International Symposium on Parameterized and Exact Computation最新文献_第4页

Computing the largest bond of a graph 计算图的最大键

International Symposium on Parameterized and Exact Computation Pub Date : 2019-10-02 DOI: 10.4230/LIPIcs.IPEC.2019.12

Gabriel L. Duarte, D. Lokshtanov, L. L. Pedrosa, R. Schouery, U. Souza

{"title":"Computing the largest bond of a graph","authors":"Gabriel L. Duarte, D. Lokshtanov, L. L. Pedrosa, R. Schouery, U. Souza","doi":"10.4230/LIPIcs.IPEC.2019.12","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2019.12","url":null,"abstract":"A bond of a graph $G$ is an inclusion-wise minimal disconnecting set of $G$, i.e., bonds are cut-sets that determine cuts $[S,Vsetminus S]$ of $G$ such that $G[S]$ and $G[Vsetminus S]$ are both connected. Given $s,tin V(G)$, an $st$-bond of $G$ is a bond whose removal disconnects $s$ and $t$. Contrasting with the large number of studies related to maximum cuts, there are very few results regarding the largest bond of general graphs. In this paper, we aim to reduce this gap on the complexity of computing the largest bond and the largest $st$-bond of a graph. Although cuts and bonds are similar, we remark that computing the largest bond of a graph tends to be harder than computing its maximum cut. We show that {sc Largest Bond} remains NP-hard even for planar bipartite graphs, and it does not admit a constant-factor approximation algorithm, unless $P = NP$. We also show that {sc Largest Bond} and {sc Largest $st$-Bond} on graphs of clique-width $w$ cannot be solved in time $f(w)times n^{o(w)}$ unless the Exponential Time Hypothesis fails, but they can be solved in time $f(w)times n^{O(w)}$. In addition, we show that both problems are fixed-parameter tractable when parameterized by the size of the solution, but they do not admit polynomial kernels unless NP $subseteq$ coNP/poly.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125289847","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

Towards a Theory of Parameterized Streaming Algorithms 参数化流算法理论探讨

International Symposium on Parameterized and Exact Computation Pub Date : 2019-07-15 DOI: 10.4230/LIPIcs.IPEC.2019.7

R. Chitnis, Graham Cormode

{"title":"Towards a Theory of Parameterized Streaming Algorithms","authors":"R. Chitnis, Graham Cormode","doi":"10.4230/LIPIcs.IPEC.2019.7","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2019.7","url":null,"abstract":"Parameterized complexity attempts to give a more fine-grained analysis of the complexity of problems: instead of measuring the running time as a function of only the input size, we analyze the running time with respect to additional parameters. This approach has proven to be highly successful in delineating our understanding of NP-hard problems. Given this success with the TIME resource, it seems but natural to use this approach for dealing with the SPACE resource. First attempts in this direction have considered a few individual problems, with some success: Fafianie and Kratsch [MFCS'14] and Chitnis et al. [SODA'15] introduced the notions of streaming kernels and parameterized streaming algorithms respectively. For example, the latter shows how to refine the $Omega(n^2)$ bit lower bound for finding a minimum Vertex Cover (VC) in the streaming setting by designing an algorithm for the parameterized $k$-VC problem which uses $O(k^{2}log n)$ bits. \u0000In this paper, we initiate a systematic study of graph problems from the paradigm of parameterized streaming algorithms. We first define a natural hierarchy of space complexity classes of FPS, SubPS, SemiPS, SupPS and BrutePS, and then obtain tight classifications for several well-studied graph problems such as Longest Path, Feedback Vertex Set, Dominating Set, Girth, Treewidth, etc. into this hierarchy. \u0000(see paper for full abstract)","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132703785","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

The Independent Set Problem Is FPT for Even-Hole-Free Graphs 偶孔无图的独立集问题是FPT

International Symposium on Parameterized and Exact Computation Pub Date : 2019-07-01 DOI: 10.4230/LIPIcs.IPEC.2019.21

Edin Husić, Stéphan Thomassé, Nicolas Trotignon

引用次数: 2

Hierarchy of Transportation Network Parameters and Hardness Results 运输网络参数的层次和硬度结果

International Symposium on Parameterized and Exact Computation Pub Date : 2019-05-27 DOI: 10.4230/LIPIcs.IPEC.2019.4

