Document

**Published in:** LIPIcs, Volume 296, 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024)

In this paper, we study for the first time the Diverse Longest Common Subsequences (LCSs) problem under Hamming distance. Given a set of a constant number of input strings, the problem asks to decide if there exists some subset X of K longest common subsequences whose diversity is no less than a specified threshold Δ, where we consider two types of diversities of a set X of strings of equal length: the Sum diversity and the Min diversity defined as the sum and the minimum of the pairwise Hamming distance between any two strings in X, respectively. We analyze the computational complexity of the respective problems with Sum- and Min-diversity measures, called the Max-Sum and Max-Min Diverse LCSs, respectively, considering both approximation algorithms and parameterized complexity. Our results are summarized as follows. When K is bounded, both problems are polynomial time solvable. In contrast, when K is unbounded, both problems become NP-hard, while Max-Sum Diverse LCSs problem admits a PTAS. Furthermore, we analyze the parameterized complexity of both problems with combinations of parameters K and r, where r is the length of the candidate strings to be selected. Importantly, all positive results above are proven in a more general setting, where an input is an edge-labeled directed acyclic graph (DAG) that succinctly represents a set of strings of the same length. Negative results are proven in the setting where an input is explicitly given as a set of strings. The latter results are equipped with an encoding such a set as the longest common subsequences of a specific input string set.

Yuto Shida, Giulia Punzi, Yasuaki Kobayashi, Takeaki Uno, and Hiroki Arimura. Finding Diverse Strings and Longest Common Subsequences in a Graph. In 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 296, pp. 27:1-27:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{shida_et_al:LIPIcs.CPM.2024.27, author = {Shida, Yuto and Punzi, Giulia and Kobayashi, Yasuaki and Uno, Takeaki and Arimura, Hiroki}, title = {{Finding Diverse Strings and Longest Common Subsequences in a Graph}}, booktitle = {35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024)}, pages = {27:1--27:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-326-3}, ISSN = {1868-8969}, year = {2024}, volume = {296}, editor = {Inenaga, Shunsuke and Puglisi, Simon J.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2024.27}, URN = {urn:nbn:de:0030-drops-201370}, doi = {10.4230/LIPIcs.CPM.2024.27}, annote = {Keywords: Sequence analysis, longest common subsequence, Hamming distance, dispersion, approximation algorithms, parameterized complexity} }

Document

**Published in:** LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Finding a maximum cardinality common independent set in two matroids (also known as Matroid Intersection) is a classical combinatorial optimization problem, which generalizes several well-known problems, such as finding a maximum bipartite matching, a maximum colorful forest, and an arborescence in directed graphs. Enumerating all maximal common independent sets in two (or more) matroids is a classical enumeration problem. In this paper, we address an "intersection" of these problems: Given two matroids and a threshold τ, the goal is to enumerate all maximal common independent sets in the matroids with cardinality at least τ. We show that this problem can be solved in polynomial delay and polynomial space. We also discuss how to enumerate all maximal common independent sets of two matroids in non-increasing order of their cardinalities.

Yasuaki Kobayashi, Kazuhiro Kurita, and Kunihiro Wasa. Polynomial-Delay Enumeration of Large Maximal Common Independent Sets in Two Matroids. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 58:1-58:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{kobayashi_et_al:LIPIcs.MFCS.2023.58, author = {Kobayashi, Yasuaki and Kurita, Kazuhiro and Wasa, Kunihiro}, title = {{Polynomial-Delay Enumeration of Large Maximal Common Independent Sets in Two Matroids}}, booktitle = {48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)}, pages = {58:1--58:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-292-1}, ISSN = {1868-8969}, year = {2023}, volume = {272}, editor = {Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.58}, URN = {urn:nbn:de:0030-drops-185921}, doi = {10.4230/LIPIcs.MFCS.2023.58}, annote = {Keywords: Polynomial-delay enumeration, Ranked Enumeration, Matroid intersection, Reverse search} }

