The computational complexity of the local postage stamp problem

Authors:
Jeffrey Shallit
Affiliations:
University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 and University of Arizona, P. O. Box 210077, Tucson, AZ
Venue:
ACM SIGACT News
Year:
2002

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Abstract

The well-studied local postage stamp problem (LPSP) is thefollowing: given a positive integer k, a set of positiveintegers 1 = a1 2 k and an integer h ≥ 1, what is the smallestpositive integer which cannot be represented as a linearcombinationΣ1≤i≤kx1aiwhere Σ1≤i≤kx1 ≤ h andeach xi is a non-negative integer? In this notewe prove that LPSP is NP-hard under Turing reductions, but can besolved in polynomial time if k is fixed.