Subset Sum Problem



While reading about the so-caled subset sum problem, I have encountered
two different versions of the problem:

1) Given a set of integers, does there exist a subset that sums to some
integer s?

2) Given a set of *positive* integers S, does there exist a subset that
sums to s?

I have read that (1) is NP-Complete. However, I do not know whether or
not (2) is NP-Complete. does anyone know whether (2) is NP-Complete?

If (2) is not NP-Complete, does there already exist an algorithm that
solves (2) in polynomial time?

Jeff Cameron

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Relevant Pages

  • Re: Subset Sum Problem
    ... > While reading about the so-caled subset sum problem, ... > 1) Given a set of integers, does there exist a subset that sums to some ... > I have read that is NP-Complete. ... only positive integers. ...
    (comp.theory)
  • Re: Subset Sum Problem
    ... => Merkle-Hellman knapsack system and its variants are all insecure." ... => describes the Subset Sum Problem (i.e. from a given set of numbers, ... The subset sum problem is NP-complete; ... Merkle-Hellman depended on disguising a simple special case. ...
    (sci.crypt)