Heuristics for minimum brauer chain problem

Authors:
Fatih Gelgi;Melih Onus
Affiliations:
Department of Computer Science and Engineering, Arizona State University;Department of Computer Science and Engineering, Arizona State University
Venue:
ISCIS'06 Proceedings of the 21st international conference on Computer and Information Sciences
Year:
2006

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Abstract

The exponentiation problem is computing xn 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.