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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 ...
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 ...
The algorithm has several stages. First, find a solution using greedy algorithm. In each iteration of the greedy algorithm the tentative solution is added the set which contains the maximum residual weight of elements divided by the residual cost of these elements along with the residual cost of the set.
This greedy algorithm actually achieves an approximation ratio of (′) where ′ is the maximum cardinality set of . For δ − {\displaystyle \delta -} dense instances, however, there exists a c ln m {\displaystyle c\ln {m}} -approximation algorithm for every c > 0 {\displaystyle c>0} .
However, this algorithm is not fixed-parameter tractable, because the exponent in its running time depends on k. When k is an input variable rather than a parameter, the problem is NP-complete. [3] The Grundy number is at most one plus the maximum degree of the graph, and it remains NP-complete to test whether it equals one plus the maximum ...
One variation of this problem assumes that the people making change will use the "greedy algorithm" for making change, even when that requires more than the minimum number of coins. Most current currencies use a 1-2-5 series , but some other set of denominations would require fewer denominations of coins or a smaller average number of coins to ...
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 ...
The greedy pure algorithm (or Gr) follows the core idea of greedy algorithms: to take optimal local decisions. In the case of the vertex k-center problem, the optimal local decision consists in selecting each center in such a way that the size of the solution (covering radius) is minimum at each iteration. In other words, the first center ...