Metropolis algorithm for solving Shortest lattice Vector Problem (SVP)

Shenoy K.B. Ajitha, Somenath Biswas, Piyush P. Kurur

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Abstract

In this paper we study the suitability of the Metropolis Algorithm and its generalization for solving the shortest lattice vector problem (SVP). SVP has numerous applications spanning from robotics to computational number theory, viz., polynomial factorization. At the same time, SVP is a notoriously hard problem. Not only it is NP-hard, there is not even any polynomial approximation known for the problem that runs in polynomial time. What one normally uses is the LLL algorithm which, although a polynomial time algorithm, may give solutions which are an exponential factor away from the optimum. In this paper, we have defined an appropriate search space for the problem which we use for implementation of the Metropolis algorithm. We have defined a suitable neighbourhood structure which makes the diameter of the space polynomially bounded, and we ensure that each search point has only polynomially many neighbours. We can use this search space formulation for some other classes of evolutionary algorithms, e.g., for genetic and go-with-the-winner algorithms. We have implemented the Metropolis algorithm and Hasting's generalization of Metropolis algorithm for the SVP. Our results are quite encouraging in all instances when compared with LLL algorithm.

Original languageEnglish
Title of host publicationProceedings of the 2011 11th International Conference on Hybrid Intelligent Systems, HIS 2011
Pages442-447
Number of pages6
DOIs
Publication statusPublished - 2011
Event2011 11th International Conference on Hybrid Intelligent Systems, HIS 2011 - Malacca, Malaysia
Duration: 05-12-201108-12-2011

Conference

Conference2011 11th International Conference on Hybrid Intelligent Systems, HIS 2011
CountryMalaysia
CityMalacca
Period05-12-1108-12-11

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All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Information Systems

Cite this

Ajitha, S. K. B., Biswas, S., & Kurur, P. P. (2011). Metropolis algorithm for solving Shortest lattice Vector Problem (SVP). In Proceedings of the 2011 11th International Conference on Hybrid Intelligent Systems, HIS 2011 (pp. 442-447). [6122146] https://doi.org/10.1109/HIS.2011.6122146