International Symposium on Parameterized and Exact Computation最新文献

{"title":"Smaller parameters for vertex cover kernelization","authors":"Eva-Maria C. Hols, Stefan Kratsch","doi":"10.4230/LIPIcs.IPEC.2017.20","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2017.20","url":null,"abstract":"We revisit the topic of polynomial kernels for Vertex Cover relative to structural parameters. Our starting point is a recent paper due to Fomin and Str{o}mme [WG 2016] who gave a kernel with $mathcal{O}(|X|^{12})$ vertices when $X$ is a vertex set such that each connected component of $G-X$ contains at most one cycle, i.e., $X$ is a modulator to a pseudoforest. We strongly generalize this result by using modulators to $d$-quasi-forests, i.e., graphs where each connected component has a feedback vertex set of size at most $d$, and obtain kernels with $mathcal{O}(|X|^{3d+9})$ vertices. Our result relies on proving that minimal blocking sets in a $d$-quasi-forest have size at most $d+2$. This bound is tight and there is a related lower bound of $mathcal{O}(|X|^{d+2-epsilon})$ on the bit size of kernels. \u0000In fact, we also get bounds for minimal blocking sets of more general graph classes: For $d$-quasi-bipartite graphs, where each connected component can be made bipartite by deleting at most $d$ vertices, we get the same tight bound of $d+2$ vertices. For graphs whose connected components each have a vertex cover of cost at most $d$ more than the best fractional vertex cover, which we call $d$-quasi-integral, we show that minimal blocking sets have size at most $2d+2$, which is also tight. Combined with existing randomized polynomial kernelizations this leads to randomized polynomial kernelizations for modulators to $d$-quasi-bipartite and $d$-quasi-integral graphs. There are lower bounds of $mathcal{O}(|X|^{d+2-epsilon})$ and $mathcal{O}(|X|^{2d+2-epsilon})$ for the bit size of such kernels.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124156178","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}

{"title":"Integer Programming in Parameterized Complexity: Three Miniatures","authors":"T. Gavenčiak, D. Knop, Martin Koutecký","doi":"10.4230/LIPIcs.IPEC.2018.21","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2018.21","url":null,"abstract":"Powerful results from the theory of integer programming have recently led to substantial advances in parameterized complexity. However, our perception is that, except for Lenstra's algorithm for solving integer linear programming in fixed dimension, there is still little understanding in the parameterized complexity community of the strengths and limitations of the available tools. This is understandable: it is often difficult to infer exact runtimes or even the distinction between FPT and XP algorithms, and some knowledge is simply unwritten folklore in a different community. We wish to make a step in remedying this situation.\u0000To that end, we first provide an easy to navigate quick reference guide of integer programming algorithms from the perspective of parameterized complexity. Then, we show their applications in three case studies, obtaining FPT algorithms with runtime f(k) poly(n). We focus on: \u0000- Modeling: since the algorithmic results follow by applying existing algorithms to new models, we shift the focus from the complexity result to the modeling result, highlighting common patterns and tricks which are used. \u0000- Optimality program: after giving an FPT algorithm, we are interested in reducing the dependence on the parameter; we show which algorithms and tricks are often useful for speed-ups. \u0000- Minding the poly(n): reducing f(k) often has the unintended consequence of increasing poly(n); so we highlight the common trade-offs and show how to get the best of both worlds. \u0000Specifically, we consider graphs of bounded neighborhood diversity which are in a sense the simplest of dense graphs, and we show several FPT algorithms for Capacitated Dominating Set, Sum Coloring, and Max-q-Cut by modeling them as convex programs in fixed dimension, n-fold integer programs, bounded dual treewidth programs, and indefinite quadratic programs in fixed dimension.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123918375","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}

