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Volume

LIPIcs, Volume 214

16th International Symposium on Parameterized and Exact Computation (IPEC 2021)

IPEC 2021, September 8-10, 2021, Lisbon, Portugal

Editors: Petr A. Golovach and Meirav Zehavi

Document

DOI: 10.4230/DagRep.13.4.58

New Frontiers of Parameterized Complexity in Graph Drawing (Dagstuhl Seminar 23162)

Authors: Robert Ganian, Fabrizio Montecchiani, Martin Nöllenburg, Meirav Zehavi, and Liana Khazaliya

Published in: Dagstuhl Reports, Volume 13, Issue 4 (2023)

Abstract

This report documents the program and the outcomes of Dagstuhl Seminar 23162 "New Frontiers of Parameterized Complexity in Graph Drawing”. The seminar was held in-person from April 16 to April 21, 2023. It brought together 32 researchers from the Graph Drawing and the Parameterized Complexity research communities to discuss and explore new research frontiers on the interface between the two fields. The report collects the abstracts of talks and open problems presented in the seminar, as well as brief progress reports from the working groups.

Cite as

Robert Ganian, Fabrizio Montecchiani, Martin Nöllenburg, Meirav Zehavi, and Liana Khazaliya. New Frontiers of Parameterized Complexity in Graph Drawing (Dagstuhl Seminar 23162). In Dagstuhl Reports, Volume 13, Issue 4, pp. 58-97, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@Article{ganian_et_al:DagRep.13.4.58,
  author =	{Ganian, Robert and Montecchiani, Fabrizio and N\"{o}llenburg, Martin and Zehavi, Meirav and Khazaliya, Liana},
  title =	{{New Frontiers of Parameterized Complexity in Graph Drawing (Dagstuhl Seminar 23162)}},
  pages =	{58--97},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2023},
  volume =	{13},
  number =	{4},
  editor =	{Ganian, Robert and Montecchiani, Fabrizio and N\"{o}llenburg, Martin and Zehavi, Meirav and Khazaliya, Liana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.13.4.58},
  URN =		{urn:nbn:de:0030-drops-192393},
  doi =		{10.4230/DagRep.13.4.58},
  annote =	{Keywords: algorithm design, computational geometry, graph drawing, parameterized complexity}
}

Document

DOI: 10.4230/LIPIcs.ESA.2023.48

Kernelization for Spreading Points

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

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

Abstract

We consider the following problem about dispersing points. Given a set of points in the plane, the task is to identify whether by moving a small number of points by small distance, we can obtain an arrangement of points such that no pair of points is "close" to each other. More precisely, for a family of n points, an integer k, and a real number d > 0, we ask whether at most k points could be relocated, each point at distance at most d from its original location, such that the distance between each pair of points is at least a fixed constant, say 1. A number of approximation algorithms for variants of this problem, under different names like distant representatives, disk dispersing, or point spreading, are known in the literature. However, to the best of our knowledge, the parameterized complexity of this problem remains widely unexplored. We make the first step in this direction by providing a kernelization algorithm that, in polynomial time, produces an equivalent instance with 𝒪(d²k³) points. As a byproduct of this result, we also design a non-trivial fixed-parameter tractable (FPT) algorithm for the problem, parameterized by k and d. Finally, we complement the result about polynomial kernelization by showing a lower bound that rules out the existence of a kernel whose size is polynomial in k alone, unless NP ⊆ coNP/poly.

Cite as

Fedor V. Fomin, Petr A. Golovach, Tanmay Inamdar, Saket Saurabh, and Meirav Zehavi. Kernelization for Spreading Points. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 48:1-48:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{fomin_et_al:LIPIcs.ESA.2023.48,
  author =	{Fomin, Fedor V. and Golovach, Petr A. and Inamdar, Tanmay and Saurabh, Saket and Zehavi, Meirav},
  title =	{{Kernelization for Spreading Points}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{48:1--48:16},
  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.2023.48},
  URN =		{urn:nbn:de:0030-drops-187017},
  doi =		{10.4230/LIPIcs.ESA.2023.48},
  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}
}

