International Symposium on Parameterized and Exact Computation最新文献_第2页

On the Complexity of Problems on Tree-structured Graphs 关于树结构图问题的复杂性

International Symposium on Parameterized and Exact Computation Pub Date : 2022-06-23 DOI: 10.48550/arXiv.2206.11828

H. Bodlaender, C. Groenland, Hugo Jacob, Marcin Pilipczuk, Michal Pilipczuk

引用次数: 7

Twin-width VIII: delineation and win-wins 双宽八:圈定共赢

International Symposium on Parameterized and Exact Computation Pub Date : 2022-04-01 DOI: 10.48550/arXiv.2204.00722

Édouard Bonnet, Dibyayan Chakraborty, Eun Jung Kim, N. Köhler, Raul Lopes, Stéphan Thomassé

{"title":"Twin-width VIII: delineation and win-wins","authors":"Édouard Bonnet, Dibyayan Chakraborty, Eun Jung Kim, N. Köhler, Raul Lopes, Stéphan Thomassé","doi":"10.48550/arXiv.2204.00722","DOIUrl":"https://doi.org/10.48550/arXiv.2204.00722","url":null,"abstract":"We introduce the notion of delineation. A graph class $mathcal C$ is said delineated if for every hereditary closure $mathcal D$ of a subclass of $mathcal C$, it holds that $mathcal D$ has bounded twin-width if and only if $mathcal D$ is monadically dependent. An effective strengthening of delineation for a class $mathcal C$ implies that tractable FO model checking on $mathcal C$ is perfectly understood: On hereditary closures $mathcal D$ of subclasses of $mathcal C$, FO model checking is fixed-parameter tractable (FPT) exactly when $mathcal D$ has bounded twin-width. Ordered graphs [BGOdMSTT, STOC '22] and permutation graphs [BKTW, JACM '22] are effectively delineated, while subcubic graphs are not. On the one hand, we prove that interval graphs, and even, rooted directed path graphs are delineated. On the other hand, we show that segment graphs, directed path graphs, and visibility graphs of simple polygons are not delineated. In an effort to draw the delineation frontier between interval graphs (that are delineated) and axis-parallel two-lengthed segment graphs (that are not), we investigate the twin-width of restricted segment intersection classes. It was known that (triangle-free) pure axis-parallel unit segment graphs have unbounded twin-width [BGKTW, SODA '21]. We show that $K_{t,t}$-free segment graphs, and axis-parallel $H_t$-free unit segment graphs have bounded twin-width, where $H_t$ is the half-graph or ladder of height $t$. In contrast, axis-parallel $H_4$-free two-lengthed segment graphs have unbounded twin-width. Our new results, combined with the known FPT algorithm for FO model checking on graphs given with $O(1)$-sequences, lead to win-win arguments. For instance, we derive FPT algorithms for $k$-Ladder on visibility graphs of 1.5D terrains, and $k$-Independent Set on visibility graphs of simple polygons.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126696894","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: 22

Vertex Cover and Feedback Vertex Set Above and Below Structural Guarantees 结构保证之上和之下的顶点覆盖和反馈顶点集

International Symposium on Parameterized and Exact Computation Pub Date : 2022-03-11 DOI: 10.48550/arXiv.2203.05887

Leon Kellerhals, Tomohiro Koana, Pascal Kunz

引用次数: 3

XNLP-completeness for Parameterized Problems on Graphs with a Linear Structure 线性结构图上参数化问题的xnlp完备性

International Symposium on Parameterized and Exact Computation Pub Date : 2022-01-31 DOI: 10.4230/LIPIcs.IPEC.2022.8

H. Bodlaender, C. Groenland, Hugo Jacob

引用次数: 9

Long paths make pattern-counting hard, and deep trees make it harder 漫长的路径使得模式计数变得困难，而茂密的树木使其更加困难

International Symposium on Parameterized and Exact Computation Pub Date : 2021-11-05 DOI: 10.4230/LIPIcs.IPEC.2021.22

V'it Jel'inek, Michal Opler, Jakub Pek'arek

{"title":"Long paths make pattern-counting hard, and deep trees make it harder","authors":"V'it Jel'inek, Michal Opler, Jakub Pek'arek","doi":"10.4230/LIPIcs.IPEC.2021.22","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2021.22","url":null,"abstract":"We study the counting problem known as #PPM, whose input is a pair of permutations $pi$ and $tau$ (called pattern and text, respectively), and the task is to find the number of subsequences of $tau$ that have the same relative order as $pi$. A simple brute-force approach solves #PPM for a pattern of length $k$ and a text of length $n$ in time $O(n^{k+1})$, while Berendsohn, Kozma and Marx have recently shown that under the exponential time hypothesis (ETH), it cannot be solved in time $f(k) n^{o(k/log k)}$ for any function $f$. In this paper, we consider the restriction of #PPM, known as $mathcal{C}$-Pattern #PPM, where the pattern $pi$ must belong to a hereditary permutation class $mathcal{C}$. Our goal is to identify the structural properties of $mathcal{C}$ that determine the complexity of $mathcal{C}$-Pattern #PPM. We focus on two such structural properties, known as the long path property (LPP) and the deep tree property (DTP). Assuming ETH, we obtain these results: 1. If $C$ has the LPP, then $mathcal{C}$-Pattern #PPM cannot be solved in time $f(k)n^{o(sqrt{k})}$ for any function $f$, and 2. if $C$ has the DTP, then $mathcal{C}$-Pattern #PPM cannot be solved in time $f(k)n^{o(k/log^2 k)}$ for any function $f$. Furthermore, when $mathcal{C}$ is one of the so-called monotone grid classes, we show that if $mathcal{C}$ has the LPP but not the DTP, then $mathcal{C}$-Pattern #PPM can be solved in time $f(k)n^{O(sqrt k)}$. In particular, the lower bounds above are tight up to the polylog terms in the exponents.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130678467","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: 0

