A T=0(2^n/2), S=0(2^n/4) Algorithm for Certain NP-Complete Problems

Abstract

In this paper we develop a general prupose algorithm that can solve a number of NP-complete problems in time T=0(2^n/2) and space S=0(2^n/4). The algorithm can be generalized to a family of algorithms whose time and space complexities are related by T*S^2=0(2^n). 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 knapsack-based cryptosystems with up to n=100 generators.