Document

DOI: 10.4230/LIPIcs.ESA.2023.65

Finding Long Directed Cycles Is Hard Even When DFVS Is Small or Girth Is Large

Authors: Ashwin Jacob, Michał Włodarczyk, and Meirav Zehavi

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

Abstract

We study the parameterized complexity of two classic problems on directed graphs: Hamiltonian Cycle and its generalization Longest Cycle. Since 2008, it is known that Hamiltonian Cycle is W[1]-hard when parameterized by directed treewidth [Lampis et al., ISSAC'08]. By now, the question of whether it is FPT parameterized by the directed feedback vertex set (DFVS) number has become a longstanding open problem. In particular, the DFVS number is the largest natural directed width measure studied in the literature. In this paper, we provide a negative answer to the question, showing that even for the DFVS number, the problem remains W[1]-hard. As a consequence, we also obtain that Longest Cycle is W[1]-hard on directed graphs when parameterized multiplicatively above girth, in contrast to the undirected case. This resolves an open question posed by Fomin et al. [ACM ToCT'21] and Gutin and Mnich [arXiv:2207.12278]. Our hardness results apply to the path versions of the problems as well. On the positive side, we show that Longest Path parameterized multiplicatively above girth belongs to the class XP.

Cite as

Ashwin Jacob, Michał Włodarczyk, and Meirav Zehavi. Finding Long Directed Cycles Is Hard Even When DFVS Is Small or Girth Is Large. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 65:1-65:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{jacob_et_al:LIPIcs.ESA.2023.65,
  author =	{Jacob, Ashwin and W{\l}odarczyk, Micha{\l} and Zehavi, Meirav},
  title =	{{Finding Long Directed Cycles Is Hard Even When DFVS Is Small or Girth Is Large}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{65:1--65:17},
  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.2023.65},
  URN =		{urn:nbn:de:0030-drops-187184},
  doi =		{10.4230/LIPIcs.ESA.2023.65},
  annote =	{Keywords: Hamiltonian cycle, longest path, directed feedback vertex set, directed graphs, parameterized complexity}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2023.49

Parameterized Analysis of the Cops and Robber Game

Authors: Harmender Gahlawat and Meirav Zehavi

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

Abstract

Pursuit-evasion games have been intensively studied for several decades due to their numerous applications in artificial intelligence, robot motion planning, database theory, distributed computing, and algorithmic theory. Cops and Robber (CnR) is one of the most well-known pursuit-evasion games played on graphs, where multiple cops pursue a single robber. The aim is to compute the cop number of a graph, k, which is the minimum number of cops that ensures the capture of the robber. From the viewpoint of parameterized complexity, CnR is W[2]-hard parameterized by k [Fomin et al., TCS, 2010]. Thus, we study structural parameters of the input graph. We begin with the vertex cover number (vcn). First, we establish that k ≤ vcn/3+1. Second, we prove that CnR parameterized by vcn is FPT by designing an exponential kernel. We complement this result by showing that it is unlikely for CnR parameterized by vcn to admit a polynomial compression. We extend our exponential kernels to the parameters cluster vertex deletion number and deletion to stars number, and design a linear vertex kernel for neighborhood diversity. Additionally, we extend all of our results to several well-studied variations of CnR.

Cite as

Harmender Gahlawat and Meirav Zehavi. Parameterized Analysis of the Cops and Robber Game. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 49:1-49:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{gahlawat_et_al:LIPIcs.MFCS.2023.49,
  author =	{Gahlawat, Harmender and Zehavi, Meirav},
  title =	{{Parameterized Analysis of the Cops and Robber Game}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{49:1--49:17},
  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.2023.49},
  URN =		{urn:nbn:de:0030-drops-185837},
  doi =		{10.4230/LIPIcs.MFCS.2023.49},
  annote =	{Keywords: Cops and Robber, Kernelization, Graph Searching, Fixed parameter tractability}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2023.13

On Computing Homological Hitting Sets

Authors: Ulrich Bauer, Abhishek Rathod, and Meirav Zehavi

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract

Cut problems form one of the most fundamental classes of problems in algorithmic graph theory. In this paper, we initiate the algorithmic study of a high-dimensional cut problem. The problem we study, namely, Homological Hitting Set (HHS), is defined as follows: Given a nontrivial r-cycle z in a simplicial complex, find a set 𝒮 of r-dimensional simplices of minimum cardinality so that 𝒮 meets every cycle homologous to z. Our first result is that HHS admits a polynomial-time solution on triangulations of closed surfaces. Interestingly, the minimal solution is given in terms of the cocycles of the surface. Next, we provide an example of a 2-complex for which the (unique) minimal hitting set is not a cocycle. Furthermore, for general complexes, we show that HHS is W[1]-hard with respect to the solution size p. In contrast, on the positive side, we show that HHS admits an FPT algorithm with respect to p+Δ, where Δ is the maximum degree of the Hasse graph of the complex 𝖪.

