{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"01","oa_version":"None","date_updated":"2023-02-09T11:28:52Z","quality_controlled":"1","doi":"10.1109/SFCS.1998.743510","publication":"Proceedings of the 39th Annual Symposium on Foundations of Computer Science","scopus_import":"1","page":"596-605","date_published":"1998-09-01T00:00:00Z","abstract":[{"lang":"eng","text":"We consider the parametric minimum spanning tree problem, in which we are given a graph with edge weights that are linear functions of a parameter /spl lambda/ and wish to compute the sequence of minimum spanning trees generated as /spl lambda/ varies. We also consider the kinetic minimum spanning tree problem, in which /spl lambda/ represents time and the graph is subject in addition to changes such as edge insertions, deletions, and modifications of the weight functions as time progresses. We solve both problems in time O(n/sup 2/3/log/sup 4/3/) per combinatorial change in the tree (or randomized O(n/sup 2/3/log/sup 4/3/ n) per change). Our time bounds reduce to O(n/sup 1/2/log/sup 3/2/ n) per change (O(n/sup 1/2/log n) randomized) for planar graphs or other minor-closed families of graphs, and O(n/sup 1/4/log/sup 3/2/ n) per change (O(n/sup 1/4/ log n) randomized) for planar graphs with weight changes but no insertions or deletions."}],"title":"Parametric and kinetic minimum spanning trees","publication_status":"published","month":"09","publication_identifier":{"isbn":["0-8186-9172-7"],"issn":["0272-5428"]},"language":[{"iso":"eng"}],"author":[{"full_name":"Agarwal, P. K.","last_name":"Agarwal","first_name":"P. K."},{"full_name":"EppsteinL. J. Guibas, D.","last_name":"EppsteinL. J. Guibas","first_name":"D."},{"first_name":"Monika H","orcid":"0000-0002-5008-6530","full_name":"Henzinger, Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","last_name":"Henzinger"}],"article_processing_charge":"No","status":"public","date_created":"2022-07-28T07:21:34Z","extern":"1","_id":"11682","conference":{"end_date":"1998-11-11","location":"Palo Alto, CA, United States","name":"Annual IEEE Symposium on Foundations of Computer Science","start_date":"1998-11-08"},"type":"conference","citation":{"chicago":"Agarwal, P. K., D. EppsteinL. J. Guibas, and Monika H Henzinger. “Parametric and Kinetic Minimum Spanning Trees.” In <i>Proceedings of the 39th Annual Symposium on Foundations of Computer Science</i>, 596–605, 1998. <a href=\"https://doi.org/10.1109/SFCS.1998.743510\">https://doi.org/10.1109/SFCS.1998.743510</a>.","ista":"Agarwal PK, EppsteinL. J. Guibas D, Henzinger MH. 1998. Parametric and kinetic minimum spanning trees. Proceedings of the 39th Annual Symposium on Foundations of Computer Science. Annual IEEE Symposium on Foundations of Computer Science, 596–605.","apa":"Agarwal, P. K., EppsteinL. J. Guibas, D., &#38; Henzinger, M. H. (1998). Parametric and kinetic minimum spanning trees. In <i>Proceedings of the 39th Annual Symposium on Foundations of Computer Science</i> (pp. 596–605). Palo Alto, CA, United States. <a href=\"https://doi.org/10.1109/SFCS.1998.743510\">https://doi.org/10.1109/SFCS.1998.743510</a>","short":"P.K. Agarwal, D. EppsteinL. J. Guibas, M.H. Henzinger, in:, Proceedings of the 39th Annual Symposium on Foundations of Computer Science, 1998, pp. 596–605.","ieee":"P. K. Agarwal, D. EppsteinL. J. Guibas, and M. H. Henzinger, “Parametric and kinetic minimum spanning trees,” in <i>Proceedings of the 39th Annual Symposium on Foundations of Computer Science</i>, Palo Alto, CA, United States, 1998, pp. 596–605.","ama":"Agarwal PK, EppsteinL. J. Guibas D, Henzinger MH. Parametric and kinetic minimum spanning trees. In: <i>Proceedings of the 39th Annual Symposium on Foundations of Computer Science</i>. ; 1998:596-605. doi:<a href=\"https://doi.org/10.1109/SFCS.1998.743510\">10.1109/SFCS.1998.743510</a>","mla":"Agarwal, P. K., et al. “Parametric and Kinetic Minimum Spanning Trees.” <i>Proceedings of the 39th Annual Symposium on Foundations of Computer Science</i>, 1998, pp. 596–605, doi:<a href=\"https://doi.org/10.1109/SFCS.1998.743510\">10.1109/SFCS.1998.743510</a>."},"year":"1998"}