{"title":"凸字、算法和匹配","authors":"Steven Kelk, Ruben Meuwese, Stephan Wagner","doi":"10.1137/21m1463999","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 380-411, March 2024. <br/> Abstract. Phylogenetic trees are used to model evolution: leaves are labeled to represent contemporary species (“taxa”), and interior vertices represent extinct ancestors. Informally, convex characters are measurements on the contemporary species in which the subset of species (both contemporary and extinct) that share a given state form a connected subtree. Kelk and Stamoulis [Adv. Appl. Math., 84 (2017), pp. 34–46] showed how to efficiently count, list, and sample certain restricted subfamilies of convex characters, and algorithmic applications were given. We continue this work in a number of directions. First, we show how combining the enumeration of convex characters with existing parameterized algorithms can be used to speed up exponential-time algorithms for the maximum agreement forest problem in phylogenetics. Second, we revisit the quantity [math], defined as the number of convex characters on [math] in which each state appears on at least 2 taxa. We use this to give an algorithm with running time [math], where [math] is the golden ratio and [math] is the number of taxa in the input trees for computation of maximum parsimony distance on two state characters. By further restricting the characters counted by [math] we open an interesting bridge to the literature on enumeration of matchings. By crossing this bridge we improve the running time of the aforementioned parsimony distance algorithm to [math] and obtain a number of new results in themselves relevant to enumeration of matchings on at most binary trees.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":"212 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Convex Characters, Algorithms, and Matchings\",\"authors\":\"Steven Kelk, Ruben Meuwese, Stephan Wagner\",\"doi\":\"10.1137/21m1463999\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 380-411, March 2024. <br/> Abstract. Phylogenetic trees are used to model evolution: leaves are labeled to represent contemporary species (“taxa”), and interior vertices represent extinct ancestors. Informally, convex characters are measurements on the contemporary species in which the subset of species (both contemporary and extinct) that share a given state form a connected subtree. Kelk and Stamoulis [Adv. Appl. Math., 84 (2017), pp. 34–46] showed how to efficiently count, list, and sample certain restricted subfamilies of convex characters, and algorithmic applications were given. We continue this work in a number of directions. First, we show how combining the enumeration of convex characters with existing parameterized algorithms can be used to speed up exponential-time algorithms for the maximum agreement forest problem in phylogenetics. Second, we revisit the quantity [math], defined as the number of convex characters on [math] in which each state appears on at least 2 taxa. We use this to give an algorithm with running time [math], where [math] is the golden ratio and [math] is the number of taxa in the input trees for computation of maximum parsimony distance on two state characters. By further restricting the characters counted by [math] we open an interesting bridge to the literature on enumeration of matchings. By crossing this bridge we improve the running time of the aforementioned parsimony distance algorithm to [math] and obtain a number of new results in themselves relevant to enumeration of matchings on at most binary trees.\",\"PeriodicalId\":49530,\"journal\":{\"name\":\"SIAM Journal on Discrete Mathematics\",\"volume\":\"212 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-01-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Journal on Discrete Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/21m1463999\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/21m1463999","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 380-411, March 2024. Abstract. Phylogenetic trees are used to model evolution: leaves are labeled to represent contemporary species (“taxa”), and interior vertices represent extinct ancestors. Informally, convex characters are measurements on the contemporary species in which the subset of species (both contemporary and extinct) that share a given state form a connected subtree. Kelk and Stamoulis [Adv. Appl. Math., 84 (2017), pp. 34–46] showed how to efficiently count, list, and sample certain restricted subfamilies of convex characters, and algorithmic applications were given. We continue this work in a number of directions. First, we show how combining the enumeration of convex characters with existing parameterized algorithms can be used to speed up exponential-time algorithms for the maximum agreement forest problem in phylogenetics. Second, we revisit the quantity [math], defined as the number of convex characters on [math] in which each state appears on at least 2 taxa. We use this to give an algorithm with running time [math], where [math] is the golden ratio and [math] is the number of taxa in the input trees for computation of maximum parsimony distance on two state characters. By further restricting the characters counted by [math] we open an interesting bridge to the literature on enumeration of matchings. By crossing this bridge we improve the running time of the aforementioned parsimony distance algorithm to [math] and obtain a number of new results in themselves relevant to enumeration of matchings on at most binary trees.
期刊介绍:
SIAM Journal on Discrete Mathematics (SIDMA) publishes research papers of exceptional quality in pure and applied discrete mathematics, broadly interpreted. The journal''s focus is primarily theoretical rather than empirical, but the editors welcome papers that evolve from or have potential application to real-world problems. Submissions must be clearly written and make a significant contribution.
Topics include but are not limited to:
properties of and extremal problems for discrete structures
combinatorial optimization, including approximation algorithms
algebraic and enumerative combinatorics
coding and information theory
additive, analytic combinatorics and number theory
combinatorial matrix theory and spectral graph theory
design and analysis of algorithms for discrete structures
discrete problems in computational complexity
discrete and computational geometry
discrete methods in computational biology, and bioinformatics
probabilistic methods and randomized algorithms.