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Heuristics for Minimum Brauer Chain Problem

  • Fatih Gelgi
  • Melih Onus
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4263)

Abstract

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.

Keywords

Brauer chain addition chain exponentiation greedy algorithms dynamic programming 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Fatih Gelgi
    • 1
  • Melih Onus
    • 1
  1. 1.Department of Computer Science and EngineeringArizona State University 

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