{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,2,19]],"date-time":"2023-02-19T17:08:49Z","timestamp":1676826529613},"reference-count":11,"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":[[1999,12]]},"abstract":"<jats:p> Given a set [Formula: see text] of n points in the plane such that each point in [Formula: see text] is asscociated with a nonnegative weight, we consider the problem of computing the single-source longest increasing chains among the points in [Formula: see text] This problem is a generalization of the plannar maximal layers problem. In this paper, we present a parallel algorithm that computes the single-source longest incresing chains in the plane in [Formula: see text] time using [Formula: see text] processors in the CREW PRAM computational model. We also solve a related problem of computing the all-pairs longest paths in an n-node weighted planar st-graph, in [Formula: see text] time using [Formula: see text] CREW PRAM processors. Both of our parallel algorithms are improvement over the previously best known results. <\/jats:p>","DOI":"10.1142\/s0129626499000475","type":"journal-article","created":{"date-parts":[[2003,4,25]],"date-time":"2003-04-25T13:10:49Z","timestamp":1051276249000},"page":"511-520","source":"Crossref","is-referenced-by-count":1,"title":["PARALLEL ALGORITHMS FOR LONGEST INCREASING CHAINS IN THE PLANE AND RELATED PROBLEMS"],"prefix":"10.1142","volume":"09","author":[{"given":"MIKHAIL J.","family":"ATALLAH","sequence":"first","affiliation":[{"name":"Dept. of Computer Sciences, Purdue University, West Lafayette,  IN 47907, USA"}]},{"given":"DANNY Z.","family":"CHEN","sequence":"additional","affiliation":[{"name":"Dept. of Computer Science and Engineering, University of  Notre Dame, Notre Dame, IN 46556-5637, USA"}]},{"given":"KEVIN S.","family":"KLENK","sequence":"additional","affiliation":[{"name":"Dept. of Computer Science and Engineering, University of  Notre Dame, Notre Dame, IN 46556-5637, USA"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1137\/0219066"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1142\/S0218195995000155"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01553888"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1016\/0196-6774(92)90046-F"},{"key":"p_7","first-page":"25","author":"Birkhoff G.","year":"1979","journal-title":"American Mathematical Society Colloquium Publications"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1006\/jagm.1996.0048"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1007\/BF00625277"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1007\/BF00288531"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1007\/BF02523680"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(75)90019-8"},{"key":"p_17","doi-asserted-by":"publisher","DOI":"10.1137\/0220045"}],"container-title":["Parallel Processing Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129626499000475","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T16:20:08Z","timestamp":1565108408000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129626499000475"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,12]]},"references-count":11,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[1999,12]]}},"alternative-id":["10.1142\/S0129626499000475"],"URL":"https:\/\/doi.org\/10.1142\/s0129626499000475","relation":{},"ISSN":["0129-6264","1793-642X"],"issn-type":[{"value":"0129-6264","type":"print"},{"value":"1793-642X","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,12]]}}}