{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T21:23:23Z","timestamp":1648675403530},"reference-count":3,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2012,3]]},"abstract":"<jats:p> A novel iterative algorithm of calculating the exact transitive closure of a parametrized graph being represented by a union of simple affine integer tuple relations is presented. When it is not possible to calculate exact transitive closure, the algorithm produces its upper bound. To calculate the transitive closure of the union of all simple relations, the algorithm recognizes the class of each simple relations, calculates its exact transitive closure, forms the union of calculated transitive closures, and applies this union in an iterative procedure. Results of experiments aimed at the comparison of the effectiveness of the presented algorithm with those of related ones are outlined and discussed. <\/jats:p>","DOI":"10.1142\/s1793830912500115","type":"journal-article","created":{"date-parts":[[2012,4,9]],"date-time":"2012-04-09T21:24:02Z","timestamp":1334006642000},"page":"1250011","source":"Crossref","is-referenced-by-count":0,"title":["AN ITERATIVE ALGORITHM OF COMPUTING THE TRANSITIVE CLOSURE OF A UNION OF PARAMETRIZED AFFINE INTEGER TUPLE RELATIONS"],"prefix":"10.1142","volume":"04","author":[{"given":"WLODZIMIERZ","family":"BIELECKI","sequence":"first","affiliation":[{"name":"Technical University of Szczecin, ul. Zolnierska 49, Szczecin, Poland"}]},{"given":"TOMASZ","family":"KLIMEK","sequence":"additional","affiliation":[{"name":"Technical University of Szczecin, ul. Zolnierska 49, Szczecin, Poland"}]},{"given":"MAREK","family":"PALKOWSKI","sequence":"additional","affiliation":[{"name":"Technical University of Szczecin, ul. Zolnierska 49, Szczecin, Poland"}]},{"given":"ANNA","family":"BELETSKA","sequence":"additional","affiliation":[{"name":"INRIA Saclay, Parc Club Universite, 3, rue J. Rostand, 91893 Orsay Cedex, France"}]}],"member":"219","published-online":{"date-parts":[[2012,4,13]]},"reference":[{"key":"rf5","volume":"55","author":"Bielecki W.","journal-title":"Meas. Automat. Monit."},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/j.endm.2009.03.002"},{"key":"rf10","doi-asserted-by":"crossref","unstructured":"W.\u00a0Kelly, Transitive Clousure of Infinite Graphs and its Applications, Languages and Compilers for Parallel Computing (Springer, 1996)\u00a0pp. 126\u2013140.","DOI":"10.1007\/BFb0014196"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830912500115","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T13:53:45Z","timestamp":1565186025000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830912500115"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,3]]},"references-count":3,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2012,4,13]]},"published-print":{"date-parts":[[2012,3]]}},"alternative-id":["10.1142\/S1793830912500115"],"URL":"https:\/\/doi.org\/10.1142\/s1793830912500115","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,3]]}}}