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Home > Art, Film & Photography > Weakly NP-Complete Problems: Subset Sum Problem, Weakly NP-Complete, 0-1 Knapsack Problem
Weakly NP-Complete Problems: Subset Sum Problem, Weakly NP-Complete, 0-1 Knapsack Problem

Weakly NP-Complete Problems: Subset Sum Problem, Weakly NP-Complete, 0-1 Knapsack Problem


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Chapters: Subset Sum Problem, Weakly Np-Complete, 0-1 Knapsack Problem. Source: Wikipedia. Pages: 22. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: In computer science, the subset sum problem is an important problem in complexity theory and cryptography. The problem is this: given a set of integers, does the sum of some non-empty subset equal exactly zero? For example, given the set { 7, 3, 2, 5, 8}, the answer is yes because the subset { 3, 2, 5} sums to zero. The problem is NP-Complete. An equivalent problem is this: given a set of integers and an integer s, does any non-empty subset sum to s? Subset sum can also be thought of as a special case of the knapsack problem. One interesting special case of subset sum is the partition problem, in which s is half of the sum of all elements in the set. The subset sum problem is a good introduction to the NP-complete class of problems. There are two reasons for this Although the subset sum problem is a decision problem, the cases when an approximate solution is sufficient have also been studied, in the field of approximations algorithms; one algorithm for the approximate version of the subset sum problem is given below. A solution that has a 1% precision is good enough for many physical problems. However, the number of place values in the problem is essentially equivalent to the number of simultaneous constraints that need to be solved. A numerical precision of 1% is approximately 0.000012%, or 7 binary places (any numerical error after that is less than of the first digit). However, if there are 100 binary place values in the problem, solving just 7 of them amounts to solving only 7% of the constraints. Moreover, given that the volume of the solution space in this case would be 2, and you have only covered a volume of 2, then there is still a s...More: http: //booksllc.net/?id=36811


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Product Details
  • ISBN-13: 9781158594986
  • Publisher: Books LLC
  • Publisher Imprint: Books LLC
  • Height: 152 mm
  • Sub Title: Subset Sum Problem, Weakly NP-Complete, 0-1 Knapsack Problem
  • Width: 229 mm
  • ISBN-10: 1158594984
  • Publisher Date: 15 Sep 2010
  • Binding: Paperback
  • Spine Width: 2 mm
  • Weight: 50 gr


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