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A common technique for proving the correctness of greedy algorithms uses an inductive exchange argument. [3] The exchange argument demonstrates that any solution different from the greedy solution can be transformed into the greedy solution without degrading its quality. This proof pattern typically follows these steps:
Charging arguments can also be used to show approximation results. In particular, it can be used to show that an algorithm is an n-approximation to an optimization problem. Instead of showing that an algorithm produces outputs with the same value of profit or cost as the optimal solution, show that it attains that value within a factor of n.
The NIST Dictionary of Algorithms and Data Structures [1] is a reference work maintained by the U.S. National Institute of Standards and Technology. It defines a large number of terms relating to algorithms and data structures. For algorithms and data structures not necessarily mentioned here, see list of algorithms and list of data structures.
A greedy algorithm is optimal for every R-compatible linear objective function over a greedoid. The intuition behind this proposition is that, during the iterative process, each optimal exchange of minimum weight is made possible by the exchange property, and optimal results are obtainable from the feasible sets in the underlying greedoid.
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This proves that the greedy algorithm indeed finds an optimal solution. A more formal explanation is given by a Charging argument. The greedy algorithm can be executed in time O(n log n), where n is the number of tasks, using a preprocessing step in which the tasks are sorted by their finishing times.
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 ...
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 ...