International Symposium on Parameterized and Exact Computation最新文献_第3页

Improved Kernels for Edge Modification Problems 边缘修正问题的改进核

International Symposium on Parameterized and Exact Computation Pub Date : 2021-04-29 DOI: 10.4230/LIPIcs.IPEC.2021.13

Yixin Cao, Yuping Ke

引用次数: 3

PACE Solver Description: Bute-Plus: A Bottom-Up Exact Solver for Treedepth PACE解算器描述:Bute-Plus:一个自下而上的树深度精确解算器

International Symposium on Parameterized and Exact Computation Pub Date : 2020-12-17 DOI: 10.4230/LIPIcs.IPEC.2020.34

James Trimble

引用次数: 2

Recognizing Proper Tree-Graphs 正确树形图的识别

International Symposium on Parameterized and Exact Computation Pub Date : 2020-11-23 DOI: 10.4230/LIPIcs.IPEC.2020.8

S. Chaplick, P. Golovach, Tim A. Hartmann, D. Knop

{"title":"Recognizing Proper Tree-Graphs","authors":"S. Chaplick, P. Golovach, Tim A. Hartmann, D. Knop","doi":"10.4230/LIPIcs.IPEC.2020.8","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2020.8","url":null,"abstract":"We investigate the parameterized complexity of the recognition problem for the proper $H$-graphs. The $H$-graphs are the intersection graphs of connected subgraphs of a subdivision of a multigraph $H$, and the properness means that the containment relationship between the representations of the vertices is forbidden. The class of $H$-graphs was introduced as a natural (parameterized) generalization of interval and circular-arc graphs by Bir'o, Hujter, and Tuza in 1992, and the proper $H$-graphs were introduced by Chaplick et al. in WADS 2019 as a generalization of proper interval and circular-arc graphs. For these graph classes, $H$ may be seen as a structural parameter reflecting the distance of a graph to a (proper) interval graph, and as such gained attention as a structural parameter in the design of efficient algorithms. We show the following results. - For a tree $T$ with $t$ nodes, it can be decided in $ 2^{mathcal{O}(t^2 log t)} cdot n^3 $ time, whether an $n$-vertex graph $ G $ is a proper $ T $-graph. For yes-instances, our algorithm outputs a proper $T$-representation. This proves that the recognition problem for proper $H$-graphs, where $H$ required to be a tree, is fixed-parameter tractable when parameterized by the size of $T$. Previously only NP-completeness was known. - Contrasting to the first result, we prove that if $H$ is not constrained to be a tree, then the recognition problem becomes much harder. Namely, we show that there is a multigraph $H$ with 4 vertices and 5 edges such that it is NP-complete to decide whether $G$ is a proper $H$-graph.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129995828","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

An Investigation of the Recoverable Robust Assignment Problem 可恢复鲁棒分配问题的研究

International Symposium on Parameterized and Exact Computation Pub Date : 2020-10-22 DOI: 10.4230/LIPIcs.IPEC.2021.19

Dennis Fischer, Tim A. Hartmann, Stefan Lendl, G. Woeginger

{"title":"An Investigation of the Recoverable Robust Assignment Problem","authors":"Dennis Fischer, Tim A. Hartmann, Stefan Lendl, G. Woeginger","doi":"10.4230/LIPIcs.IPEC.2021.19","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2021.19","url":null,"abstract":"We investigate the so-called recoverable robust assignment problem on balanced bipartite graphs with $2n$ vertices, a mainstream problem in robust optimization: For two given linear cost functions $c_1$ and $c_2$ on the edges and a given integer $k$, the goal is to find two perfect matchings $M_1$ and $M_2$ that minimize the objective value $c_1(M_1)+c_2(M_2)$, subject to the constraint that $M_1$ and $M_2$ have at least $k$ edges in common. \u0000We derive a variety of results on this problem. First, we show that the problem is W[1]-hard with respect to the parameter $k$, and also with respect to the recoverability parameter $k'=n-k$. This hardness result holds even in the highly restricted special case where both cost functions $c_1$ and $c_2$ only take the values $0$ and $1$. (On the other hand, containment of the problem in XP is straightforward to see.) Next, as a positive result we construct a polynomial time algorithm for the special case where one cost function is Monge, whereas the other one is Anti-Monge. Finally, we study the variant where matching $M_1$ is frozen, and where the optimization goal is to compute the best corresponding matching $M_2$, the second stage recoverable assignment problem. We show that this problem variant is contained in the randomized parallel complexity class $text{RNC}_2$, and that it is at least as hard as the infamous problem probl{Exact Matching in Red-Blue Bipartite Graphs} whose computational complexity is a long-standing open problem","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"113 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123045010","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: 13