Cite as

Ulrich Bauer, Abhishek Rathod, and Meirav Zehavi. On Computing Homological Hitting Sets. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 13:1-13:21, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bauer_et_al:LIPIcs.ITCS.2023.13,
  author =	{Bauer, Ulrich and Rathod, Abhishek and Zehavi, Meirav},
  title =	{{On Computing Homological Hitting Sets}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{13:1--13:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.13},
  URN =		{urn:nbn:de:0030-drops-175169},
  doi =		{10.4230/LIPIcs.ITCS.2023.13},
  annote =	{Keywords: Algorithmic topology, Cut problems, Surfaces, Parameterized complexity}
}

Document

DOI: 10.4230/LIPIcs.IPEC.2022.1

A Finite Algorithm for the Realizabilty of a Delaunay Triangulation

Authors: Akanksha Agrawal, Saket Saurabh, and Meirav Zehavi

Published in: LIPIcs, Volume 249, 17th International Symposium on Parameterized and Exact Computation (IPEC 2022)

Abstract

The Delaunay graph of a point set P ⊆ ℝ² is the plane graph with the vertex-set P and the edge-set that contains {p,p'} if there exists a disc whose intersection with P is exactly {p,p'}. Accordingly, a triangulated graph G is Delaunay realizable if there exists a triangulation of the Delaunay graph of some P ⊆ ℝ², called a Delaunay triangulation of P, that is isomorphic to G. The objective of Delaunay Realization is to compute a point set P ⊆ ℝ² that realizes a given graph G (if such a P exists). Known algorithms do not solve Delaunay Realization as they are non-constructive. Obtaining a constructive algorithm for Delaunay Realization was mentioned as an open problem by Hiroshima et al. [Hiroshima et al., 2000]. We design an n^𝒪(n)-time constructive algorithm for Delaunay Realization. In fact, our algorithm outputs sets of points with integer coordinates.

Cite as

Akanksha Agrawal, Saket Saurabh, and Meirav Zehavi. A Finite Algorithm for the Realizabilty of a Delaunay Triangulation. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 1:1-1:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{agrawal_et_al:LIPIcs.IPEC.2022.1,
  author =	{Agrawal, Akanksha and Saurabh, Saket and Zehavi, Meirav},
  title =	{{A Finite Algorithm for the Realizabilty of a Delaunay Triangulation}},
  booktitle =	{17th International Symposium on Parameterized and Exact Computation (IPEC 2022)},
  pages =	{1:1--1:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-260-0},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{249},
  editor =	{Dell, Holger and Nederlof, Jesper},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2022.1},
  URN =		{urn:nbn:de:0030-drops-173573},
  doi =		{10.4230/LIPIcs.IPEC.2022.1},
  annote =	{Keywords: Delaunay Triangulation, Delaunay Realization, Finite Algorithm, Integer Coordinate Realization}
}

Document

DOI: 10.4230/LIPIcs.WABI.2022.11

New Algorithms for Structure Informed Genome Rearrangement

Authors: Eden Ozery, Meirav Zehavi, and Michal Ziv-Ukelson

Published in: LIPIcs, Volume 242, 22nd International Workshop on Algorithms in Bioinformatics (WABI 2022)

