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Documents authored by Blažej, Václav

Document
DOI: 10.4230/LIPIcs.IPEC.2024.4
On the Parameterized Complexity of Eulerian Strong Component Arc Deletion

Authors: Václav Blažej, Satyabrata Jana, M. S. Ramanujan, and Peter Strulo

Published in: LIPIcs, Volume 321, 19th International Symposium on Parameterized and Exact Computation (IPEC 2024)

Abstract
In this paper, we study the Eulerian Strong Component Arc Deletion problem, where the input is a directed multigraph and the goal is to delete the minimum number of arcs to ensure every strongly connected component of the resulting digraph is Eulerian. This problem is a natural extension of the Directed Feedback Arc Set problem and is also known to be motivated by certain scenarios arising in the study of housing markets. The complexity of the problem, when parameterized by solution size (i.e., size of the deletion set), has remained unresolved and has been highlighted in several papers. In this work, we answer this question by ruling out (subject to the usual complexity assumptions) a fixed-parameter tractable (FPT) algorithm for this parameter and conduct a broad analysis of the problem with respect to other natural parameterizations. We prove both positive and negative results. Among these, we demonstrate that the problem is also hard (W[1]-hard or even para-NP-hard) when parameterized by either treewidth or maximum degree alone. Complementing our lower bounds, we establish that the problem is in XP when parameterized by treewidth and FPT when parameterized either by both treewidth and maximum degree or by both treewidth and solution size. We show that these algorithms have near-optimal asymptotic dependence on the treewidth assuming the Exponential Time Hypothesis.
Cite as

Václav Blažej, Satyabrata Jana, M. S. Ramanujan, and Peter Strulo. On the Parameterized Complexity of Eulerian Strong Component Arc Deletion. In 19th International Symposium on Parameterized and Exact Computation (IPEC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 321, pp. 4:1-4:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{blazej_et_al:LIPIcs.IPEC.2024.4,
  author =	{Bla\v{z}ej, V\'{a}clav and Jana, Satyabrata and Ramanujan, M. S. and Strulo, Peter},
  title =	{{On the Parameterized Complexity of Eulerian Strong Component Arc Deletion}},
  booktitle =	{19th International Symposium on Parameterized and Exact Computation (IPEC 2024)},
  pages =	{4:1--4:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-353-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{321},
  editor =	{Bonnet, \'{E}douard and Rz\k{a}\.{z}ewski, Pawe{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2024.4},
  URN =		{urn:nbn:de:0030-drops-222306},
  doi =		{10.4230/LIPIcs.IPEC.2024.4},
  annote =	{Keywords: Parameterized complexity, Eulerian graphs, Treewidth}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2024.7
On Controlling Knockout Tournaments Without Perfect Information

Authors: Václav Blažej, Sushmita Gupta, M. S. Ramanujan, and Peter Strulo

Published in: LIPIcs, Volume 321, 19th International Symposium on Parameterized and Exact Computation (IPEC 2024)

Abstract
Over the last decade, extensive research has been conducted on the algorithmic aspects of designing single-elimination (SE) tournaments. Addressing natural questions of algorithmic tractability, we identify key properties of input instances that enable the tournament designer to efficiently schedule the tournament in a way that maximizes the chances of a preferred player winning. Much of the prior algorithmic work on this topic focuses on the perfect (complete and deterministic) information scenario, especially in the context of fixed-parameter algorithm design. Our contributions constitute the first fixed-parameter tractability results applicable to more general settings of SE tournament design with potential imperfect information.
Cite as

