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Improved Algorithms and Combinatorial Bounds for Independent Feedback Vertex Set 独立反馈顶点集的改进算法与组合界
International Symposium on Parameterized and Exact Computation Pub Date : 2017-01-31 DOI: 10.4230/LIPIcs.IPEC.2016.2
A. Agrawal, Sushmita Gupta, Saket Saurabh, Roohani Sharma
{"title":"Improved Algorithms and Combinatorial Bounds for Independent Feedback Vertex Set","authors":"A. Agrawal, Sushmita Gupta, Saket Saurabh, Roohani Sharma","doi":"10.4230/LIPIcs.IPEC.2016.2","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2016.2","url":null,"abstract":"In this paper we study the \"independent\" version of the classic Feedback Vertex Set problem in the realm of parameterized algorithms and moderately exponential time algorithms. More precisely, we study the Independent Feedback Vertex Set problem, where we are given an undirected graph G on n vertices and a positive integer k, and the objective is to check if there is an independent feedback vertex set of size at most k. A set S subseteq V(G) is called an independent feedback vertex set (ifvs) if S is an independent set and GS is a forest. In this paper we design two deterministic exact algorithms for Independent Feedback Vertex Set with running times O*(4.1481^k) and O*(1.5981^n). In fact, the algorithm with O*(1.5981^n) running time finds the smallest sized ifvs, if an ifvs exists. Both the algorithms are based on interesting measures and improve the best known algorithms for the problem in their respective domains. In particular, the algorithm with running time O*(4.1481^k) is an improvement over the previous algorithm that ran in time O*(5^k). On the other hand, the algorithm with running time O*(1.5981^n) is the first moderately exponential time algorithm that improves over the naive algorithm that enumerates all the subsets of V(G). Additionally, we show that the number of minimal ifvses in any graph on n vertices is upper bounded by 1.7485^n.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128374191","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}
引用次数: 16
Computing Graph Distances Parameterized by Treewidth and Diameter 计算由树宽和直径参数化的图距离
International Symposium on Parameterized and Exact Computation Pub Date : 2017-01-31 DOI: 10.4230/LIPIcs.IPEC.2016.16
T. Husfeldt
{"title":"Computing Graph Distances Parameterized by Treewidth and Diameter","authors":"T. Husfeldt","doi":"10.4230/LIPIcs.IPEC.2016.16","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2016.16","url":null,"abstract":"We show that the eccentricity of every vertex in an undirected graph on n vertices can be computed in time n exp O(k*log(d)), where k is the treewidth of the graph and d is the diameter. This means that the diameter and the radius of the graph can be computed in the same time. In particular, if the diameter is constant, it can be determined in time n*exp(O(k)). This result matches a recent hardness result by Abboud, Vassilevska Williams, and Wang [SODA 2016] that shows that under the Strong Exponential Time Hypothesis of Impagliazzo, Paturi, and Zane [J. Comp. Syst. Sc., 2001], for any epsilon > 0, no algorithm with running time n^{2-epsilon}*exp(o(k)) can distinguish between graphs with diameter 2 and 3.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121560935","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}
引用次数: 18
A Fast Parameterized Algorithm for Co-Path Set 一种快速参数化共径集算法
International Symposium on Parameterized and Exact Computation Pub Date : 2016-03-14 DOI: 10.4230/LIPIcs.IPEC.2016.28
Blair D. Sullivan, Andrew van der Poel
{"title":"A Fast Parameterized Algorithm for Co-Path Set","authors":"Blair D. Sullivan, Andrew van der Poel","doi":"10.4230/LIPIcs.IPEC.2016.28","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2016.28","url":null,"abstract":"The k-CO-PATH SET problem asks, given a graph G and a positive integer k, whether one can delete k edges from G so that the remainder is a collection of disjoint paths. We give a linear-time fpt algorithm with complexity O^*(1.588^k) for deciding k-CO-PATH SET, significantly improving the previously best known O^*(2.17^k) of Feng, Zhou, and Wang (2015). Our main tool is a new O^*(4^{tw(G)}) algorithm for CO-PATH SET using the Cut&Count framework, where tw(G) denotes treewidth. In general graphs, we combine this with a branching algorithm which refines a 6k-kernel into reduced instances, which we prove have bounded treewidth.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115080042","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}
引用次数: 1
Definability Equals Recognizability for $k$-Outerplanar Graphs $k$-外平面图的可定义性等于可识别性
International Symposium on Parameterized and Exact Computation Pub Date : 2015-09-28 DOI: 10.4230/LIPIcs.IPEC.2015.175
L. Jaffke, H. Bodlaender
