{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T20:56:55Z","timestamp":1648673815205},"reference-count":4,"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":[[2015,12]]},"abstract":"<jats:p> For a connected graph, a vertex separator is a set of vertices whose removal creates at least two components and a minimum vertex separator is a vertex separator of least cardinality. The vertex connectivity refers to the size of a minimum vertex separator. For a connected graph G with vertex connectivity [Formula: see text], the connectivity augmentation refers to a set S of edges whose augmentation to G increases its vertex connectivity by one. A minimum connectivity augmentation of G is the one in which S is minimum. In this paper, we focus our attention on biconnectivity augmentation for trees. Towards this end, we present a new sequential algorithm for biconnectivity augmentation in trees by simplifying the algorithm reported in [1]. The simplicity is achieved with the help of edge contraction tool. This tool helps us in getting a recursive subproblem preserving all connectivity information. Subsequently, we present a parallel algorithm to obtain a minimum biconnectivity augmentation set in trees. Our parallel algorithm essentially follows the overall structure of sequential algorithm. Our implementation is based on CREW PRAM model with [Formula: see text] processors, where [Formula: see text] refers to the maximum degree of a tree. We also show that our parallel algorithm is optimal with a processor-time product of [Formula: see text] where n is the number of vertices of a tree. <\/jats:p>","DOI":"10.1142\/s0129626415500103","type":"journal-article","created":{"date-parts":[[2015,12,30]],"date-time":"2015-12-30T21:13:35Z","timestamp":1451510015000},"page":"1550010","source":"Crossref","is-referenced-by-count":1,"title":["Simpler Sequential and Parallel Biconnectivity Augmentation in Trees"],"prefix":"10.1142","volume":"25","author":[{"given":"Surabhi","family":"Jain","sequence":"first","affiliation":[{"name":"Department of Computer Science and Engineering, Indian Institute of Information Technology, Design and Manufacturing, Kancheepuram, Chennai, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"N.","family":"Sadagopan","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, Indian Institute of Information Technology, Design and Manufacturing, Kancheepuram, Chennai, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2015,12,30]]},"reference":[{"key":"p_2","first-page":"653","volume":"5","author":"Eswaran K. P.","year":"1976","journal-title":"Computing"},{"key":"p_3","first-page":"889","volume":"22","author":"Hsu T. S.","year":"1993","journal-title":"Computing"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1006\/jagm.2000.1077"},{"key":"p_8","first-page":"1","volume":"18","author":"Kriesell M.","year":"2002","journal-title":"Combinatorics"}],"container-title":["Parallel Processing Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129626415500103","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T13:52:07Z","timestamp":1565185927000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129626415500103"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,12]]},"references-count":4,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2015,12,30]]},"published-print":{"date-parts":[[2015,12]]}},"alternative-id":["10.1142\/S0129626415500103"],"URL":"https:\/\/doi.org\/10.1142\/s0129626415500103","relation":{},"ISSN":["0129-6264","1793-642X"],"issn-type":[{"value":"0129-6264","type":"print"},{"value":"1793-642X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,12]]}}}