Document

**Published in:** LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Given a graph and two vertex sets satisfying a certain feasibility condition, a reconfiguration problem asks whether we can reach one vertex set from the other by repeating prescribed modification steps while maintaining feasibility. In this setting, Mouawad et al. [IPEC 2014] presented an algorithmic meta-theorem for reconfiguration problems that says if the feasibility can be expressed in monadic second-order logic (MSO), then the problem is fixed-parameter tractable parameterized by treewidth + 𝓁, where 𝓁 is the number of steps allowed to reach the target set. On the other hand, it is shown by Wrochna [J. Comput. Syst. Sci. 2018] that if 𝓁 is not part of the parameter, then the problem is PSPACE-complete even on graphs of bounded bandwidth.
In this paper, we present the first algorithmic meta-theorems for the case where 𝓁 is not part of the parameter, using some structural graph parameters incomparable with bandwidth. We show that if the feasibility is defined in MSO, then the reconfiguration problem under the so-called token jumping rule is fixed-parameter tractable parameterized by neighborhood diversity. We also show that the problem is fixed-parameter tractable parameterized by treedepth + k, where k is the size of sets being transformed. We finally complement the positive result for treedepth by showing that the problem is PSPACE-complete on forests of depth 3.

Tatsuya Gima, Takehiro Ito, Yasuaki Kobayashi, and Yota Otachi. Algorithmic Meta-Theorems for Combinatorial Reconfiguration Revisited. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 61:1-61:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{gima_et_al:LIPIcs.ESA.2022.61, author = {Gima, Tatsuya and Ito, Takehiro and Kobayashi, Yasuaki and Otachi, Yota}, title = {{Algorithmic Meta-Theorems for Combinatorial Reconfiguration Revisited}}, booktitle = {30th Annual European Symposium on Algorithms (ESA 2022)}, pages = {61:1--61:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-247-1}, ISSN = {1868-8969}, year = {2022}, volume = {244}, editor = {Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.61}, URN = {urn:nbn:de:0030-drops-169991}, doi = {10.4230/LIPIcs.ESA.2022.61}, annote = {Keywords: Combinatorial reconfiguration, monadic second-order logic, fixed-parameter tractability, treedepth, neighborhood diversity} }

Document

**Published in:** LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

For a connected graph G = (V, E) and s, t ∈ V, a non-separating s-t path is a path P between s and t such that the set of vertices of P does not separate G, that is, G - V(P) is connected. An s-t path P is non-disconnecting if G - E(P) is connected. The problems of finding shortest non-separating and non-disconnecting paths are both known to be NP-hard. In this paper, we consider the problems from the viewpoint of parameterized complexity. We show that the problem of finding a non-separating s-t path of length at most k is W[1]-hard parameterized by k, while the non-disconnecting counterpart is fixed-parameter tractable (FPT) parameterized by k. We also consider the shortest non-separating path problem on several classes of graphs and show that this problem is NP-hard even on bipartite graphs, split graphs, and planar graphs. As for positive results, the shortest non-separating path problem is FPT parameterized by k on planar graphs and on unit disk graphs (where no s, t is given). Further, we give a polynomial-time algorithm on chordal graphs if k is the distance of the shortest path between s and t.

Ankit Abhinav, Susobhan Bandopadhyay, Aritra Banik, Yasuaki Kobayashi, Shunsuke Nagano, Yota Otachi, and Saket Saurabh. Parameterized Complexity of Non-Separating and Non-Disconnecting Paths and Sets. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 6:1-6:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{abhinav_et_al:LIPIcs.MFCS.2022.6, author = {Abhinav, Ankit and Bandopadhyay, Susobhan and Banik, Aritra and Kobayashi, Yasuaki and Nagano, Shunsuke and Otachi, Yota and Saurabh, Saket}, title = {{Parameterized Complexity of Non-Separating and Non-Disconnecting Paths and Sets}}, booktitle = {47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)}, pages = {6:1--6:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-256-3}, ISSN = {1868-8969}, year = {2022}, volume = {241}, editor = {Szeider, Stefan and Ganian, Robert and Silva, Alexandra}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.6}, URN = {urn:nbn:de:0030-drops-168041}, doi = {10.4230/LIPIcs.MFCS.2022.6}, annote = {Keywords: Non-separating path, Parameterized complexity} }

