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Speeding up Dualization in the Fredman-Khachiyan Algorithm B

Authors Nafiseh Sedaghat, Tamon Stephen, Leonid Chindelevitch

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LIPIcs.SEA.2018.6.pdf
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Subject Classification

ACM Subject Classification
  • Computing methodologies → Boolean algebra algorithms
Keywords
  • Monotone boolean functions
  • dualization
  • Fredman-Khachiyan algorithm
  • algorithm engineering
  • metabolic networks

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Abstract

The problem of computing the dual of a monotone Boolean function f is a fundamental problem in theoretical computer science with numerous applications. The related problem of duality testing (given two monotone Boolean functions f and g, declare that they are dual or provide a certificate that shows they are not) has a complexity that is not yet known. However, two quasi-polynomial time algorithms for it, often referred to as FK-A and FK-B, were proposed by Fredman and Khachiyan in 1996, with the latter having a better complexity guarantee. These can be naturally used as a subroutine in computing the dual of f.
In this paper, we investigate this use of the FK-B algorithm for the computation of the dual of a monotone Boolean function, and present practical improvements to its performance. First, we show how FK-B can be modified to produce multiple certificates (Boolean vectors on which the functions defined by the original f and the current dual g do not provide outputs consistent with duality). Second, we show how the number of redundancy tests - one of the more costly and time-consuming steps of FK-B - can be substantially reduced in this context. Lastly, we describe a simple memoization technique that avoids the solution of multiple identical subproblems.
We test our approach on a number of inputs coming from computational biology as well as combinatorics. These modifications provide a substantial speed-up, as much as an order of magnitude, for FK-B dualization relative to a naive implementation. Although other methods may end up being faster in practice, our work paves the way for a principled optimization process for the generation of monotone Boolean functions and their duals from an oracle.

Cite As Get BibTex

Nafiseh Sedaghat, Tamon Stephen, and Leonid Chindelevitch. Speeding up Dualization in the Fredman-Khachiyan Algorithm B. In 17th International Symposium on Experimental Algorithms (SEA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 103, pp. 6:1-6:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.SEA.2018.6

Author Details

Nafiseh Sedaghat
  • School of Computing Science, Simon Fraser University
Tamon Stephen
  • Department of Mathematics, Simon Fraser University
Leonid Chindelevitch
  • School of Computing Science, Simon Fraser University

Funding

  • Stephen, Tamon: Partially supported by an NSERC Discovery grant.
  • Chindelevitch, Leonid: Partially supported by an NSERC Discovery grant and a Sloan Foundation fellowship.

References

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