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. © 2014 Springer-Verlag.
CITATION STYLE
England, M., Bradford, R., Davenport, J. H., & Wilson, D. (2014). Choosing a variable ordering for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8592 LNCS, pp. 450–457). Springer Verlag. https://doi.org/10.1007/978-3-662-44199-2_68
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