Search results
Results from the WOW.Com Content Network
A 1999 study of the Stony Brook University Algorithm Repository showed that, out of 75 algorithmic problems related to the field of combinatorial algorithms and algorithm engineering, the knapsack problem was the 19th most popular and the third most needed after suffix trees and the bin packing problem.
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.
The knapsack problem is one of the most studied problems in combinatorial optimization, with many real-life applications. For this reason, many special cases and generalizations have been examined. For this reason, many special cases and generalizations have been examined.
For the problem variant in which not every item must be assigned to a bin, there is a family of algorithms for solving the GAP by using a combinatorial translation of any algorithm for the knapsack problem into an approximation algorithm for the GAP. [3] Using any -approximation algorithm ALG for the knapsack problem, it is possible to ...
The budgeting method most common in practice is a greedy solution to a variant of the knapsack problem: the projects are ordered by decreasing order of the number of votes they received, and selected one-by-one until the budget is exhausted. Alternatively, if the number of projects is sufficiently small, the knapsack problem may be solved ...
The matching pursuit is an example of a greedy algorithm applied on signal approximation. A greedy algorithm finds the optimal solution to Malfatti's problem of finding three disjoint circles within a given triangle that maximize the total area of the circles; it is conjectured that the same greedy algorithm is optimal for any number of circles.
Here are some examples of benevolent problems, that have an FPTAS by the above theorem. [6] 1. The 0-1 knapsack problem is benevolent. Here, we have a=2: each input is a 2-vector (weight, value). There is a DP with b=2: each state encodes (current weight, current value).
The knapsack problem can be solved by dynamic programming in pseudo-polynomial time: (), where m is the number of inputs and V is the number of different possible values. To get a polynomial-time algorithm, we can solve the knapsack problem approximately, using input rounding.