# OpenDreamKit

## A project funded by the Horizon 2020

European Research Infrastructures Work Program

# PASCO 2017 Kaiserslautern, Germany, July 23-24, 2017

## Main goals

The 8th International Workshop on Parallel Symbolic Computation (PASCO) is the latest instance in a series of workshops dedicated to the promotion and advancement of parallel algorithms and software in all areas of symbolic mathematical computation. It is a two days event which is a satellite of ISSAC, one of the main conference in symbolic computation.

## OpenDreamKit implication

Florent Hivert was invited keynote speaker. The cost for OpenDreamKit was therefore null.

## Event summary

Florent Hivert was invited to give a keynote talk presenting his work on WP5 T5.6. The talk was entitled \emph{High Performance Computing Experiments in Enumerative and Algebraic Combinatorics}. Here is the abstract:

In this talk, I will report on several experiments around large scale enumerations in enumerative and algebraic combinatorics. In a first part, I’ll present a small framework implemented in Sagemath allowing to perform map/reduce like computations on large recursively defined sets. Though it doesn’t really qualify as HPC, it allowed to efficiently parallelize a dozen of experiments ranging from Coxeter group and representation theory of monoids to the combinatorial study of the C3 linearization algorithm used to compute the method resolution order (MRO) in script language such as Python and Perl.

In a second part, I’ll describe a methodology used to achieve large speedups in several enumeration problems. Indeed, in many combinatorial structures (permutations, partitions, monomials, young tableaux), the data can be encoded as a small sequence of small integers that can often efficiently be handled by a creative use of vector instructions. Through the challenging example of numerical monoids, I will then report on how Cilkplus allows for a extremely fast parallelization of the enumeration. Indeed, we have been able to enumerate sets with more that $10^15$ elements on a single multicore machine. This is joint work with Jean Fromentin.

## Results and impact

The talk was a chance to disseminate OpenDreamKit work in a wider audience and to present the result on deliverable D5.1 and the ongoing progress on the overall work package. The fact that it was an invited keynote talk witnesses that the community is particularly interested and attentive on the OpenDreamKit progress on this matters.

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