Anti-Factor is FPT Parameterized by Treewidth and List Size (but Counting is Hard) 反因子是由树宽和列表大小参数化的FPT(但计数很难)

International Symposium on Parameterized and Exact Computation Pub Date : 2021-10-18 DOI: 10.4230/LIPIcs.IPEC.2022.22

D. Marx, Govind S. Sankar, Philipp Schepper

{"title":"Anti-Factor is FPT Parameterized by Treewidth and List Size (but Counting is Hard)","authors":"D. Marx, Govind S. Sankar, Philipp Schepper","doi":"10.4230/LIPIcs.IPEC.2022.22","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2022.22","url":null,"abstract":"In the general AntiFactor problem, a graph $G$ is given with a set $X_vsubseteq mathbb{N}$ of forbidden degrees for every vertex $v$ and the task is to find a set $S$ of edges such that the degree of $v$ in $S$ is not in the set $X_v$. Standard techniques (dynamic programming + fast convolution) can be used to show that if $M$ is the largest forbidden degree, then the problem can be solved in time $(M+2)^kcdot n^{O(1)}$ if a tree decomposition of width $k$ is given. However, significantly faster algorithms are possible if the sets $X_v$ are sparse: our main algorithmic result shows that if every vertex has at most $x$ forbidden degrees (we call this special case AntiFactor$_x$), then the problem can be solved in time $(x+1)^{O(k)}cdot n^{O(1)}$. That is, the AntiFactor$_x$ is fixed-parameter tractable parameterized by treewidth $k$ and the maximum number $x$ of excluded degrees. Our algorithm uses the technique of representative sets, which can be generalized to the optimization version, but (as expected) not to the counting version of the problem. In fact, we show that #AntiFactor$_1$ is already #W[1]-hard parameterized by the width of the given decomposition. Moreover, we show that, unlike for the decision version, the standard dynamic programming algorithm is essentially optimal for the counting version. Formally, for a fixed nonempty set $X$, we denote by $X$-AntiFactor the special case where every vertex $v$ has the same set $X_v=X$ of forbidden degrees. We show the following lower bound for every fixed set $X$: if there is an $epsilon>0$ such that #$X$-AntiFactor can be solved in time $(max X+2-epsilon)^kcdot n^{O(1)}$ on a tree decomposition of width $k$, then the Counting Strong Exponential-Time Hypothesis (#SETH) fails.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"215 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116888693","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: 3

Fixed-Parameter Algorithms for Longest Heapable Subsequence and Maximum Binary Tree 最长可堆子序列和最大二叉树的固定参数算法

International Symposium on Parameterized and Exact Computation Pub Date : 2021-10-01 DOI: 10.4230/LIPIcs.IPEC.2020.7

Karthekeyan Chandrasekaran, Elena Grigorescu, Gabriel Istrate, Shubhang Kulkarni, Young-San Lin, Minshen Zhu

引用次数: 0

FPT Approximation for Fair Minimum-Load Clustering 公平最小负载聚类的FPT近似

International Symposium on Parameterized and Exact Computation Pub Date : 2021-07-20 DOI: 10.4230/LIPIcs.IPEC.2022.4

Sayan Bandyapadhyay, F. Fomin, P. Golovach, Nidhi Purohit, Kirill Simonov

{"title":"FPT Approximation for Fair Minimum-Load Clustering","authors":"Sayan Bandyapadhyay, F. Fomin, P. Golovach, Nidhi Purohit, Kirill Simonov","doi":"10.4230/LIPIcs.IPEC.2022.4","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2022.4","url":null,"abstract":"In this paper, we consider the Minimum-Load $k$-Clustering/Facility Location (MLkC) problem where we are given a set $P$ of $n$ points in a metric space that we have to cluster and an integer $k$ that denotes the number of clusters. Additionally, we are given a set $F$ of cluster centers in the same metric space. The goal is to select a set $Csubseteq F$ of $k$ centers and assign each point in $P$ to a center in $C$, such that the maximum load over all centers is minimized. Here the load of a center is the sum of the distances between it and the points assigned to it. Although clustering/facility location problems have a rich literature, the minimum-load objective is not studied substantially, and hence MLkC has remained a poorly understood problem. More interestingly, the problem is notoriously hard even in some special cases including the one in line metrics as shown by Ahmadian et al. [ACM Trans. Algo. 2018]. They also show APX-hardness of the problem in the plane. On the other hand, the best-known approximation factor for MLkC is $O(k)$, even in the plane. In this work, we study a fair version of MLkC inspired by the work of Chierichetti et al. [NeurIPS, 2017], which generalizes MLkC. Here the input points are colored by one of the $ell$ colors denoting the group they belong to. MLkC is the special case with $ell=1$. Considering this problem, we are able to obtain a $3$-approximation in $f(k,ell)cdot n^{O(1)}$ time. Also, our scheme leads to an improved $(1 + epsilon)$-approximation in case of Euclidean norm, and in this case, the running time depends only polynomially on the dimension $d$. Our results imply the same approximations for MLkC with running time $f(k)cdot n^{O(1)}$, achieving the first constant approximations for this problem in general and Euclidean metric spaces.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117021534","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