Close relatives of Feedback Vertex Set without single-exponential algorithms parameterized by treewidth 无树宽参数化单指数算法的反馈顶点集的近亲

International Symposium on Parameterized and Exact Computation Pub Date : 2020-07-28 DOI: 10.4230/LIPIcs.IPEC.2020.3

Benjamin Bergougnoux, 'Edouard Bonnet, Nick Brettell, O-joung Kwon

引用次数: 8

FPT Approximation for Constrained Metric k-Median/Means 约束度量k-中值/均值的FPT近似

International Symposium on Parameterized and Exact Computation Pub Date : 2020-07-23 DOI: 10.4230/LIPIcs.IPEC.2020.14

Dishant Goyal, Ragesh Jaiswal, Amit Kumar

{"title":"FPT Approximation for Constrained Metric k-Median/Means","authors":"Dishant Goyal, Ragesh Jaiswal, Amit Kumar","doi":"10.4230/LIPIcs.IPEC.2020.14","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2020.14","url":null,"abstract":"The Metric $k$-median problem over a metric space $(mathcal{X}, d)$ is defined as follows: given a set $L subseteq mathcal{X}$ of facility locations and a set $C subseteq mathcal{X}$ of clients, open a set $F subseteq L$ of $k$ facilities such that the total service cost, defined as $Phi(F, C) equiv sum_{x in C} min_{f in F} d(x, f)$, is minimised. The metric $k$-means problem is defined similarly using squared distances. In many applications there are additional constraints that any solution needs to satisfy. This gives rise to different constrained versions of the problem such as $r$-gather, fault-tolerant, outlier $k$-means/$k$-median problem. Surprisingly, for many of these constrained problems, no constant-approximation algorithm is known. We give FPT algorithms with constant approximation guarantee for a range of constrained $k$-median/means problems. For some of the constrained problems, ours is the first constant factor approximation algorithm whereas for others, we improve or match the approximation guarantee of previous works. We work within the unified framework of Ding and Xu that allows us to simultaneously obtain algorithms for a range of constrained problems. In particular, we obtain a $(3+varepsilon)$-approximation and $(9+varepsilon)$-approximation for the constrained versions of the $k$-median and $k$-means problem respectively in FPT time. In many practical settings of the $k$-median/means problem, one is allowed to open a facility at any client location, i.e., $C subseteq L$. For this special case, our algorithm gives a $(2+varepsilon)$-approximation and $(4+varepsilon)$-approximation for the constrained versions of $k$-median and $k$-means problem respectively in FPT time. Since our algorithm is based on simple sampling technique, it can also be converted to a constant-pass log-space streaming algorithm.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129944144","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

The Asymmetric Travelling Salesman Problem in Sparse Digraphs 稀疏有向图中的不对称旅行商问题

International Symposium on Parameterized and Exact Computation Pub Date : 2020-07-23 DOI: 10.4230/LIPIcs.IPEC.2020.23

