The computational complexity of the local postage stamp problem
Number Theory
2007-05-23 v1 Computational Complexity
Combinatorics
Abstract
The well-studied local postage stamp problem (LPSP) is the following: given a positive integer k, a set of postive integers 1 = a1 < a2 < ... < ak and an integer h >= 1, what is the smallest positive integer which cannot be represented as a linear combination x1 a1 + ... + xk ak where x1 + ... + xk <= h and each xi 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.
Cite
@article{arxiv.math/0112257,
title = {The computational complexity of the local postage stamp problem},
author = {Jeffrey Shallit},
journal= {arXiv preprint arXiv:math/0112257},
year = {2007}
}