5 Search Results for "Le, Tien-Nam"

Document
DOI: 10.4230/LIPIcs.STACS.2026.78
Protrusion Decompositions Revisited: Uniform Lossy Kernels for Reducing Treewidth and Linear Kernels for Hitting Disconnected Minors

Authors: Roohani Sharma and Michał Włodarczyk

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
Let ℱ be a finite family of graphs. In the ℱ-Deletion problem, one is given a graph G and an integer k, and the goal is to find k vertices whose deletion results in a graph with no minor from the family ℱ. This may be regarded as a far-reaching generalization of Vertex Cover and Feedback vertex Set. In their seminal work, Fomin, Lokshtanov, Misra & Saurabh [FOCS 2012] gave a polynomial kernel for this problem when the family ℱ contains a planar graph. As the size of their kernel is g(ℱ) ⋅ k^{f(ℱ)}, a natural follow-up question was whether the dependence on ℱ in the exponent of k can be avoided. The answer turned out to be negative: Giannopoulou, Jansen, Lokshtanov & Saurabh [TALG 2017] proved that this is already inevitable for the special case of the Treewidth-η-Deletion problem. In this work, we show that this non-uniformity can be avoided at the expense of a small loss. First, we present a simple 2-approximate kernelization algorithm for Treewidth-η-Deletion with a kernel size g(η) ⋅ k⁶. Next, we show that the approximation factor can be made arbitrarily close to 1, if we settle for a kernelization protocol with 𝒪(1) calls to an oracle that solves instances of size bounded by a uniform polynomial in k. We extend the above results to general ℱ-Deletion, whenever ℱ contains a planar graph, as long as an oracle for Treewidth-η-Deletion is available for small instances. Notably, all our constants are computable functions of ℱ and our techniques work also when some graphs in ℱ may be disconnected. Our results rely on two novel techniques. First, we transform so-called "near-protrusion decompositions" into true protrusion decompositions by sacrificing a small accuracy loss. Secondly, we show how to optimally compress such a decomposition with respect to general ℱ-Deletion. Using our second technique, we also obtain linear kernels on sparse graph classes when ℱ contains a planar graph, whereas the previously known theorems required all graphs in ℱ to be connected. Specifically, we generalize the kernelization algorithm by Kim, Langer, Paul, Reidl, Rossmanith, Sau & Sikdar [TALG 2015] on graph classes that exclude a topological minor.
Cite as

Roohani Sharma and Michał Włodarczyk. Protrusion Decompositions Revisited: Uniform Lossy Kernels for Reducing Treewidth and Linear Kernels for Hitting Disconnected Minors. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 78:1-78:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{sharma_et_al:LIPIcs.STACS.2026.78,
  author =	{Sharma, Roohani and W{\l}odarczyk, Micha{\l}},
  title =	{{Protrusion Decompositions Revisited: Uniform Lossy Kernels for Reducing Treewidth and Linear Kernels for Hitting Disconnected Minors}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{78:1--78:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.78},
  URN =		{urn:nbn:de:0030-drops-255674},
  doi =		{10.4230/LIPIcs.STACS.2026.78},
  annote =	{Keywords: kernelization, graph minors, treewidth, uniform kernels, minor hitting}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.23
Enumeration Kernels for Vertex Cover and Feedback Vertex Set

Authors: Marin Bougeret, Guilherme C. M. Gomes, Vinicius F. dos Santos, and Ignasi Sau

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
Enumerative kernelization is a recent and promising area sitting at the intersection of parameterized complexity and enumeration algorithms. Its study began with the paper of Creignou et al. [Theory Comput. Syst., 2017], and development in the area has started to accelerate with the work of Golovach et al. [J. Comput. Syst. Sci., 2022]. The latter introduced polynomial-delay enumeration kernels and applied them in the study of structural parameterizations of the Matching Cut problem and some variants. Few other results, mostly on Longest Path and some generalizations of Matching Cut, have also been developed. However, little success has been seen in enumeration versions of Vertex Cover and Feedback Vertex Set, some of the most studied problems in kernelization. In this paper, we address this shortcoming. Our first result is a polynomial-delay enumeration kernel with 2k vertices for Enum Vertex Cover, where we wish to list all solutions with at most k vertices. This is obtained by developing a non-trivial lifting algorithm for the classical crown decomposition reduction rule, and directly improves upon the kernel with 𝒪(k²) vertices derived from the work of Creignou et al. Our other result is a polynomial-delay enumeration kernel with 𝒪(k³) vertices and edges for Enum Feedback Vertex Set; the proof is inspired by some ideas of Thomassé [TALG, 2010], but with a weaker bound on the kernel size due to difficulties in applying the q-expansion technique.
Cite as

