{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,1]],"date-time":"2023-10-01T13:28:16Z","timestamp":1696166896279},"reference-count":0,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Parallel Process. Lett."],"published-print":{"date-parts":[[1992,12]]},"abstract":"<jats:p> In this work we address the parallel complexity of two combinatorial problems, specifically the problems of the existence and of the construction of a parity base of preassigned weight (exact parity base for short) in a 0-1 weighted, represented matroid, subject to parity conditions. We prove that these problems lie in the parallel complexity class RNC <jats:sup>2<\/jats:sup>, i.e. they are solvable with one-sided error by a logspace uniform family of bounded fan-in circuits of polynomial size and quadratic logarithmic depth which receive, in addition to the problem input, a polynomial number of random input bits. We also show that the more general cases of these problems, defined over matroids weighted with integral instead of 0-1 weights, also belong to RNC <jats:sup>2<\/jats:sup>, as long as the weights are given in unary notation. As a consequence some special cases of these problems, which are of independent interest, belong to the same parallel complexity class: examples of these are the problem of the construction of a perfect matching of preassigned weight in a 0-1 weighted graph, recently addressed in [1], or that of the construction of a base of preassigned weight, in the intersection of two 0-1 weighted represented matroids. <\/jats:p>","DOI":"10.1142\/s0129626492000441","type":"journal-article","created":{"date-parts":[[2004,11,23]],"date-time":"2004-11-23T03:29:30Z","timestamp":1101180570000},"page":"301-309","source":"Crossref","is-referenced-by-count":3,"title":["CONSTRUCTING AN EXACT PARITY BASE IS IN <font>RNC<\/font><sup>2<\/sup>"],"prefix":"10.1142","volume":"02","author":[{"given":"G.","family":"GALBIATI","sequence":"first","affiliation":[{"name":"Dipartimento di Informatica e Sistemistica, Universit\u00e0 di Pavia, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"F.","family":"MAFFIOLI","sequence":"additional","affiliation":[{"name":"Dipartimento di Elettronica e Informazione, Politecnico di Milano, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"container-title":["Parallel Processing Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129626492000441","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T16:24:00Z","timestamp":1565108640000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129626492000441"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,12]]},"references-count":0,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[1992,12]]}},"alternative-id":["10.1142\/S0129626492000441"],"URL":"https:\/\/doi.org\/10.1142\/s0129626492000441","relation":{},"ISSN":["0129-6264","1793-642X"],"issn-type":[{"value":"0129-6264","type":"print"},{"value":"1793-642X","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,12]]}}}