{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article6489","name":"Fixed Parameter Polynomial Time Algorithms for Maximum Agreement and Compatible Supertrees","abstract":"Consider a set of labels $L$ and a set of trees ${mathcal T} = {\r\n {mathcal T}^{(1), {mathcal T}^{(2), ldots, {mathcal T}^{(k) $\r\n where each tree ${mathcal T}^{(i)$ is distinctly leaf-labeled by\r\n some subset of $L$. One fundamental problem is to find the biggest\r\n tree (denoted as supertree) to represent $mathcal T}$ which\r\n minimizes the disagreements with the trees in ${mathcal T}$ under\r\n certain criteria. This problem finds applications in\r\n phylogenetics, database, and data mining. In this paper, we focus\r\n on two particular supertree problems, namely, the maximum agreement\r\n supertree problem (MASP) and the maximum compatible supertree\r\n problem (MCSP). These two problems are known to be NP-hard for $k\r\n geq 3$. This paper gives the first polynomial time algorithms for\r\n both MASP and MCSP when both $k$ and the maximum degree $D$ of the\r\n trees are constant.","keywords":["Maximum agreement supertree","maximum compatible supertree"],"author":[{"@type":"Person","name":"Hoang, Viet Tung","givenName":"Viet Tung","familyName":"Hoang"},{"@type":"Person","name":"Sung, Wing-Kin","givenName":"Wing-Kin","familyName":"Sung"}],"position":32,"pageStart":361,"pageEnd":372,"dateCreated":"2008-02-06","datePublished":"2008-02-06","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by-nd\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Hoang, Viet Tung","givenName":"Viet Tung","familyName":"Hoang"},{"@type":"Person","name":"Sung, Wing-Kin","givenName":"Wing-Kin","familyName":"Sung"}],"copyrightYear":"2008","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.STACS.2008.1357","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6204","volumeNumber":1,"name":"25th International Symposium on Theoretical Aspects of Computer Science","dateCreated":"2008-02-05","datePublished":"2008-02-05","editor":[{"@type":"Person","name":"Albers, Susanne","givenName":"Susanne","familyName":"Albers"},{"@type":"Person","name":"Weil, Pascal","givenName":"Pascal","familyName":"Weil"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article6489","isPartOf":{"@type":"Periodical","@id":"#series116","name":"Leibniz International Proceedings in Informatics","issn":"1868-8969","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume6204"}}}