Abstract
This paper reports our effort to parallelize on a network of workstations the partial cylindrical algebraic decomposition based quantifier elimination algorithm over the reals, which was devised by Collins and improved by the author. We have parallelized the lifting phase of the algorithm, so that cylinders are constructed in parallel. An interesting feature is that the algorithm sometimes appears to produce super-linear speedups, due to speculative parallelism. Thus it suggests a possible further improvement of the sequential algorithm via simulating parallelism.
This research was carried out in the framework of the Austrian science foundation (FWF) project S5302-PHY (Parallel Algebraic Computation) and the European project (ESPRIT II) POSSO (Polynomial Systems Solving).
I thank for the anonymous referees for their many valuable suggestions for improving the paper. I also would like to thank Dan Teodosiu for implementing the underlying communication primitives.
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Hong, H. (1993). Parallelization of quantifier elimination on a workstation network. In: Cohen, G., Mora, T., Moreno, O. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1993. Lecture Notes in Computer Science, vol 673. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56686-4_42
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DOI: https://doi.org/10.1007/3-540-56686-4_42
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