Abstract

We define two new computational problems in the domain of perfect genome rearrangements, and propose three algorithms to solve them. The rearrangement scenarios modeled by the problems consider Reversal and Block Interchange operations, and a PQ-tree is utilized to guide the allowed operations and to compute their weights. In the first problem, Constrained TreeToString Divergence (CTTSD), we define the basic structure-informed rearrangement based divergence measure. Here, we assume that the gene order members of the gene cluster from which the PQ-tree is constructed are permutations. The PQ-tree representing the gene cluster is ordered such that the series of gene IDs spelled by its leaves is equivalent to the reference gene order. Then, a structure-informed gene rearrangement measure is computed between the ordered PQ-tree and the target gene order. The second problem, TreeToString Divergence (TTSD), generalizes CTTSD, where the gene order members are not necessarily permutations and the structure-informed rearrangement based divergence measure is extended to also consider up to d_S and d_T gene insertion and deletion operations, respectively, when modelling the PQ-tree informed divergence process from the reference order to the target order. The first algorithm solves CTTSD in O(n γ² ⋅ (m_p ⋅ 1.381^γ + m_q)) time and O(n²) space, where γ is the maximum number of children of a node, n is the length of the string and the number of leaves in the tree, and m_p and m_q are the number of P-nodes and Q-nodes in the tree, respectively. If one of the penalties of CTTSD is 0, then the algorithm runs in O(n m γ²) time and O(n²) space. The second algorithm solves TTSD in O(n² γ² {d_T}² {d_S}² m² (m_p ⋅ 5^γ γ + m_q)) time and O(d_T d_S m (m n + 5^γ)) space, where γ is the maximum number of children of a node, n is the length of the string, m is the number of leaves in the tree, m_p and m_q are the number of P-nodes and Q-nodes in the tree, respectively, and allowing d_T deletions from the tree and d_S deletions from the string. The third algorithm is intended to reduce the space complexity of the second algorithm. It solves a variant of the problem (where one of the penalties of TTSD is 0) in O(n γ² {d_T}² {d_S}² m² (m_p ⋅ 4^γ γ²n(d_T+d_S+m+n) + m_q)) time and O(γ² n m² d_T d_S (d_T+d_S+m+n)) space. The algorithm is implemented as a software tool, denoted MEM-Rearrange, and applied to the comparative and evolutionary analysis of 59 chromosomal gene clusters extracted from a dataset of 1,487 prokaryotic genomes.

Cite as

Eden Ozery, Meirav Zehavi, and Michal Ziv-Ukelson. New Algorithms for Structure Informed Genome Rearrangement. In 22nd International Workshop on Algorithms in Bioinformatics (WABI 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 242, pp. 11:1-11:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{ozery_et_al:LIPIcs.WABI.2022.11,
  author =	{Ozery, Eden and Zehavi, Meirav and Ziv-Ukelson, Michal},
  title =	{{New Algorithms for Structure Informed Genome Rearrangement}},
  booktitle =	{22nd International Workshop on Algorithms in Bioinformatics (WABI 2022)},
  pages =	{11:1--11:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-243-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{242},
  editor =	{Boucher, Christina and Rahmann, Sven},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2022.11},
  URN =		{urn:nbn:de:0030-drops-170454},
  doi =		{10.4230/LIPIcs.WABI.2022.11},
  annote =	{Keywords: PQ-tree, Gene Cluster, Breakpoint Distance}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2022.60

(Re)packing Equal Disks into Rectangle

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

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract

The problem of packing of equal disks (or circles) into a rectangle is a fundamental geometric problem. (By a packing here we mean an arrangement of disks in a rectangle without overlapping.) We consider the following algorithmic generalization of the equal disk packing problem. In this problem, for a given packing of equal disks into a rectangle, the question is whether by changing positions of a small number of disks, we can allocate space for packing more disks. More formally, in the repacking problem, for a given set of n equal disks packed into a rectangle and integers k and h, we ask whether it is possible by changing positions of at most h disks to pack n+k disks. Thus the problem of packing equal disks is the special case of our problem with n = h = 0. While the computational complexity of packing equal disks into a rectangle remains open, we prove that the repacking problem is NP-hard already for h = 0. Our main algorithmic contribution is an algorithm that solves the repacking problem in time (h+k)^𝒪(h+k)⋅|I|^𝒪(1), where |I| is the input size. That is, the problem is fixed-parameter tractable parameterized by k and h.