Václav Blažej, Sushmita Gupta, M. S. Ramanujan, and Peter Strulo. On Controlling Knockout Tournaments Without Perfect Information. In 19th International Symposium on Parameterized and Exact Computation (IPEC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 321, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{blazej_et_al:LIPIcs.IPEC.2024.7,
  author =	{Bla\v{z}ej, V\'{a}clav and Gupta, Sushmita and Ramanujan, M. S. and Strulo, Peter},
  title =	{{On Controlling Knockout Tournaments Without Perfect Information}},
  booktitle =	{19th International Symposium on Parameterized and Exact Computation (IPEC 2024)},
  pages =	{7:1--7:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-353-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{321},
  editor =	{Bonnet, \'{E}douard and Rz\k{a}\.{z}ewski, Pawe{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2024.7},
  URN =		{urn:nbn:de:0030-drops-222337},
  doi =		{10.4230/LIPIcs.IPEC.2024.7},
  annote =	{Keywords: Parameterized algorithms, Tournament design, Imperfect information}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.29
Equitable Connected Partition and Structural Parameters Revisited: N-Fold Beats Lenstra

Authors: Václav Blažej, Dušan Knop, Jan Pokorný, and Šimon Schierreich

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
In the Equitable Connected Partition (ECP for short) problem, we are given a graph G = (V,E) together with an integer p ∈ ℕ, and our goal is to find a partition of V into p parts such that each part induces a connected sub-graph of G and the size of each two parts differs by at most 1. On the one hand, the problem is known to be NP-hard in general and W[1]-hard with respect to the path-width, the feedback-vertex set, and the number of parts p combined. On the other hand, fixed-parameter algorithms are known for parameters the vertex-integrity and the max leaf number. In this work, we systematically study ECP with respect to various structural restrictions of the underlying graph and provide a clear dichotomy of its parameterised complexity. Specifically, we show that the problem is in FPT when parameterized by the modular-width and the distance to clique. Next, we prove W[1]-hardness with respect to the distance to cluster, the 4-path vertex cover number, the distance to disjoint paths, and the feedback-edge set, and NP-hardness for constant shrub-depth graphs. Our hardness results are complemented by matching algorithmic upper-bounds: we give an XP algorithm for parameterisation by the tree-width and the distance to cluster. We also give an improved FPT algorithm for parameterisation by the vertex integrity and the first explicit FPT algorithm for the 3-path vertex cover number. The main ingredient of these algorithms is a formulation of ECP as N-fold IP, which clearly indicates that such formulations may, in certain scenarios, significantly outperform existing algorithms based on the famous algorithm of Lenstra.
Cite as

Václav Blažej, Dušan Knop, Jan Pokorný, and Šimon Schierreich. Equitable Connected Partition and Structural Parameters Revisited: N-Fold Beats Lenstra. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 29:1-29:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{blazej_et_al:LIPIcs.MFCS.2024.29,
  author =	{Bla\v{z}ej, V\'{a}clav and Knop, Du\v{s}an and Pokorn\'{y}, Jan and Schierreich, \v{S}imon},
  title =	{{Equitable Connected Partition and Structural Parameters Revisited: N-Fold Beats Lenstra}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{29:1--29:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.29},
  URN =		{urn:nbn:de:0030-drops-205857},
  doi =		{10.4230/LIPIcs.MFCS.2024.29},
  annote =	{Keywords: Equitable Connected Partition, structural parameters, fixed-parameter tractability, N-fold integer programming, tree-width, shrub-depth, modular-width}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2024.20
Constrained and Ordered Level Planarity Parameterized by the Number of Levels

Authors: Václav Blažej, Boris Klemz, Felix Klesen, Marie Diana Sieper, Alexander Wolff, and Johannes Zink

Published in: LIPIcs, Volume 293, 40th International Symposium on Computational Geometry (SoCG 2024)