{"title":"Definability Equals Recognizability for $k$-Outerplanar Graphs","authors":"L. Jaffke, H. Bodlaender","doi":"10.4230/LIPIcs.IPEC.2015.175","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2015.175","url":null,"abstract":"One of the most famous algorithmic meta-theorems states that every graph property that can be defined by a sentence in counting monadic second order logic (CMSOL) can be checked in linear time for graphs of bounded treewidth, which is known as Courcelle's Theorem. These algorithms are constructed as finite state tree automata, and hence every CMSOL-definable graph property is recognizable. Courcelle also conjectured that the converse holds, i.e., every recognizable graph property is definable in CMSOL for graphs of bounded treewidth. We prove this conjecture for k-outerplanar graphs, which are known to have treewidth at most 3k-1.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129434407","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}
引用次数: 7
Practical Algorithms for Linear Boolean-width 线性布尔宽度的实用算法
International Symposium on Parameterized and Exact Computation Pub Date : 2015-09-25 DOI: 10.4230/LIPIcs.IPEC.2015.187
C. B. T. Brinke, Frank J. P. van Houten, H. Bodlaender
{"title":"Practical Algorithms for Linear Boolean-width","authors":"C. B. T. Brinke, Frank J. P. van Houten, H. Bodlaender","doi":"10.4230/LIPIcs.IPEC.2015.187","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2015.187","url":null,"abstract":"In this paper, we give a number of new exact algorithms and heuristics to compute linear boolean decompositions, and experimentally evaluate these algorithms. The experimental evaluation shows that significant improvements can be made with respect to running time without increasing the width of the generated decompositions. We also evaluated dynamic programming algorithms on linear boolean decompositions for several vertex subset problems. This evaluation shows that such algorithms are often much faster (up to several orders of magnitude) compared to theoretical worst case bounds.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"89 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114222441","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}
引用次数: 1
Bidimensionality and Parameterized Algorithms (Invited Talk) 二维与参数化算法(特邀演讲)
International Symposium on Parameterized and Exact Computation Pub Date : 2015-09-16 DOI: 10.4230/LIPIcs.IPEC.2015.1
D. Thilikos
{"title":"Bidimensionality and Parameterized Algorithms (Invited Talk)","authors":"D. Thilikos","doi":"10.4230/LIPIcs.IPEC.2015.1","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2015.1","url":null,"abstract":"We provide an exposition of the main results of the theory of bidimensionality in parameterized algorithm design. This theory applies to graph problems that are bidimensional in the sense that i) their solution value is not increasing when we take minors or contractions of the input graph and ii) their solution value for the (triangulated) (k x k)-grid graph grows as a quadratic function of k. Under certain additional conditions, mainly of logical and combinatorial nature, such problems admit subexponential parameterized algorithms and linear kernels when their inputs are restricted to certain topologically defined graph classes. We provide all formal definitions and concepts in order to present these results in a rigorous way and in their latest update.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115329432","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}
引用次数: 6
Variants of Plane Diameter Completion 平面直径补全的变体
International Symposium on Parameterized and Exact Computation Pub Date : 2015-09-02 DOI: 10.4230/LIPIcs.IPEC.2015.30
P. Golovach, Clément Requilé, D. Thilikos
{"title":"Variants of Plane Diameter Completion","authors":"P. Golovach, Clément Requilé, D. Thilikos","doi":"10.4230/LIPIcs.IPEC.2015.30","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2015.30","url":null,"abstract":"The {sc Plane Diameter Completion} problem asks, given a plane graph $G$ and a positive integer $d$, if it is a spanning subgraph of a plane graph $H$ that has diameter at most $d$. We examine two variants of this problem where the input comes with another parameter $k$. In the first variant, called BPDC, $k$ upper bounds the total number of edges to be added and in the second, called BFPDC, $k$ upper bounds the number of additional edges per face. We prove that both problems are {sf NP}-complete, the first even for 3-connected graphs of face-degree at most 4 and the second even when $k=1$ on 3-connected graphs of face-degree at most 5. In this paper we give parameterized algorithms for both problems that run in $O(n^{3})+2^{2^{O((kd)^2log d)}}cdot n$ steps.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115079348","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}
引用次数: 1
