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Journals ACM SIGACT News Volume 33 Issue 1

The well-studied local postage stamp problem (LPSP) is the following: given a positive integer k, a set of positive integers 1 = a 1 < a 2 < … < a k and an integer h ≥ 1, what is the smallest positive integer which cannot be represented as a linear combination Σ 1≤i≤k x 1 a i where Σ 1≤i≤k x 1 ≤ h and each x i is a non-negative integer? In this note we prove that LPSP is NP-hard under Turing reductions, but can be solved in polynomial time if k is fixed.

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The computational complexity of the local postage stamp problem

Shallit, Jeffrey
ACM SIGACT News , Volume 33 (1)
Association for Computing Machinery – Mar 1, 2002

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