Pub Date : 2014-11-01DOI: 10.4230/LIPIcs.STACS.2013.8
F. Fomin, Yngve Villanger
Abstract Minimum Fill-in is a fundamental and classical problem arising in sparse matrix computations. In terms of graphs it can be formulated as a problem of finding a triangulation of a given graph with the minimum number of edges. In this paper, we study the parameterized complexity of local search for the Minimum Fill-in problem in the following form: Given a triangulation H of a graph G, is there a better triangulation, i.e. triangulation with less edges than H, within a given distance from H? We prove that this problem is fixed-parameter tractable (FPT) being parameterized by the distance from the initial triangulation, by providing an algorithm that in time f ( k ) | G | O ( 1 ) decides if a better triangulation of G can be obtained by swapping at most k edges of H. Our result adds Minimum Fill-in to the list of very few problems for which local search is known to be FPT.
最小填充是稀疏矩阵计算中的一个基本问题和经典问题。就图而言，它可以被表述为一个用最小边数找到给定图的三角剖分问题。本文以如下形式研究最小填充问题局部搜索的参数化复杂度:给定图G的一个三角剖分H，在距H的给定距离内是否存在比H更优的三角剖分，即边数少于H的三角剖分?通过提供一种算法，在时间f (k) | G | O(1)决定是否可以通过交换h的最多k条边来获得G的更好的三角剖分，我们证明了该问题是由与初始三角剖分的距离参数化的固定参数可处理(FPT)问题。我们的结果将最小填充添加到已知局部搜索为FPT的极少数问题列表中。
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Pub Date : 2012-06-21DOI: 10.1007/978-3-642-33293-7_11
F. Fomin, B. Jansen, Michal Pilipczuk
{"title":"Preprocessing subgraph and minor problems: When does a small vertex cover help?","authors":"F. Fomin, B. Jansen, Michal Pilipczuk","doi":"10.1007/978-3-642-33293-7_11","DOIUrl":"https://doi.org/10.1007/978-3-642-33293-7_11","url":null,"abstract":"","PeriodicalId":346691,"journal":{"name":"Journal of computer and system sciences (Print)","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115435454","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2010-12-15DOI: 10.1007/978-3-642-17514-5_6
E. D. Giacomo, W. Didimo, G. Liotta, H. Meijer
{"title":"Drawing a tree as a minimum spanning tree approximation","authors":"E. D. Giacomo, W. Didimo, G. Liotta, H. Meijer","doi":"10.1007/978-3-642-17514-5_6","DOIUrl":"https://doi.org/10.1007/978-3-642-17514-5_6","url":null,"abstract":"","PeriodicalId":346691,"journal":{"name":"Journal of computer and system sciences (Print)","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122072862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2009-12-04DOI: 10.1007/978-3-642-11409-0_8
M. Fellows, Jiong Guo, Iyad A. Kanj
{"title":"The parameterized complexity of some minimum label problems","authors":"M. Fellows, Jiong Guo, Iyad A. Kanj","doi":"10.1007/978-3-642-11409-0_8","DOIUrl":"https://doi.org/10.1007/978-3-642-11409-0_8","url":null,"abstract":"","PeriodicalId":346691,"journal":{"name":"Journal of computer and system sciences (Print)","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126849695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2009-07-20DOI: 10.1007/978-3-642-10631-6_29
F. Fomin, Serge Gaspers, Saket Saurabh, Stéphan Thomassé
{"title":"A linear vertex kernel for maximum internal spanning tree","authors":"F. Fomin, Serge Gaspers, Saket Saurabh, Stéphan Thomassé","doi":"10.1007/978-3-642-10631-6_29","DOIUrl":"https://doi.org/10.1007/978-3-642-10631-6_29","url":null,"abstract":"","PeriodicalId":346691,"journal":{"name":"Journal of computer and system sciences (Print)","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134270052","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2009-03-05DOI: 10.1007/978-3-642-02882-3_5
Nathann Cohen, F. Fomin, G. Gutin, Eun Jung Kim, Saket Saurabh, Anders Yeo
{"title":"Algorithm for finding k-vertex out-trees and its application to k-internal out-branching problem","authors":"Nathann Cohen, F. Fomin, G. Gutin, Eun Jung Kim, Saket Saurabh, Anders Yeo","doi":"10.1007/978-3-642-02882-3_5","DOIUrl":"https://doi.org/10.1007/978-3-642-02882-3_5","url":null,"abstract":"","PeriodicalId":346691,"journal":{"name":"Journal of computer and system sciences (Print)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126935932","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2008-09-15DOI: 10.1007/978-3-540-87744-8_2
L. Valiant
{"title":"A bridging model for multi-core computing","authors":"L. Valiant","doi":"10.1007/978-3-540-87744-8_2","DOIUrl":"https://doi.org/10.1007/978-3-540-87744-8_2","url":null,"abstract":"","PeriodicalId":346691,"journal":{"name":"Journal of computer and system sciences (Print)","volume":"92 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131289032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2008-07-07DOI: 10.1007/978-3-540-70575-8_3
David Buchfuhrer, C. Umans
{"title":"The complexity of Boolean formula minimization","authors":"David Buchfuhrer, C. Umans","doi":"10.1007/978-3-540-70575-8_3","DOIUrl":"https://doi.org/10.1007/978-3-540-70575-8_3","url":null,"abstract":"","PeriodicalId":346691,"journal":{"name":"Journal of computer and system sciences (Print)","volume":"143 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116357784","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2008-07-07DOI: 10.1007/978-3-540-70575-8_49
F. Dragan, F. Fomin, P. Golovach
{"title":"Spanners in sparse graphs","authors":"F. Dragan, F. Fomin, P. Golovach","doi":"10.1007/978-3-540-70575-8_49","DOIUrl":"https://doi.org/10.1007/978-3-540-70575-8_49","url":null,"abstract":"","PeriodicalId":346691,"journal":{"name":"Journal of computer and system sciences (Print)","volume":"144 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123266493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2007-08-15DOI: 10.1007/978-3-540-73951-7_37
Jianer Chen, F. Fomin, Yang Liu, Songjian Lu, Yngve Villanger
{"title":"Improved algorithms for feedback vertex set problems","authors":"Jianer Chen, F. Fomin, Yang Liu, Songjian Lu, Yngve Villanger","doi":"10.1007/978-3-540-73951-7_37","DOIUrl":"https://doi.org/10.1007/978-3-540-73951-7_37","url":null,"abstract":"","PeriodicalId":346691,"journal":{"name":"Journal of computer and system sciences (Print)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129157964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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