Heuristics for Minimum Brauer Chain Problem

摘要

The exponentiation problem is computing x~n for positive integer exponents n where the quality is measured by number of multiplications it requires. However, finding minimum number of multiplications is an NP-complete problem. This problem is very important for many applications such as RSA encryption and ElGamal decryption. Solving minimum Brauer chain problem is a way to solve the exponentiation problem. In this paper, five heuristics for approximating minimum length Brauer chain for a given number n is discussed. These heuristics are based on some greedy approaches and dynamic programming. As a result, we empirically get 1.1-approximation for the problem.