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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.
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.
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.
A random walk algorithm sometimes moves like a greedy algorithm but sometimes moves randomly. It depends on a parameter p {\displaystyle p} , which is a real number between 0 and 1. At every move, with probability p {\displaystyle p} the algorithm proceeds like a greedy algorithm, trying to maximally decrease the cost of the assignment.
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.
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:
In mathematics, the greedy algorithm for Egyptian fractions is a greedy algorithm, first described by Fibonacci, for transforming rational numbers into Egyptian fractions. An Egyptian fraction is a representation of an irreducible fraction as a sum of distinct unit fractions , such as 5 / 6 = 1 / 2 + 1 / 3 .