Algorithms for the local and the global postage stamp problem

TL;DR

This paper introduces new algorithms for the local and global postage stamp problems, improving computational efficiency and enabling applications in secure multi-party computations.

Contribution

It presents a novel, more efficient algorithm for the NP-hard local problem and a polynomial approximation for the global problem, with complexity analysis and practical applications.

Findings

Improved algorithm reduces time complexity and memory usage for the local problem.

Polynomial approximation algorithm effectively maximizes the smallest unattainable value.

Enhanced algorithms enable more efficient secure multi-party computations.

Abstract

We consider stamps with different values (denominations) and same dimensions, and an envelope with a fixed maximum number of stamp positions. The local postage stamp problem is to find the smallest value that cannot be realized by the sum of the stamps on the envelope. The global postage stamp problem is to find the set of denominations that maximize that smallest value for a fixed number of distinct denominations. The local problem is NP-hard and we propose here a novel algorithm that improves on both the time complexity bound and the amount of required memory. We also propose a polynomial approximation algorithm for the global problem together with its complexity analysis. Finally we show that our algorithms allow to improve secure multi-party computations on sets via a more efficient homomorphic evaluation of polynomials on ciphered values.