{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,1,24]],"date-time":"2023-01-24T01:52:09Z","timestamp":1674525129574},"reference-count":13,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2005,2]]},"abstract":"<jats:p> A k-forward numbering of a graph is a labeling of the nodes with integers such that each node has less than k neighbors whose labels are equal or larger. Distributed algorithms that reach a legitimate state, starting from any illegitimate state, are called self-stabilizing. We obtain three self-stabilizing (s-s) algorithms for finding a k-forward numbering, provided one exists. One such algorithm also finds the k-height numbering of graph, generalizing s-s algorithms by Bruell et al. [4] and Antonoiu et al. [1] for finding the center of a tree. Another k-forward numbering algorithm runs in polynomial time. The motivation of k-forward numberings is to obtain new s-s graph coloring algorithms. We use a k-forward numbering algorithm to obtain an s-s algorithm that is more general than previous coloring algorithms in the literature, and which k-colors any graph having a k-forward numbering. Special cases of the algorithm 6-color planar graphs, thus generalizing an s-s algorithm by Ghosh and Karaata [13], as well as 2-color trees and 3-color series-parallel graphs. We discuss how our s-s algorithms can be extended to the synchronous model. <\/jats:p>","DOI":"10.1142\/s012905410500284x","type":"journal-article","created":{"date-parts":[[2005,3,14]],"date-time":"2005-03-14T08:00:11Z","timestamp":1110787211000},"page":"19-36","source":"Crossref","is-referenced-by-count":7,"title":["SELF-STABILIZING ALGORITHMS FOR ORDERINGS AND COLORINGS"],"prefix":"10.1142","volume":"16","author":[{"given":"WAYNE","family":"GODDARD","sequence":"first","affiliation":[{"name":"Department of Computer Science,  Clemson University, Clemson, SC 29634-0974, USA"}]},{"given":"STEPHEN T.","family":"HEDETNIEMI","sequence":"additional","affiliation":[{"name":"Department of Computer Science,  Clemson University, Clemson, SC 29634-0974, USA"}]},{"given":"DAVID P.","family":"JACOBS","sequence":"additional","affiliation":[{"name":"Department of Computer Science,  Clemson University, Clemson, SC 29634-0974, USA"}]},{"given":"PRADIP K.","family":"SRIMANI","sequence":"additional","affiliation":[{"name":"Department of Computer Science,  Clemson University, Clemson, SC 29634-0974, USA"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1080\/10637199708915620"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(89)90031-0"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539798427156"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1137\/0608044"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1145\/361179.361202"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/BF01843566"},{"key":"rf9","volume":"3","author":"Dolev S.","journal-title":"Chicago Journal of Theoretical Computer Science"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/6156.001.0001"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1007\/BF02278856"},{"key":"rf14","unstructured":"M.\u00a0Gradinariu and S.\u00a0Tixeuil, 4th International Conference On Principles Of Distributed Systems, OPODIS'2000 (Studia Informatica Universalis, 2000)\u00a0pp. 55\u201370."},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-001-0052-4"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0190(03)00299-0"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1002\/9781118032497"}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S012905410500284X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T15:26:50Z","timestamp":1565191610000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S012905410500284X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,2]]},"references-count":13,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2005,2]]}},"alternative-id":["10.1142\/S012905410500284X"],"URL":"https:\/\/doi.org\/10.1142\/s012905410500284x","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,2]]}}}