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Choosing a Variable Ordering for Truth-Table Invariant Cylindrical Algebraic Decomposition by Incremental Triangular Decomposition

  • Matthew England
  • Russell Bradford
  • James H. Davenport
  • David Wilson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8592)

Abstract

Cylindrical algebraic decomposition (CAD) is a key tool for solving problems in real algebraic geometry and beyond. In recent years a new approach has been developed, where regular chains technology is used to first build a decomposition in complex space. We consider the latest variant of this which builds the complex decomposition incrementally by polynomial and produces CADs on whose cells a sequence of formulae are truth-invariant. Like all CAD algorithms the user must provide a variable ordering which can have a profound impact on the tractability of a problem. We evaluate existing heuristics to help with the choice for this algorithm, suggest improvements and then derive a new heuristic more closely aligned with the mechanics of the new algorithm.

Keywords

Variable Ordering Time Saving Epidemic Modelling Cell Saving Triangular Decomposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Matthew England
    • 1
  • Russell Bradford
    • 1
  • James H. Davenport
    • 1
  • David Wilson
    • 1
  1. 1.University of BathUK

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