Abstract
The problem Level Planarity asks for a crossing-free drawing of a graph in the plane such that vertices are placed at prescribed y-coordinates (called levels) and such that every edge is realized as a y-monotone curve. In the variant Constrained Level Planarity (CLP), each level y is equipped with a partial order ≺_y on its vertices and in the desired drawing the left-to-right order of vertices on level y has to be a linear extension of ≺_y. Ordered Level Planarity (OLP) corresponds to the special case of CLP where the given partial orders ≺_y are total orders. Previous results by Brückner and Rutter [SODA 2017] and Klemz and Rote [ACM Trans. Alg. 2019] state that both CLP and OLP are NP-hard even in severely restricted cases. In particular, they remain NP-hard even when restricted to instances whose width (the maximum number of vertices that may share a common level) is at most two. In this paper, we focus on the other dimension: we study the parameterized complexity of CLP and OLP with respect to the height (the number of levels). We show that OLP parameterized by the height is complete with respect to the complexity class XNLP, which was first studied by Elberfeld, Stockhusen, and Tantau [Algorithmica 2015] (under a different name) and recently made more prominent by Bodlaender, Groenland, Nederlof, and Swennenhuis [FOCS 2021]. It contains all parameterized problems that can be solved nondeterministically in time f(k)⋅ n^O(1) and space f(k)⋅ log n (where f is a computable function, n is the input size, and k is the parameter). If a problem is XNLP-complete, it lies in XP, but is W[t]-hard for every t. In contrast to the fact that OLP parameterized by the height lies in XP, it turns out that CLP is NP-hard even when restricted to instances of height 4. We complement this result by showing that CLP can be solved in polynomial time for instances of height at most 3.
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Václav Blažej, Boris Klemz, Felix Klesen, Marie Diana Sieper, Alexander Wolff, and Johannes Zink. Constrained and Ordered Level Planarity Parameterized by the Number of Levels. In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 20:1-20:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{blazej_et_al:LIPIcs.SoCG.2024.20,
  author =	{Bla\v{z}ej, V\'{a}clav and Klemz, Boris and Klesen, Felix and Sieper, Marie Diana and Wolff, Alexander and Zink, Johannes},
  title =	{{Constrained and Ordered Level Planarity Parameterized by the Number of Levels}},
  booktitle =	{40th International Symposium on Computational Geometry (SoCG 2024)},
  pages =	{20:1--20:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-316-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{293},
  editor =	{Mulzer, Wolfgang and Phillips, Jeff M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2024.20},
  URN =		{urn:nbn:de:0030-drops-199652},
  doi =		{10.4230/LIPIcs.SoCG.2024.20},
  annote =	{Keywords: Parameterized Complexity, Graph Drawing, XNLP, XP, W\lbrackt\rbrack-hard, Level Planarity, Planar Poset Diagram, Computational Geometry}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.22
On Polynomial Kernels for Traveling Salesperson Problem and Its Generalizations

Authors: Václav Blažej, Pratibha Choudhary, Dušan Knop, Šimon Schierreich, Ondřej Suchý, and Tomáš Valla

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

Abstract
For many problems, the important instances from practice possess certain structure that one should reflect in the design of specific algorithms. As data reduction is an important and inextricable part of today’s computation, we employ one of the most successful models of such precomputation - the kernelization. Within this framework, we focus on Traveling Salesperson Problem (TSP) and some of its generalizations. We provide a kernel for TSP with size polynomial in either the feedback edge set number or the size of a modulator to constant-sized components. For its generalizations, we also consider other structural parameters such as the vertex cover number and the size of a modulator to constant-sized paths. We complement our results from the negative side by showing that the existence of a polynomial-sized kernel with respect to the fractioning number, the combined parameter maximum degree and treewidth, and, in the case of {Subset TSP}, modulator to disjoint cycles (i.e., the treewidth two graphs) is unlikely.
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Václav Blažej, Pratibha Choudhary, Dušan Knop, Šimon Schierreich, Ondřej Suchý, and Tomáš Valla. On Polynomial Kernels for Traveling Salesperson Problem and Its Generalizations. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 22:1-22:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{blazej_et_al:LIPIcs.ESA.2022.22,
  author =	{Bla\v{z}ej, V\'{a}clav and Choudhary, Pratibha and Knop, Du\v{s}an and Schierreich, \v{S}imon and Such\'{y}, Ond\v{r}ej and Valla, Tom\'{a}\v{s}},
  title =	{{On Polynomial Kernels for Traveling Salesperson Problem and Its Generalizations}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{22:1--22:16},
  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.2022.22},
  URN =		{urn:nbn:de:0030-drops-169600},
  doi =		{10.4230/LIPIcs.ESA.2022.22},
  annote =	{Keywords: Traveling Salesperson, Subset TSP, Waypoint Routing, Kernelization}
}
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