Subset Summation Decision Task

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A Subset Sum Problem is a computational decision task that is a summation task on a subset of a non-empty integer set.



  • (Wikipedia, 2014) ⇒ Retrieved:2014-3-3.
    • 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, is there a non-empty subset whose sum is 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.[1] 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.

  1. Martello, Silvano; Toth, Paolo (1990). "4 Subset-sum problem". Knapsack problems: Algorithms and computer interpretations. Wiley-Interscience. pp. 105–136. ISBN 0-471-92420-2. MR1086874.