{"title":"Finding Small Weight Isomorphisms with Additional Constraints is Fixed-Parameter Tractable","authors":"V. Arvind, J. Köbler, Sebastian Kuhnert, J. Torán","doi":"10.4230/LIPIcs.IPEC.2017.2","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2017.2","url":null,"abstract":"Lubiw showed that several variants of Graph Isomorphism are NP-complete, where the solutions are required to satisfy certain additional constraints [SICOMP 10, 1981]. One of these, called Isomorphism With Restrictions, is to decide for two given graphs $X_1=(V,E_1)$ and $X_2=(V,E_2)$ and a subset $Rsubseteq Vtimes V$ of forbidden pairs whether there is an isomorphism $pi$ from $X_1$ to $X_2$ such that $pi(i)neq j$ for all $(i,j)in R$. We prove that this problem and several of its generalizations are in fact in FPT: \u0000- The problem of deciding whether there is an isomorphism between two graphs that moves k vertices and satisfies Lubiw-style constraints is in FPT, with k and the size of $R$ as parameters. The problem remains in FPT if a CNF of such constraints is allowed. It follows that the problem to decide whether there is an isomorphism that moves exactly k vertices is in FPT. This solves a question left open in our article on exact weight automorphisms [STACS 2017]. \u0000- When the weight and complexity are unrestricted, finding isomorphisms that satisfy a CNF of Lubiw-style constraints can be solved in FPT with access to a GI oracle. \u0000- Checking if there is an isomorphism $pi$ between two graphs with complexity t is also in FPT with t as parameter, where the complexity of a permutation is the Cayley measure defined as the minimum number t such that $pi$ can be expressed as a product of t transpositions. \u0000- We consider a more general problem in which the vertex set of a graph X is partitioned into Red and Blue, and we are interested in an automorphism that stabilizes Red and Blue and moves exactly k vertices in Blue, where k is the parameter. This problem was introduced by [Downey and Fellows 1999], and we showed [STACS 2017] that it is W[1]-hard even with color classes of size 4 inside Red. Now, for color classes of size at most 3 inside Red, we show the problem is in FPT.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"282 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122950865","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}

{"title":"Computing Treewidth on the GPU","authors":"Tom C. van der Zanden, H. Bodlaender","doi":"10.4230/LIPIcs.IPEC.2017.29","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2017.29","url":null,"abstract":"We present a parallel algorithm for computing the treewidth of a graph on a GPU. We implement this algorithm in OpenCL, and experimentally evaluate its performance. Our algorithm is based on an O*(2^n)-time algorithm that explores the elimination orderings of the graph using a Held-Karp like dynamic programming approach. We use Bloom filters to detect duplicate solutions. \u0000 \u0000GPU programming presents unique challenges and constraints, such as constraints on the use of memory and the need to limit branch divergence. We experiment with various optimizations to see if it is possible to work around these issues. We achieve a very large speed up (up to 77x) compared to running the same algorithm on the CPU.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"124 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132013070","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}

{"title":"DynASP2.5: Dynamic Programming on Tree Decompositions in Action","authors":"J. Fichte, Markus Hecher, Michael Morak, S. Woltran","doi":"10.4230/LIPIcs.IPEC.2017.17","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2017.17","url":null,"abstract":"Efficient exact parameterized algorithms are an active research area. Such algorithms exhibit a broad interest in the theoretical community. In the last few years, implementations for computing various parameters (parameter detection) have been established in parameterized challenges, such as treewidth, treedepth, hypertree width, feedback vertex set, or vertex cover. In theory, instances, for which the considered parameter is small, can be solved fast (problem evaluation), i.e., the runtime is bounded exponential in the parameter. While such favorable theoretical guarantees exists, it is often unclear whether one can successfully implement these algorithms under practical considerations. In other words, can we design and construct implementations of parameterized algorithms such that they perform similar or even better than well-established problem solvers on instances where the parameter is small. Indeed, we can build an implementation that performs well under the theoretical assumptions. However, it could also well be that an existing solver implicitly takes advantage of a structure, which is often claimed for solvers that build on Sat-solving. In this paper, we consider finding one solution to instances of answer set programming (ASP), which is a logic-based declarative modeling and solving framework. Solutions for ASP instances are so-called answer sets. Interestingly, the problem of deciding whether an instance has an answer set is already located on the second level of the polynomial hierarchy. An ASP solver that employs treewidth as parameter and runs dynamic programming on tree decompositions is DynASP2. Empirical experiments show that this solver is fast on instances of small treewidth and can outperform modern ASP when one counts answer sets. It remains open, whether one can improve the solver such that it also finds one answer set fast and shows competitive behavior to modern ASP solvers on instances of low treewidth. Unfortunately, theoretical models of modern ASP solvers already indicate that these solvers can solve instances of low treewidth fast, since they are based on Sat-solving algorithms. In this paper, we improve DynASP2 and construct the solver DynASP2.5, which uses a different approach. The new solver shows competitive behavior to state-of-the-art ASP solvers even for finding just one solution. We present empirical experiments where one can see that our new implementation solves ASP instances, which encode the Steiner tree problem on graphs with low treewidth, fast. Our implementation is based on a novel approach that we call multi-pass dynamic programming (M-DPSINC). In the paper, we describe the underlying concepts of our implementation (DynASP2.5) and we argue why the techniques still yield correct algorithms.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133120697","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}

