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Journal of Global Optimization

, Volume 54, Issue 2, pp 261–274 | Cite as

Parallel branch and bound for multidimensional scaling with city-block distances

  • Julius Žilinskas
Article

Abstract

Multidimensional scaling is a technique for exploratory analysis of multidimensional data. The essential part of the technique is minimization of a multimodal function with unfavorable properties like invariants and non-differentiability. Recently a branch and bound algorithm for multidimensional scaling with city-block distances has been proposed for solution of medium-size problems exactly. The algorithm exploits piecewise quadratic structure of the objective function. In this paper a parallel version of the branch and bound algorithm for multidimensional scaling with city-block distances has been proposed and investigated. Parallel computing enabled solution of larger problems what was not feasible with the sequential version.

Keywords

Multidimensional scaling City-block distances Multilevel optimization Global optimization Branch and bound Parallel computing 

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Copyright information

© Springer Science+Business Media, LLC. 2010

Authors and Affiliations

  1. 1.Institute of Mathematics and InformaticsVilnius UniversityVilniusLithuania

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