A TcS2 = 0 (2n) time/space tradeoff for certain NP-complete problems

Abstract

In this paper we develop a general purpose algorithm that can solve a number of NP-complete problems in time T = O(2n/2) and space S = O(2n/4). The algorithm can be generalized to a family of algorithms whose time and space complexities are related by T¿S2 = O(2n). The problems it can handle are characterized by a few decomposition axioms, and they include knapsack problems, exact satisfiability problems, set covering problems, etc. The new algorithm has a considerable cryptanalytic significance, since it can break the Merkle-Hellman public key cryptosystem whose recommended size is n = 100.