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

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

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

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

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

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

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

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.

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

My main reference was [1]. Greedy algorithms and matroids are nicely described in Chapter 16 of [1]; there is a much more mathematically-oriented presentation in Chapter 1 of [2]. Spanning trees are discussed in depth in Chapter 23 of [1]; union-find (and other algorithms for disjoint sets