Parameterized lower bound and improved kernel for Diamond-free Edge Deletion 无菱形边删除的参数化下界和改进核
International Symposium on Parameterized and Exact Computation Pub Date : 2015-07-31 DOI: 10.4230/LIPIcs.IPEC.2015.365
R. B. Sandeep, N. Sivadasan
{"title":"Parameterized lower bound and improved kernel for Diamond-free Edge Deletion","authors":"R. B. Sandeep, N. Sivadasan","doi":"10.4230/LIPIcs.IPEC.2015.365","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2015.365","url":null,"abstract":"A diamond is a graph obtained by removing an edge from a complete graph on four vertices. A graph is diamond-free if it does not contain an induced diamond. The Diamond-free Edge Deletion problem asks to find whether there exist at most k edges in the input graph whose deletion results in a diamond-free graph. The problem was proved to be NP-complete and a polynomial kernel of O(k^4) vertices was found by Fellows et. al. (Discrete Optimization, 2011). \u0000 \u0000In this paper, we give an improved kernel of O(k^3) vertices for Diamond-free Edge Deletion. We give an alternative proof of the NP-completeness of the problem and observe that it cannot be solved in time 2^{o(k)} * n^{O(1)}, unless the Exponential Time Hypothesis fails.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127023211","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}
引用次数: 17
Fast Biclustering by Dual Parameterization 基于双参数化的快速双聚类
International Symposium on Parameterized and Exact Computation Pub Date : 2015-07-29 DOI: 10.4230/LIPIcs.IPEC.2015.402
Pål Grønås Drange, F. Reidl, Fernando Sánchez Villaamil, S. Sikdar
{"title":"Fast Biclustering by Dual Parameterization","authors":"Pål Grønås Drange, F. Reidl, Fernando Sánchez Villaamil, S. Sikdar","doi":"10.4230/LIPIcs.IPEC.2015.402","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2015.402","url":null,"abstract":"We study two clustering problems, Starforest Editing, the problem of adding and deleting edges to obtain a disjoint union of stars, and the generalization Bicluster Editing. We show that, in addition to being NP-hard, none of the problems can be solved in subexponential time unless the exponential time hypothesis fails. \u0000Misra, Panolan, and Saurabh (MFCS 2013) argue that introducing a bound on the number of connected components in the solution should not make the problem easier: In particular, they argue that the subexponential time algorithm for editing to a fixed number of clusters (p-Cluster Editing) by Fomin et al. (J. Comput. Syst. Sci., 80(7) 2014) is an exception rather than the rule. Here, p is a secondary parameter, bounding the number of components in the solution. \u0000However, upon bounding the number of stars or bicliques in the solution, we obtain algorithms which run in time $2^{5 sqrt{pk}} + O(n+m)$ for p-Starforest Editing and $2^{O(p sqrt{k} log(pk))} + O(n+m)$ for p-Bicluster Editing. We obtain a similar result for the more general case of t-Partite p-Cluster Editing. This is subexponential in k for fixed number of clusters, since p is then considered a constant. \u0000Our results even out the number of multivariate subexponential time algorithms and give reasons to believe that this area warrants further study.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128332807","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}
引用次数: 11
Parameterized Complexity of Graph Constraint Logic 图约束逻辑的参数化复杂度
International Symposium on Parameterized and Exact Computation Pub Date : 2015-07-21 DOI: 10.4230/LIPIcs.IPEC.2015.282
Tom C. van der Zanden
{"title":"Parameterized Complexity of Graph Constraint Logic","authors":"Tom C. van der Zanden","doi":"10.4230/LIPIcs.IPEC.2015.282","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2015.282","url":null,"abstract":"Graph constraint logic is a framework introduced by Hearn and Demaine, which provides several problems that are often a convenient starting point for reductions. We study the parameterized complexity of Constraint Graph Satisfiability and both bounded and unbounded versions of Nondeterministic Constraint Logic (NCL) with respect to solution length, treewidth and maximum degree of the underlying constraint graph as parameters. As a main result we show that restricted NCL remains PSPACE-complete on graphs of bounded bandwidth, strengthening Hearn and Demaine's framework. This allows us to improve upon existing results obtained by reduction from NCL. We show that reconfiguration versions of several classical graph problems (including independent set, feedback vertex set and dominating set) are PSPACE-complete on planar graphs of bounded bandwidth and that Rush Hour, generalized to $ktimes n$ boards, is PSPACE-complete even when $k$ is at most a constant.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125188891","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}
引用次数: 28
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