Florent Hivert
ABSTRACT
The goal of this abstract is to report on some parallel and high performance computations in combinatorics, each involving large datasets generated recursively: we start by presenting a small framework implemented in Sagemath [12] allowing performance of map/reduce like computations on such recursively defined sets. In the second part, we describe a methodology used to achieve large speedups in several enumeration problems involving similar map/reduced computations. We illustrate this methodology on the challenging problem of counting the number of numerical semigroups [5], and present briefly another problem about enumerating integer vectors upto the action of a permutation group [2]. We believe that these techniques are fairly general for those kinds of algorithms.
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Digital Library
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- J.-B. Priez F. Hivert and N. Cohen. 2016. Parallel computations using RecursivelyEnumeratedSet and Map-Reduce. The Sage Development Team. http://doc.sagemath.org/html/en/reference/parallel/sage/parallel/map_reduce.htmlGoogle Scholar
- Jean Fromentin and Florent Hivert. 2016. Exploring the tree of numerical semigroups. Math. Comput. 85, 301 (2016), 2553--2568.Google ScholarCross Ref
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- Florent Hivert. 2016. Integer vectors modulo the action of a permutation group. https://github.com/hivert/IVMPGGoogle Scholar
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- Software.intel.com. 2013. Intel® Cilk™ Homepage. https://www.cilkplus.org/. (2013).Google Scholar
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- Nicolas M. Thiéry. 2016. The C3 algorithm, under control of a total order. The Sage Development Team. http://doc.sagemath.org/html/en/reference/misc/sage/misc/c3_controlled.htmlGoogle Scholar
Index Terms
- High Performance Computing Experiments in Enumerative and Algebraic Combinatorics
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