Johannes Blum

{"title":"Hierarchy of Transportation Network Parameters and Hardness Results","authors":"Johannes Blum","doi":"10.4230/LIPIcs.IPEC.2019.4","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2019.4","url":null,"abstract":"The graph parameters highway dimension and skeleton dimension were introduced to capture the properties of transportation networks. As many important optimization problems like Travelling Salesperson, Steiner Tree or $k$-Center arise in such networks, it is worthwhile to study them on graphs of bounded highway or skeleton dimension. \u0000We investigate the relationships between mentioned parameters and how they are related to other important graph parameters that have been applied successfully to various optimization problems. We show that the skeleton dimension is incomparable to any of the parameters distance to linear forest, bandwidth, treewidth and highway dimension and hence, it is worthwhile to study mentioned problems also on graphs of bounded skeleton dimension. Moreover, we prove that the skeleton dimension is upper bounded by the max leaf number and that for any graph on at least three vertices there are edge weights such that both parameters are equal. \u0000Then we show that computing the highway dimension according to most recent definition is NP-hard, which answers an open question stated by Feldmann et al. Finally we prove that on graphs $G=(V,E)$ of skeleton dimension $mathcal{O}(log^2 vert V vert)$ it is NP-hard to approximate the $k$-Center problem within a factor less than $2$.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125849784","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: 9

A Complexity Dichotomy for Hitting Small Planar Minors Parameterized by Treewidth 用Treewidth参数化的平面小分支的复杂度二分法

International Symposium on Parameterized and Exact Computation Pub Date : 2019-01-25 DOI: 10.4230/LIPIcs.IPEC.2018.2

Julien Baste, Ignasi Sau, D. Thilikos

{"title":"A Complexity Dichotomy for Hitting Small Planar Minors Parameterized by Treewidth","authors":"Julien Baste, Ignasi Sau, D. Thilikos","doi":"10.4230/LIPIcs.IPEC.2018.2","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2018.2","url":null,"abstract":"For a fixed graph H, we are interested in the parameterized complexity of the following problem, called {H}-M-Deletion, parameterized by the treewidth tw of the input graph: given an n-vertex graph G and an integer k, decide whether there exists S subseteq V(G) with |S| <= k such that G setminus S does not contain H as a minor. In previous work [IPEC, 2017] we proved that if H is planar and connected, then the problem cannot be solved in time 2^{o(tw)} * n^{O(1)} under the ETH, and can be solved in time 2^{O(tw * log tw)} * n^{O(1)}. In this article we manage to classify the optimal asymptotic complexity of {H}-M-Deletion when H is a connected planar graph on at most 5 vertices. Out of the 29 possibilities (discarding the trivial case H = K_1), we prove that 9 of them are solvable in time 2^{Theta (tw)} * n^{O(1)}, and that the other 20 ones are solvable in time 2^{Theta (tw * log tw)} * n^{O(1)}. Namely, we prove that K_4 and the diamond are the only graphs on at most 4 vertices for which the problem is solvable in time 2^{Theta (tw * log tw)} * n^{O(1)}, and that the chair and the banner are the only graphs on 5 vertices for which the problem is solvable in time 2^{Theta (tw)} * n^{O(1)}. For the version of the problem where H is forbidden as a topological minor, the case H = K_{1,4} can be solved in time 2^{Theta (tw)} * n^{O(1)}. This exhibits, to the best of our knowledge, the first difference between the computational complexity of both problems.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"133 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133310081","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

Resolving Conflicts for Lower-Bounded Clustering 解决下限聚类的冲突

International Symposium on Parameterized and Exact Computation Pub Date : 2019-01-25 DOI: 10.4230/LIPIcs.IPEC.2018.23

Katrin Casel

{"title":"Resolving Conflicts for Lower-Bounded Clustering","authors":"Katrin Casel","doi":"10.4230/LIPIcs.IPEC.2018.23","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2018.23","url":null,"abstract":"This paper considers the effect of non-metric distances for lower-bounded clustering, i.e., the problem of computing a partition for a given set of objects with pairwise distance, such that each set has a certain minimum cardinality (as required for anonymisation or balanced facility location problems). We discuss lower-bounded clustering with the objective to minimise the maximum radius or diameter of the clusters. For these problems there exists a 2-approximation but only if the pairwise distance on the objects satisfies the triangle inequality, without this property no polynomial-time constant factor approximation is possible, unless P = NP. We try to resolve or at least soften this effect of non-metric distances by devising particular strategies to deal with violations of the triangle inequality (conflicts). With parameterised algorithmics, we find that if the number of such conflicts is not too large, constant factor approximations can still be computed efficiently. In particular, we introduce parameterised approximations with respect to not just the number of conflicts but also for the vertex cover number of the conflict graph (graph induced by conflicts). Interestingly, we salvage the approximation ratio of 2 for diameter while for radius it is only possible to show a ratio of 3. For the parameter vertex cover number of the conflict graph this worsening in ratio is shown to be unavoidable, unless FPT = W[2]. We further discuss improvements for diameter by choosing the (induced) P3-cover number of the conflict graph as parameter and complement these by showing that, unless FPT = W[1], there exists no constant factor parameterised approximation with respect to the parameter split vertex deletion set. 2012 ACM Subject Classification Theory of computation: Approximation algorithms analysis, Parameterized complexity and exact algorithms, Facility location and clustering","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129129118","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: 2

Lower Bounds for Dynamic Programming on Planar Graphs of Bounded Cutwidth 有界切面图上动态规划的下界