Marin Bougeret, Guilherme C. M. Gomes, Vinicius F. dos Santos, and Ignasi Sau. Enumeration Kernels for Vertex Cover and Feedback Vertex Set. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 23:1-23:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bougeret_et_al:LIPIcs.IPEC.2025.23,
  author =	{Bougeret, Marin and C. M. Gomes, Guilherme and dos Santos, Vinicius F. and Sau, Ignasi},
  title =	{{Enumeration Kernels for Vertex Cover and Feedback Vertex Set}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{23:1--23:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.23},
  URN =		{urn:nbn:de:0030-drops-251552},
  doi =		{10.4230/LIPIcs.IPEC.2025.23},
  annote =	{Keywords: Kernelization, Enumeration, Vertex cover, Crown decomposition, Feedback vertex set}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.48
Quadratic Kernel for Cliques or Trees Vertex Deletion

Authors: Soh Kumabe

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
We consider Cliques or Trees Vertex Deletion, which is a hybrid of two fundamental parameterized problems: Cluster Vertex Deletion and Feedback Vertex Set. In this problem, we are given an undirected graph G and an integer k, and asked to find a vertex subset X of size at most k such that each connected component of G-X is either a clique or a tree. Jacob et al. (ISAAC, 2024) provided a kernel of O(k⁵) vertices for this problem, which was recently improved to O(k⁴) by Tsur (IPL, 2025). Our main result is a kernel of O(k²) vertices. This result closes the gap between the kernelization result for Feedback Vertex Set, which corresponds to the case where each connected component of G-X must be a tree. Although both cluster vertex deletion number and feedback vertex set number are well-studied structural parameters, little attention has been given to parameters that generalize both of them. In fact, the lowest common well-known generalization of them is clique-width, which is a highly general parameter. To fill the gap here, we initiate the study of the cliques or trees vertex deletion number as a structural parameter. We prove that Longest Cycle, which is a fundamental problem that does not admit o(n^k)-time algorithm unless ETH fails when k is the clique-width, becomes fixed-parameter tractable when parameterized by the cliques or trees vertex deletion number.
Cite as

Soh Kumabe. Quadratic Kernel for Cliques or Trees Vertex Deletion. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 48:1-48:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kumabe:LIPIcs.ISAAC.2025.48,
  author =	{Kumabe, Soh},
  title =	{{Quadratic Kernel for Cliques or Trees Vertex Deletion}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{48:1--48:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.48},
  URN =		{urn:nbn:de:0030-drops-249568},
  doi =		{10.4230/LIPIcs.ISAAC.2025.48},
  annote =	{Keywords: Fixed-Parameter Tractability, Kernelization, Deletion to Scattered Graph Classes, Cluster Vertex Deletion, Feedback Vertex Set}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.51
Parameterized Geometric Graph Modification with Disk Scaling

Authors: Fedor V. Fomin, Petr A. Golovach, Tanmay Inamdar, Saket Saurabh, and Meirav Zehavi

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
The parameterized analysis of graph modification problems represents the most extensively studied area within Parameterized Complexity. Given a graph G and an integer k ∈ ℕ as input, the goal is to determine whether we can perform at most k operations on G to transform it into a graph belonging to a specified graph class ℱ. Typical operations are combinatorial and include vertex deletions and edge deletions, insertions, and contractions. However, in many real-world scenarios, when the input graph is constrained to be a geometric intersection graph, the modification of the graph is influenced by changes in the geometric properties of the underlying objects themselves, rather than by combinatorial modifications. It raises the question of whether vertex deletions or adjacency modifications are necessarily the most appropriate modification operations for studying modifications of geometric graphs. We propose the study of the disk intersection graph modification through the scaling of disks. This operation is typical in the realm of topology control but has not yet been explored in the context of Parameterized Complexity. We design parameterized algorithms and kernels for modifying to the most basic graph classes: edgeless, connected, and acyclic. Our technical contributions encompass a novel combination of linear programming, branching, and kernelization techniques, along with a fresh application of bidimensionality theory to analyze the area covered by disks, which may have broader applicability.
Cite as