{"title":"Optimal Algorithms for Hitting (Topological) Minors on Graphs of Bounded Treewidth","authors":"Julien Baste, Ignasi Sau, D. Thilikos","doi":"10.4230/LIPIcs.IPEC.2017.4","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2017.4","url":null,"abstract":"For a fixed collection of graphs ${cal F}$, the ${cal F}$-M-DELETION problem consists in, given a graph $G$ and an integer $k$, decide whether there exists $S subseteq V(G)$ with $|S| leq k$ such that $G setminus S$ does not contain any of the graphs in ${cal F}$ as a minor. We are interested in the parameterized complexity of ${cal F}$-M-DELETION when the parameter is the treewidth of $G$, denoted by $tw$. Our objective is to determine, for a fixed ${cal F}$, the smallest function $f_{{cal F}}$ such that ${cal F}$-M-DELETION can be solved in time $f_{{cal F}}(tw) cdot n^{O(1)}$ on $n$-vertex graphs. Using and enhancing the machinery of boundaried graphs and small sets of representatives introduced by Bodlaender et al. [J ACM, 2016], we prove that when all the graphs in ${cal F}$ are connected and at least one of them is planar, then $f_{{cal F}}(w) = 2^{O (w cdotlog w)}$. When ${cal F}$ is a singleton containing a clique, a cycle, or a path on $i$ vertices, we prove the following asymptotically tight bounds: \u0000$bullet$ $f_{{K_4}}(w) = 2^{Theta (w cdot log w)}$. \u0000$bullet$ $f_{{C_i}}(w) = 2^{Theta (w)}$ for every $i leq 4$, and $f_{{C_i}}(w) = 2^{Theta (w cdotlog w)}$ for every $i geq 5$. \u0000$bullet$ $f_{{P_i}}(w) = 2^{Theta (w)}$ for every $i leq 4$, and $f_{{P_i}}(w) = 2^{Theta (w cdot log w)}$ for every $i geq 6$. \u0000The lower bounds hold unless the Exponential Time Hypothesis fails, and the superexponential ones are inspired by a reduction of Marcin Pilipczuk [Discrete Appl Math, 2016]. The single-exponential algorithms use, in particular, the rank-based approach introduced by Bodlaender et al. [Inform Comput, 2015]. We also consider the version of the problem where the graphs in ${cal F}$ are forbidden as topological minors, and prove that essentially the same set of results holds.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125439399","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}