Document

**Published in:** LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Directed Token Sliding asks, given a directed graph and two sets of pairwise nonadjacent vertices, whether one can reach from one set to the other by repeatedly applying a local operation that exchanges a vertex in the current set with one of its out-neighbors, while keeping the nonadjacency. It can be seen as a reconfiguration process where a token is placed on each vertex in the current set, and the local operation slides a token along an arc respecting its direction. Previously, such a problem was extensively studied on undirected graphs, where the edges have no directions and thus the local operation is symmetric. Directed Token Sliding is a generalization of its undirected variant since an undirected edge can be simulated by two arcs of opposite directions.
In this paper, we initiate the algorithmic study of Directed Token Sliding. We first observe that the problem is PSPACE-complete even if we forbid parallel arcs in opposite directions and that the problem on directed acyclic graphs is NP-complete and W[1]-hard parameterized by the size of the sets in consideration. We then show our main result: a linear-time algorithm for the problem on directed graphs whose underlying undirected graphs are trees, which are called polytrees. Such a result is also known for the undirected variant of the problem on trees [Demaine et al. TCS 2015], but the techniques used here are quite different because of the asymmetric nature of the directed problem. We present a characterization of yes-instances based on the existence of a certain set of directed paths, and then derive simple equivalent conditions from it by some observations, which yield an efficient algorithm. For the polytree case, we also present a quadratic-time algorithm that outputs, if the input is a yes-instance, one of the shortest reconfiguration sequences.

Takehiro Ito, Yuni Iwamasa, Yasuaki Kobayashi, Yu Nakahata, Yota Otachi, Masahiro Takahashi, and Kunihiro Wasa. Independent Set Reconfiguration on Directed Graphs. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 58:1-58:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{ito_et_al:LIPIcs.MFCS.2022.58, author = {Ito, Takehiro and Iwamasa, Yuni and Kobayashi, Yasuaki and Nakahata, Yu and Otachi, Yota and Takahashi, Masahiro and Wasa, Kunihiro}, title = {{Independent Set Reconfiguration on Directed Graphs}}, booktitle = {47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)}, pages = {58:1--58:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-256-3}, ISSN = {1868-8969}, year = {2022}, volume = {241}, editor = {Szeider, Stefan and Ganian, Robert and Silva, Alexandra}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.58}, URN = {urn:nbn:de:0030-drops-168567}, doi = {10.4230/LIPIcs.MFCS.2022.58}, annote = {Keywords: Combinatorial reconfiguration, token sliding, directed graph, independent set, graph algorithm} }

Document

**Published in:** LIPIcs, Volume 180, 15th International Symposium on Parameterized and Exact Computation (IPEC 2020)

Graph Burning asks, given a graph G = (V,E) and an integer k, whether there exists (b₀,… ,b_{k-1}) ∈ V^{k} such that every vertex in G has distance at most i from some b_i. This problem is known to be NP-complete even on connected caterpillars of maximum degree 3. We study the parameterized complexity of this problem and answer all questions arose by Kare and Reddy [IWOCA 2019] about parameterized complexity of the problem. We show that the problem is W[2]-complete parameterized by k and that it does not admit a polynomial kernel parameterized by vertex cover number unless NP ⊆ coNP/poly. We also show that the problem is fixed-parameter tractable parameterized by clique-width plus the maximum diameter among all connected components. This implies the fixed-parameter tractability parameterized by modular-width, by treedepth, and by distance to cographs. Although the parameterization by distance to split graphs cannot be handled with the clique-width argument, we show that this is also tractable by a reduction to a generalized problem with a smaller solution size.

Yasuaki Kobayashi and Yota Otachi. Parameterized Complexity of Graph Burning. In 15th International Symposium on Parameterized and Exact Computation (IPEC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 180, pp. 21:1-21:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{kobayashi_et_al:LIPIcs.IPEC.2020.21, author = {Kobayashi, Yasuaki and Otachi, Yota}, title = {{Parameterized Complexity of Graph Burning}}, booktitle = {15th International Symposium on Parameterized and Exact Computation (IPEC 2020)}, pages = {21:1--21:10}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-172-6}, ISSN = {1868-8969}, year = {2020}, volume = {180}, editor = {Cao, Yixin and Pilipczuk, Marcin}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2020.21}, URN = {urn:nbn:de:0030-drops-133241}, doi = {10.4230/LIPIcs.IPEC.2020.21}, annote = {Keywords: Graph burning, parameterized complexity, fixed-parameter tractability} }

Document

**Published in:** LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Let G = (V, E) be an undirected graph and let B ⊆ V × V be a set of terminal pairs. A node/edge multicut is a subset of vertices/edges of G whose removal destroys all the paths between every terminal pair in B. The problem of computing a minimum node/edge multicut is NP-hard and extensively studied from several viewpoints. In this paper, we study the problem of enumerating all minimal node multicuts. We give an incremental polynomial delay enumeration algorithm for minimal node multicuts, which extends an enumeration algorithm due to Khachiyan et al. (Algorithmica, 2008) for minimal edge multicuts.
Important special cases of node/edge multicuts are node/edge multiway cuts, where the set of terminal pairs contains every pair of vertices in some subset T ⊆ V, that is, B = T × T. We improve the running time bound for this special case: We devise a polynomial delay and exponential space enumeration algorithm for minimal node multiway cuts and a polynomial delay and space enumeration algorithm for minimal edge multiway cuts.