International Symposium on Parameterized and Exact Computation Pub Date : 2018-06-27 DOI: 10.4230/LIPIcs.IPEC.2018.3

B. A. M. V. Geffen, B. Jansen, A. D. Kroon, Rolf Morel

引用次数: 7

Faster Subgraph Counting in Sparse Graphs 稀疏图中更快的子图计数

International Symposium on Parameterized and Exact Computation Pub Date : 2018-05-05 DOI: 10.4230/LIPIcs.IPEC.2019.6

M. Bressan

{"title":"Faster Subgraph Counting in Sparse Graphs","authors":"M. Bressan","doi":"10.4230/LIPIcs.IPEC.2019.6","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2019.6","url":null,"abstract":"A fundamental graph problem asks to compute the number of induced copies of a $k$-node pattern graph $H$ in an $n$-node graph $G$. The fastest algorithm to date is still the 35-years-old algorithm by Nev{s}etv{r}il and Poljak [31], with running time $f(k) cdot O(n^{omegalfloorfrac{k}{3}rfloor + 2})$ where $omega le 2.373$ is the matrix multiplication exponent. In this work we show that, if one takes into account the degeneracy $d$ of $G$, then the picture becomes substantially richer and leads to faster algorithms when $G$ is sufficiently sparse. More precisely, after introducing a novel notion of graph width, the emph{DAG-treewidth}, we prove what follows. If $H$ has DAG-treewidth $tau(H)$ and $G$ has degeneracy $d$, then the induced copies of $H$ in $G$ can be counted in time $f(d,k) cdot tilde{O}(n^{tau(H)})$; and, under the Exponential Time Hypothesis, no algorithm can solve the problem in time $f(d,k) cdot n^{o(tau(H)/ln tau(H))}$ for all $H$. This result characterises the complexity of counting subgraphs in a $d$-degenerate graph. Developing bounds on $tau(H)$, then, we obtain natural generalisations of classic results and faster algorithms for sparse graphs. For example, when $d=O(operatorname{poly}log(n))$ we can count the induced copies of any $H$ in time $f(k) cdottilde{O}(n^{lfloor frac{k}{4} rfloor + 2})$, beating the Nev{s}etv{r}il-Poljak algorithm by essentially a cubic factor in $n$.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133678531","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: 14

Generalized distance domination problems and their complexity on graphs of bounded mim-width 有界中宽图上的广义距离支配问题及其复杂性

International Symposium on Parameterized and Exact Computation Pub Date : 2018-03-01 DOI: 10.4230/LIPIcs.IPEC.2018.6

L. Jaffke, O-joung Kwon, Torstein J. F. Strømme, J. A. Telle

引用次数: 12

Treewidth with a Quantifier Alternation Revisited 带量词交替的树宽度

International Symposium on Parameterized and Exact Computation Pub Date : 2018-02-23 DOI: 10.4230/LIPIcs.IPEC.2017.26

M. Lampis, V. Mitsou

{"title":"Treewidth with a Quantifier Alternation Revisited","authors":"M. Lampis, V. Mitsou","doi":"10.4230/LIPIcs.IPEC.2017.26","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2017.26","url":null,"abstract":"In this paper we take a closer look at the parameterized complexity of ∃∀SAT, the prototypical complete problem of the class Σp2, the second level of the polynomial hierarchy. We provide a number of tight fine-grained bounds on the complexity of this problem and its variants with respect to the most important structural graph parameters. Specifically, we show the following lower bounds (assuming the ETH): It is impossible to decide ∃∀SAT in time less than double-exponential in the input formula’s treewidth. More strongly, we establish the same bound with respect to the formula’s primal vertex cover, a much more restrictive measure. This lower bound, which matches the performance of known algorithms, shows that the degeneration of the performance of treewidth-based algorithms to a tower of exponentials already begins in problems with one quantifier alternation. For the more general ∃∀CSP problem over a non-boolean domain of size B, there is no algorithm running in time 2B , where vc is the input’s primal vertex cover. ∃∀SAT is already NP-hard even when the input formula has constant modular treewidth (or clique-width), indicating that dense graph parameters are less useful for problems in Σp2. For the two weighted versions of ∃∀SAT recently introduced by de Haan and Szeider, called ∃k∀SAT and ∃∀kSAT, we give tight upper and lower bounds parameterized by treewidth (or primal vertex cover) and the weight k. Interestingly, the complexity of these two problems turns out to be quite different: one is double-exponential in treewidth, while the other is double-exponential in k. We complement the above negative results by showing a double-exponential FPT algorithm for QBF parameterized by vertex cover, showing that for this parameter the complexity never goes beyond double-exponential, for any number of quantifier alternations. 1998 ACM Subject Classification F.1.3 Complexity Measures and Classes, F.2.2 Nonnumerical Algorithms and Problems, G.2.1 Combinatorics, G.2.2 Graph Theory","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127452510","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: 25