{"title":"H-Free Graphs, Independent Sets, and Subexponential-Time Algorithms","authors":"G. Bacsó, D. Marx, Z. Tuza","doi":"10.4230/LIPIcs.IPEC.2016.3","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2016.3","url":null,"abstract":"It is an outstanding open question in algorithmic graph theory to determine the complexity of the MAXIMUM INDEPENDENT SET problem on P_t-free graphs, that is, on graphs not containing any induced path on t vertices. So far, polynomial-time algorithms are known only for t at most 5 [Lokshtanov et al., SODA 2014, 570-581, 2014]. Here we study the existence of subexponential-time algorithms for the problem: by generalizing an earlier result of Randerath and Schiermeyer for t=5 [Discrete App. Math., 158 (2010), 1041-1044], we show that for any t at least 5, there is an algorithm for MAXIMUM INDEPENDENT SET on P_t-free graphs whose running time is subexponential in the number of vertices. \u0000 \u0000SCATTERED SET is the generalization of MAXIMUM INDEPENDENT SET where the vertices of the solution are required to be at distance at least $d$ from each other. We give a complete characterization of those graphs H for which SCATTERED SET on H-free graphs can be solved in time subexponential in the size of the input (that is, in the number of vertices plus the number of edges): \u0000 \u0000* If every component of H is a path, then d-SCATTERED SET on H-free graphs with n vertices and m edges can be solved in time 2^{(n+m)^{1-O(1/|V(H)|)}}, even if d is part of the input. \u0000 \u0000* Otherwise, assuming ETH, there is no 2^{o(n+m)} time algorithm for d-SCATTERED SET for any fixed d at least 3 on H-free graphs with n vertices and m edges.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125989374","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}

{"title":"The First Parameterized Algorithms and Computational Experiments Challenge","authors":"Holger Dell, T. Husfeldt, B. Jansen, P. Kaski, Christian Komusiewicz, Frances A. Rosamond","doi":"10.4230/LIPIcs.IPEC.2016.30","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2016.30","url":null,"abstract":"In this article, the steering committee of the Parameterized Algorithms and Computational Experiments challenge (PACE) reports on the first iteration of the challenge. Where did PACE come from, how did it go, who won, and what's next?","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127450415","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}

{"title":"Cut and Count and Representative Sets on Branch Decompositions","authors":"Willem J. A. Pino, H. Bodlaender, Johan M. M. van Rooij","doi":"10.4230/LIPIcs.IPEC.2016.27","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2016.27","url":null,"abstract":"Recently, new techniques have been introduced to speed up dynamic programming algorithms on tree decompositions for connectivity problems: the 'Cut and Count' method and a method called the rank-based approach, based on representative sets and Gaussian elimination. These methods respectively give randomised and deterministic algorithms that are single exponential in the treewidth, and polynomial, respectively linear in the number of vertices. In this paper, we adapt these methods to branch decompositions yielding algorithms, both randomised and deterministic, that are in many cases faster than when tree decompositions would be used. \u0000 \u0000In particular, we obtain the currently fastest randomised algorithms for several problems on planar graphs. When the involved weights are O(n^{O(1)}), we obtain faster randomised algorithms on planar graphs for Steiner Tree, Connected Dominating Set, Feedback Vertex Set and TSP, and a faster deterministic algorithm for TSP. When considering planar graphs with arbitrary real weights, we obtain faster deterministic algorithms for all four mentioned problems.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126466050","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}

{"title":"A Faster Parameterized Algorithm for Pseudoforest Deletion","authors":"H. Bodlaender, H. Ono, Y. Otachi","doi":"10.4230/LIPIcs.IPEC.2016.7","DOIUrl":"https://doi.org/10.4230/LIPIcs.IPEC.2016.7","url":null,"abstract":"A pseudoforest is a graph where each connected component contains at most one cycle, or alternatively, a graph that can be turned into a forest by removing at most one edge from each connected component. In this paper, we show that the following problem can be solved in O(3^k n k^{O(1)}) time: given a graph G and an integer k, can we delete at most k vertices from G such that we obtain a pseudoforest? The result improves upon an earlier result by Philip et al. [MFCS 2015] who gave a (nonlinear) 7.56^k n^{O(1)}-time algorithm both in the exponential factor depending on k as well as in the polynomial factor depending on n.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129404620","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}