Towards exact structural thresholds for parameterized complexity 对参数化复杂性的精确结构阈值

International Symposium on Parameterized and Exact Computation Pub Date : 2021-07-13 DOI: 10.4230/LIPIcs.IPEC.2022.17

Falko Hegerfeld, Stefan Kratsch

{"title":"Towards exact structural thresholds for parameterized complexity","authors":"Falko Hegerfeld, Stefan Kratsch","doi":"10.4230/LIPIcs.IPEC.2022.17","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2022.17","url":null,"abstract":"Parameterized complexity seeks to use input structure to obtain faster algorithms for NP-hard problems. This has been most successful for graphs of low treewidth: Many problems admit fast algorithms relative to treewidth and many of them are optimal under SETH. Fewer such results are known for more general structure such as low clique-width and more restrictive structure such as low deletion distance to a sparse graph class. Despite these successes, such results remain\"islands'' within the realm of possible structure. Rather than adding more islands, we seek to determine the transitions between them, that is, we aim for structural thresholds where the complexity increases as input structure becomes more general. Going from deletion distance to treewidth, is a single deletion set to a graph with simple components enough to yield the same lower bound as for treewidth or does it take many disjoint separators? Going from treewidth to clique-width, how much more density entails the same complexity as clique-width? Conversely, what is the most restrictive structure that yields the same lower bound? For treewidth, we obtain both refined and new lower bounds that apply already to graphs with a single separator $X$ such that $G-X$ has treewidth $r=O(1)$, while $G$ has treewidth $|X|+O(1)$. We rule out algorithms running in time $O^*((r+1-epsilon)^{k})$ for Deletion to $r$-Colorable parameterized by $k=|X|$. For clique-width, we rule out time $O^*((2^r-epsilon)^k)$ for Deletion to $r$-Colorable, where $X$ is now allowed to consist of $k$ twinclasses. There are further results on Vertex Cover, Dominating Set and Maximum Cut. All lower bounds are matched by existing and newly designed algorithms.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121847352","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: 3

Close relatives (of Feedback Vertex Set), revisited (反馈顶点集)的近亲，重新访问

International Symposium on Parameterized and Exact Computation Pub Date : 2021-06-30 DOI: 10.4230/LIPIcs.IPEC.2021.21

Hugo Jacob, Thomas Bellitto, Oscar Defrain, Marcin Pilipczuk

{"title":"Close relatives (of Feedback Vertex Set), revisited","authors":"Hugo Jacob, Thomas Bellitto, Oscar Defrain, Marcin Pilipczuk","doi":"10.4230/LIPIcs.IPEC.2021.21","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2021.21","url":null,"abstract":"At IPEC 2020, Bergougnoux, Bonnet, Brettell, and Kwon showed that a number of problems related to the classic Feedback Vertex Set (FVS) problem do not admit a $2^{o(k log k)} cdot n^{mathcal{O}(1)}$-time algorithm on graphs of treewidth at most $k$, assuming the Exponential Time Hypothesis. This contrasts with the $3^{k} cdot k^{mathcal{O}(1)} cdot n$-time algorithm for FVS using the Cut&Count technique. During their live talk at IPEC 2020, Bergougnoux et al.~posed a number of open questions, which we answer in this work. - Subset Even Cycle Transversal, Subset Odd Cycle Transversal, Subset Feedback Vertex Set can be solved in time $2^{mathcal{O}(k log k)} cdot n$ in graphs of treewidth at most $k$. This matches a lower bound for Even Cycle Transversal of Bergougnoux et al.~and improves the polynomial factor in some of their upper bounds. - Subset Feedback Vertex Set and Node Multiway Cut can be solved in time $2^{mathcal{O}(k log k)} cdot n$, if the input graph is given as a clique-width expression of size $n$ and width $k$. - Odd Cycle Transversal can be solved in time $4^k cdot k^{mathcal{O}(1)} cdot n$ if the input graph is given as a clique-width expression of size $n$ and width $k$. Furthermore, the existence of a constant $varepsilon>0$ and an algorithm performing this task in time $(4-varepsilon)^k cdot n^{mathcal{O}(1)}$ would contradict the Strong Exponential Time Hypothesis.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"115 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124133120","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: 4