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A greedy algorithm is any algorithm that follows the problem-solving heuristic of making the locally optimal choice at each stage. [1] In many problems, a greedy strategy does not produce an optimal solution, but a greedy heuristic can yield locally optimal solutions that approximate a globally optimal solution in a reasonable amount of time.
In the study of graph coloring problems in mathematics and computer science, a greedy coloring or sequential coloring [1] is a coloring of the vertices of a graph formed by a greedy algorithm that considers the vertices of the graph in sequence and assigns each vertex its first available color. Greedy colorings can be found in linear time, but ...
In computer science, greedy number partitioning is a class of greedy algorithms for multiway number partitioning. The input to the algorithm is a set S of numbers, and a parameter k. The required output is a partition of S into k subsets, such that the sums in the subsets are as nearly equal as possible. Greedy algorithms process the numbers ...
A basic problem regarding weighted matroids is to find an independent set with a maximum total weight. This problem can be solved using the following simple greedy algorithm: Initialize the set A to an empty set. Note that, by definition of a matroid, A is an independent set. For each element x in E\A, check whether Au{x} is still an ...
Another example is attempting to make 40 US cents without nickels (denomination 25, 10, 1) with similar result — the greedy chooses seven coins (25, 10, and 5 × 1), but the optimal is four (4 × 10). A coin system is called "canonical" if the greedy algorithm always solves its change-making problem optimally.
This property is used to determine the usefulness of greedy algorithms for a problem. [1] Typically, a greedy algorithm is used to solve a problem with optimal substructure if it can be proven by induction that this is optimal at each step. [1] Otherwise, provided the problem exhibits overlapping subproblems as well, divide-and-conquer methods ...
Pages in category "Greedy algorithms" The following 9 pages are in this category, out of 9 total. This list may not reflect recent changes. A. A* search algorithm; B.
Longest-processing-time-first (LPT) is a greedy algorithm for job scheduling. The input to the algorithm is a set of jobs, each of which has a specific processing-time. There is also a number m specifying the number of machines that can process the jobs. The LPT algorithm works as follows: