f), ϕj(f) ∈ ..."
Abstract - Cited by 28 (1 self) - Add to MetaCart
Abstract. We study nonlinear m-term approximation with regard to a redundant dictionary D in a Hilbert space H. It is known that the Pure Greedy Algorithm (or, more generally, the Weak Greedy Algorithm) provides for each f ∈ H and any dictionary D an expansion into a series f = cj(f)ϕj(f), ϕj

Evaluating the Reverse Greedy Algorithm

by Shady Copty, Shmuel Ur, Elad Yom Tov , 2004
"... This paper present two meta heuristics, reverse greedy and future aware greedy, which are variants of the greedy algorithm. Both are based on the observation that guessing the impact of future selections is useful for the current selection. While the greedy algorithm makes the best local selection g ..."
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This paper present two meta heuristics, reverse greedy and future aware greedy, which are variants of the greedy algorithm. Both are based on the observation that guessing the impact of future selections is useful for the current selection. While the greedy algorithm makes the best local selection

Algorithm, and a Relaxed Greedy Algorithm.

by R. A. Devore, V. N. Temlyakov
"... Estimates are given for the rate of approximation of a function by means of greedy algorithms. The estimates apply to approximation from an arbitrary dictionary of functions. Three greedy algorithms are discussed: the Pure Greedy Algorithm, an Orthogonal Greedy ..."
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Estimates are given for the rate of approximation of a function by means of greedy algorithms. The estimates apply to approximation from an arbitrary dictionary of functions. Three greedy algorithms are discussed: the Pure Greedy Algorithm, an Orthogonal Greedy

When the greedy algorithm fails

by Jørgen Bang-jensen, Gregory Gutin, Anders Yeo
"... We provide a characterization of the cases when the greedy algorithm may produce the unique worst possible solution for the problem of finding a minimum weight base in a uniform independence system when the weights are taken from a finite range. We apply this theorem to TSP and the minimum bisection ..."
Abstract - Cited by 12 (3 self) - Add to MetaCart
We provide a characterization of the cases when the greedy algorithm may produce the unique worst possible solution for the problem of finding a minimum weight base in a uniform independence system when the weights are taken from a finite range. We apply this theorem to TSP and the minimum
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