Kazuhiro Kurita and Yasuaki Kobayashi. Efficient Enumerations for Minimal Multicuts and Multiway Cuts. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 60:1-60:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{kurita_et_al:LIPIcs.MFCS.2020.60, author = {Kurita, Kazuhiro and Kobayashi, Yasuaki}, title = {{Efficient Enumerations for Minimal Multicuts and Multiway Cuts}}, booktitle = {45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)}, pages = {60:1--60:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-159-7}, ISSN = {1868-8969}, year = {2020}, volume = {170}, editor = {Esparza, Javier and Kr\'{a}l', Daniel}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.60}, URN = {urn:nbn:de:0030-drops-127272}, doi = {10.4230/LIPIcs.MFCS.2020.60}, annote = {Keywords: Multicuts, Multiway cuts, Enumeration algorithms} }

Document

**Published in:** LIPIcs, Volume 148, 14th International Symposium on Parameterized and Exact Computation (IPEC 2019)

We study two variants of Maximum Cut, which we call Connected Maximum Cut and Maximum Minimal Cut, in this paper. In these problems, given an unweighted graph, the goal is to compute a maximum cut satisfying some connectivity requirements. Both problems are known to be NP-complete even on planar graphs whereas Maximum Cut on planar graphs is solvable in polynomial time. We first show that these problems are NP-complete even on planar bipartite graphs and split graphs. Then we give parameterized algorithms using graph parameters such as clique-width, tree-width, and twin-cover number. Finally, we obtain FPT algorithms with respect to the solution size.

Hiroshi Eto, Tesshu Hanaka, Yasuaki Kobayashi, and Yusuke Kobayashi. Parameterized Algorithms for Maximum Cut with Connectivity Constraints. In 14th International Symposium on Parameterized and Exact Computation (IPEC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 148, pp. 13:1-13:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{eto_et_al:LIPIcs.IPEC.2019.13, author = {Eto, Hiroshi and Hanaka, Tesshu and Kobayashi, Yasuaki and Kobayashi, Yusuke}, title = {{Parameterized Algorithms for Maximum Cut with Connectivity Constraints}}, booktitle = {14th International Symposium on Parameterized and Exact Computation (IPEC 2019)}, pages = {13:1--13:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-129-0}, ISSN = {1868-8969}, year = {2019}, volume = {148}, editor = {Jansen, Bart M. P. and Telle, Jan Arne}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2019.13}, URN = {urn:nbn:de:0030-drops-114747}, doi = {10.4230/LIPIcs.IPEC.2019.13}, annote = {Keywords: Maximum cut, Parameterized algorithm, NP-hardness, Graph parameter} }

Document

**Published in:** LIPIcs, Volume 149, 30th International Symposium on Algorithms and Computation (ISAAC 2019)

In this paper, we investigate the computational complexity of lattice puzzle, which is one of the traditional puzzles. A lattice puzzle consists of 2n plates with some slits, and the goal of this puzzle is to assemble them to form a lattice of size n x n. It has a long history in the puzzle society; however, there is no known research from the viewpoint of theoretical computer science. This puzzle has some natural variants, and they characterize representative computational complexity classes in the class NP. Especially, one of the natural variants gives a characterization of the graph isomorphism problem. That is, the variant is GI-complete in general. As far as the authors know, this is the first non-trivial GI-complete problem characterized by a classic puzzle. Like the sliding block puzzles, this simple puzzle can be used to characterize several representative computational complexity classes. That is, it gives us new insight of these computational complexity classes.

