{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T21:48:47Z","timestamp":1725572927537},"reference-count":0,"publisher":"EasyChair","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>In applications of symbolic computation an often required but complex procedure is the computation of Gr\u00f6bner bases and hence it is obvious<\/jats:p><jats:p>to realize parallel algorithms to compute them. There are parallel flavours of the F4 algorithm using the special structure of the occurring matrices<\/jats:p><jats:p>to speed up the reduction. In this paper we start from this and present modifications allowing efficient computations of Gr\u00f6bner bases on parallel architectures<\/jats:p><jats:p>using shared as well as distributed memory. To achieve this we concentrate on one objective: reducing the memory consumption and avoiding communication overhead.<\/jats:p><jats:p>We remove unrequired steps of the reduction, split the columns of the matrix in blocks for distribution and review the effectiveness of the SIMPLIFY function.<\/jats:p><jats:p>Finally we provide benchmarks with up to 256 distributed threads of an implementation which will be available at https:\/\/github.com\/svrnm\/parallelGBC.<\/jats:p>","DOI":"10.29007\/98fh","type":"proceedings-article","created":{"date-parts":[[2018,1,23]],"date-time":"2018-01-23T17:59:06Z","timestamp":1516730346000},"page":"70-58","source":"Crossref","is-referenced-by-count":0,"title":["A modified parallel F4 algorithm for shared and distributed memory architectures"],"prefix":"10.29007","volume":"15","author":[{"given":"Severin","family":"Neumann","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"11545","event":{"name":"SCSS 2013. 5th International Symposium on Symbolic Computation in Software Science"},"container-title":["EPiC Series in Computing"],"original-title":[],"deposited":{"date-parts":[[2018,1,23]],"date-time":"2018-01-23T17:59:07Z","timestamp":1516730347000},"score":1,"resource":{"primary":{"URL":"https:\/\/easychair.org\/publications\/paper\/wS5z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"references-count":0,"URL":"https:\/\/doi.org\/10.29007\/98fh","relation":{},"ISSN":["2398-7340"],"issn-type":[{"type":"print","value":"2398-7340"}],"subject":[]}}