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.

翻译：本文研究具有不同面值（面额）但尺寸相同的邮票，以及一个具有固定最大邮票粘贴位置的信封。局部邮票问题旨在找出无法通过信封上邮票面值之和实现的最小值。全局邮票问题则是在固定不同面额数量的条件下，寻找能使该最小值最大化的面额集合。局部问题是NP难问题，本文提出一种新颖算法，该算法在时间复杂度界限和所需内存量两方面均有所改进。同时，针对全局问题，我们提出一种多项式近似算法并给出其复杂度分析。最后，我们证明所提算法能够通过更高效地对加密值进行多项式同态求值，从而改进基于集合的安全多方计算。