Fedor V. Fomin, Petr A. Golovach, Tanmay Inamdar, Saket Saurabh, and Meirav Zehavi. Parameterized Geometric Graph Modification with Disk Scaling. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 51:1-51:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fomin_et_al:LIPIcs.ITCS.2025.51,
  author =	{Fomin, Fedor V. and Golovach, Petr A. and Inamdar, Tanmay and Saurabh, Saket and Zehavi, Meirav},
  title =	{{Parameterized Geometric Graph Modification with Disk Scaling}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{51:1--51:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.51},
  URN =		{urn:nbn:de:0030-drops-226795},
  doi =		{10.4230/LIPIcs.ITCS.2025.51},
  annote =	{Keywords: parameterized algorithms, kernelization, spreading points, distant representatives, unit disk packing}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.49
Lossy Kernelization for (Implicit) Hitting Set Problems

Authors: Fedor V. Fomin, Tien-Nam Le, Daniel Lokshtanov, Saket Saurabh, Stéphan Thomassé, and Meirav Zehavi

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
We re-visit the complexity of polynomial time pre-processing (kernelization) for the d-Hitting Set problem. This is one of the most classic problems in Parameterized Complexity by itself, and, furthermore, it encompasses several other of the most well-studied problems in this field, such as Vertex Cover, Feedback Vertex Set in Tournaments (FVST) and Cluster Vertex Deletion (CVD). In fact, d-Hitting Set encompasses any deletion problem to a hereditary property that can be characterized by a finite set of forbidden induced subgraphs. With respect to bit size, the kernelization complexity of d-Hitting Set is essentially settled: there exists a kernel with 𝒪(k^d) bits (𝒪(k^d) sets and 𝒪(k^{d-1}) elements) and this it tight by the result of Dell and van Melkebeek [STOC 2010, JACM 2014]. Still, the question of whether there exists a kernel for d-Hitting Set with fewer elements has remained one of the most major open problems in Kernelization. In this paper, we first show that if we allow the kernelization to be lossy with a qualitatively better loss than the best possible approximation ratio of polynomial time approximation algorithms, then one can obtain kernels where the number of elements is linear for every fixed d. Further, based on this, we present our main result: we show that there exist approximate Turing kernelizations for d-Hitting Set that even beat the established bit-size lower bounds for exact kernelizations - in fact, we use a constant number of oracle calls, each with "near linear" (𝒪(k^{1+ε})) bit size, that is, almost the best one could hope for. Lastly, for two special cases of implicit 3-Hitting set, namely, FVST and CVD, we obtain the "best of both worlds" type of results - (1+ε)-approximate kernelizations with a linear number of vertices. In terms of size, this substantially improves the exact kernels of Fomin et al. [SODA 2018, TALG 2019], with simpler arguments.
Cite as

Fedor V. Fomin, Tien-Nam Le, Daniel Lokshtanov, Saket Saurabh, Stéphan Thomassé, and Meirav Zehavi. Lossy Kernelization for (Implicit) Hitting Set Problems. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 49:1-49:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{fomin_et_al:LIPIcs.ESA.2023.49,
  author =	{Fomin, Fedor V. and Le, Tien-Nam and Lokshtanov, Daniel and Saurabh, Saket and Thomass\'{e}, St\'{e}phan and Zehavi, Meirav},
  title =	{{Lossy Kernelization for (Implicit) Hitting Set Problems}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{49:1--49:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. 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.2023.49},
  URN =		{urn:nbn:de:0030-drops-187020},
  doi =		{10.4230/LIPIcs.ESA.2023.49},
  annote =	{Keywords: Hitting Set, Lossy Kernelization}
}
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