Yasuaki Kobayashi, Koki Suetsugu, Hideki Tsuiki, and Ryuhei Uehara. On the Complexity of Lattice Puzzles. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 32:1-32:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{kobayashi_et_al:LIPIcs.ISAAC.2019.32, author = {Kobayashi, Yasuaki and Suetsugu, Koki and Tsuiki, Hideki and Uehara, Ryuhei}, title = {{On the Complexity of Lattice Puzzles}}, booktitle = {30th International Symposium on Algorithms and Computation (ISAAC 2019)}, pages = {32:1--32:12}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-130-6}, ISSN = {1868-8969}, year = {2019}, volume = {149}, editor = {Lu, Pinyan and Zhang, Guochuan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2019.32}, URN = {urn:nbn:de:0030-drops-115287}, doi = {10.4230/LIPIcs.ISAAC.2019.32}, annote = {Keywords: Lattice puzzle, NP-completeness, GI-completeness, FPT algorithm} }

Document

**Published in:** LIPIcs, Volume 89, 12th International Symposium on Parameterized and Exact Computation (IPEC 2017)

Book embedding is one of the most well-known graph drawing models and is extensively studied in the literature. The special case where the number of pages is one is of particular interest: an embedding in this case has a natural circular representation useful for visualization and graphs that can be embedded in one page without crossings form an important graph class, namely that of outerplanar graphs.
In this paper, we consider the problem of minimizing the number of crossings in a one-page book embedding, which we call one-page crossing minimization. Here, we are given a graph G with n vertices together with a non-negative integer k and are asked whether G can be embedded into a single page with at most k crossings. Bannister and Eppstein (GD 2014) showed that this problem is fixed-parameter tractable. Their algorithm is derived through the application of Courcelle's theorem (on graph properties definable in the monadic second-order logic of graphs) and runs in f(L)n time, where L = 2^{O(k^2)} is the length of the formula defining the property that the one-page crossing number is at most k and f is a computable function without any known upper bound expressible as an elementary function. We give an explicit dynamic programming algorithm with a drastically improved running time of 2^{O(k log k)}n.

Yasuaki Kobayashi, Hiromu Ohtsuka, and Hisao Tamaki. An Improved Fixed-Parameter Algorithm for One-Page Crossing Minimization. In 12th International Symposium on Parameterized and Exact Computation (IPEC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 89, pp. 25:1-25:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{kobayashi_et_al:LIPIcs.IPEC.2017.25, author = {Kobayashi, Yasuaki and Ohtsuka, Hiromu and Tamaki, Hisao}, title = {{An Improved Fixed-Parameter Algorithm for One-Page Crossing Minimization}}, booktitle = {12th International Symposium on Parameterized and Exact Computation (IPEC 2017)}, pages = {25:1--25:12}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-051-4}, ISSN = {1868-8969}, year = {2018}, volume = {89}, editor = {Lokshtanov, Daniel and Nishimura, Naomi}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2017.25}, URN = {urn:nbn:de:0030-drops-85661}, doi = {10.4230/LIPIcs.IPEC.2017.25}, annote = {Keywords: Book Embedding, Fixed-Parameter Tractability, Graph Drawing, Treewidth} }

Document

**Published in:** LIPIcs, Volume 63, 11th International Symposium on Parameterized and Exact Computation (IPEC 2016)

To solve hard graph problems from the parameterized perspective, structural parameters have commonly been used. In particular, vertex cover number is frequently used in this context. In this paper, we study the problem of computing the treedepth of a given graph G. We show that there are an O(tau(G)^3) vertex kernel and an O(4^{tau(G)}*tau(G)*n) time fixed-parameter algorithm for this problem, where tau(G) is the size of a minimum vertex cover of G and n is the number of vertices of G.

Yasuaki Kobayashi and Hisao Tamaki. Treedepth Parameterized by Vertex Cover Number. In 11th International Symposium on Parameterized and Exact Computation (IPEC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 63, pp. 18:1-18:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{kobayashi_et_al:LIPIcs.IPEC.2016.18, author = {Kobayashi, Yasuaki and Tamaki, Hisao}, title = {{Treedepth Parameterized by Vertex Cover Number}}, booktitle = {11th International Symposium on Parameterized and Exact Computation (IPEC 2016)}, pages = {18:1--18:11}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-023-1}, ISSN = {1868-8969}, year = {2017}, volume = {63}, editor = {Guo, Jiong and Hermelin, Danny}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2016.18}, URN = {urn:nbn:de:0030-drops-69438}, doi = {10.4230/LIPIcs.IPEC.2016.18}, annote = {Keywords: Fixed-parameter algorithm, Polynomial kernelization, Structural parameterization, Treedepth, Vertex cover} }