Lukasz Kowalik, Konrad Majewski

{"title":"The Asymmetric Travelling Salesman Problem in Sparse Digraphs","authors":"Lukasz Kowalik, Konrad Majewski","doi":"10.4230/LIPIcs.IPEC.2020.23","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2020.23","url":null,"abstract":"Asymmetric Travelling Salesman Problem (ATSP) and its special case Directed Hamiltonicity are among the most fundamental problems in computer science. The dynamic programming algorithm running in time $O^*(2^n)$ developed almost 60 years ago by Bellman, Held and Karp, is still the state of the art for both of these problems. \u0000In this work we focus on sparse digraphs. First, we recall known approaches for Undirected Hamiltonicity and TSP in sparse graphs and we analyse their consequences for Directed Hamiltonicity and ATSP in sparse digraphs, either by adapting the algorithm, or by using reductions. In this way, we get a number of running time upper bounds for a few classes of sparse digraphs, including $O^*(2^{n/3})$ for digraphs with both out- and indegree bounded by 2, and $O^*(3^{n/2})$ for digraphs with outdegree bounded by 3. \u0000Our main results are focused on digraphs of bounded average outdegree $d$. The baseline for ATSP here is a simple enumeration of cycle covers which can be done in time bounded by $O^*(mu(d)^n)$ for a function $mu(d)le(lceil{d}rceil!)^{1/{lceil{d}rceil}}$. One can also observe that Directed Hamiltonicity can be solved in randomized time $O^*((2-2^{-d})^n)$ and polynomial space, by adapting a recent result of Bjorklund [ISAAC 2018] stated originally for Undirected Hamiltonicity in sparse bipartite graphs. \u0000We present two new deterministic algorithms for ATSP: the first running in time $O(2^{0.441(d-1)n})$ and polynomial space, and the second in exponential space with running time of $O^*(tau(d)^{n/2})$ for a function $tau(d)le d$.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128920041","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 Complexity of Scheduling Chains of Jobs with Delays 时滞作业调度链的参数化复杂度

International Symposium on Parameterized and Exact Computation Pub Date : 2020-07-17 DOI: 10.4230/LIPIcs.IPEC.2020.4

H. Bodlaender, M. V. D. Wegen

{"title":"Parameterized Complexity of Scheduling Chains of Jobs with Delays","authors":"H. Bodlaender, M. V. D. Wegen","doi":"10.4230/LIPIcs.IPEC.2020.4","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2020.4","url":null,"abstract":"In this paper, we consider the parameterized complexity of the following scheduling problem. We must schedule a number of jobs on $m$ machines, where each job has unit length, and the graph of precedence constraints consists of a set of chains. Each precedence constraint is labelled with an integer that denotes the exact (or minimum) delay between the jobs. We study different cases; delays can be given in unary and in binary, and the case that we have a single machine is discussed separately. We consider the complexity of this problem parameterized by the number of chains, and by the thickness of the instance, which is the maximum number of chains whose intervals between release date and deadline overlap. \u0000We show that this scheduling problem with exact delays in unary is $W[t]$-hard for all $t$, when parameterized by the thickness, even when we have a single machine ($m = 1$). When parameterized by the number of chains, this problem is $W[1]$-complete when we have a single or a constant number of machines, and $W[2]$-complete when the number of machines is a variable. The problem with minimum delays, given in unary, parameterized by the number of chains (and as a simple corollary, also when parameterized by the thickness) is $W[1]$-hard for a single or a constant number of machines, and $W[2]$-hard when the number of machines is variable. \u0000With a dynamic programming algorithm, one can show membership in XP for exact and minimum delays in unary, for any number of machines, when parameterized by thickness or number of chains. For a single machine, with exact delays in binary, parameterized by the number of chains, membership in XP can be shown with branching and solving a system of difference constraints. For all other cases for delays in binary, membership in XP is open.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"51 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120891178","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

New Algorithms for Mixed Dominating Set 混合支配集的新算法

International Symposium on Parameterized and Exact Computation Pub Date : 2019-11-20 DOI: 10.46298/dmtcs.6824

L. Dublois, M. Lampis, V. Paschos

引用次数: 2

A Polynomial Kernel for Paw-Free Editing 无爪编辑的多项式核

International Symposium on Parameterized and Exact Computation Pub Date : 2019-11-09 DOI: 10.4230/LIPIcs.IPEC.2020.10

E. Eiben, W. Lochet, Saket Saurabh

引用次数: 9