Cite as

Fedor V. Fomin, Petr A. Golovach, Tanmay Inamdar, and Meirav Zehavi. (Re)packing Equal Disks into Rectangle. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 60:1-60:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{fomin_et_al:LIPIcs.ICALP.2022.60,
  author =	{Fomin, Fedor V. and Golovach, Petr A. and Inamdar, Tanmay and Zehavi, Meirav},
  title =	{{(Re)packing Equal Disks into Rectangle}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{60:1--60:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.60},
  URN =		{urn:nbn:de:0030-drops-164011},
  doi =		{10.4230/LIPIcs.ICALP.2022.60},
  annote =	{Keywords: circle packing, unit disks, parameterized complexity, fixed-parameter tractability}
}

Document

DOI: 10.4230/DagRep.11.6.82

Parameterized Complexity in Graph Drawing (Dagstuhl Seminar 21293)

Authors: Robert Ganian, Fabrizio Montecchiani, Martin Nöllenburg, and Meirav Zehavi

Published in: Dagstuhl Reports, Volume 11, Issue 6 (2021)

Abstract

This report documents the program and the outcomes of Dagstuhl Seminar 21293 "Parameterized Complexity in Graph Drawing". The seminar was held mostly in-person from July 18 to July 23, 2021. It brought together 28 researchers from the Graph Drawing and the Parameterized Complexity research communities with the aim to discuss and explore open research questions on the interface between the two fields. The report collects the abstracts of talks and open problems presented in the seminar, as well as brief progress reports from the working groups.

Cite as

Robert Ganian, Fabrizio Montecchiani, Martin Nöllenburg, and Meirav Zehavi. Parameterized Complexity in Graph Drawing (Dagstuhl Seminar 21293). In Dagstuhl Reports, Volume 11, Issue 6, pp. 82-123, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@Article{ganian_et_al:DagRep.11.6.82,
  author =	{Ganian, Robert and Montecchiani, Fabrizio and N\"{o}llenburg, Martin and Zehavi, Meirav},
  title =	{{Parameterized Complexity in Graph Drawing (Dagstuhl Seminar 21293)}},
  pages =	{82--123},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2021},
  volume =	{11},
  number =	{6},
  editor =	{Ganian, Robert and Montecchiani, Fabrizio and N\"{o}llenburg, Martin and Zehavi, Meirav},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.11.6.82},
  URN =		{urn:nbn:de:0030-drops-155817},
  doi =		{10.4230/DagRep.11.6.82},
  annote =	{Keywords: exact computation, graph algorithms, graph drawing, parameterized complexity}
}

Document

DOI: 10.4230/LIPIcs.ISAAC.2021.37

Grid Recognition: Classical and Parameterized Computational Perspectives

Authors: Siddharth Gupta, Guy Sa'ar, and Meirav Zehavi

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)

Abstract

Grid graphs, and, more generally, k×r grid graphs, form one of the most basic classes of geometric graphs. Over the past few decades, a large body of works studied the (in)tractability of various computational problems on grid graphs, which often yield substantially faster algorithms than general graphs. Unfortunately, the recognition of a grid graph (given a graph G, decide whether it can be embedded into a grid graph) is particularly hard - it was shown to be NP-hard even on trees of pathwidth 3 already in 1987. Yet, in this paper, we provide several positive results in this regard in the framework of parameterized complexity (additionally, we present new and complementary hardness results). Specifically, our contribution is threefold. First, we show that the problem is fixed-parameter tractable (FPT) parameterized by k+mcc where mcc is the maximum size of a connected component of G. This also implies that the problem is FPT parameterized by td+k where td is the treedepth of G, as td ≤ mcc (to be compared with the hardness for pathwidth 2 where k = 3). (We note that when k and r are unrestricted, the problem is trivially FPT parameterized by td.) Further, we derive as a corollary that strip packing is FPT with respect to the height of the strip plus the maximum of the dimensions of the packed rectangles, which was previously only known to be in XP. Second, we present a new parameterization, denoted a_G, relating graph distance to geometric distance, which may be of independent interest. We show that the problem is para-NP-hard parameterized by a_G, but FPT parameterized by a_G on trees, as well as FPT parameterized by k+a_G. Third, we show that the recognition of k× r grid graphs is NP-hard on graphs of pathwidth 2 where k = 3. Moreover, when k and r are unrestricted, we show that the problem is NP-hard on trees of pathwidth 2, but trivially solvable in polynomial time on graphs of pathwidth 1.

Cite as

Siddharth Gupta, Guy Sa'ar, and Meirav Zehavi. Grid Recognition: Classical and Parameterized Computational Perspectives. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 37:1-37:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{gupta_et_al:LIPIcs.ISAAC.2021.37,
  author =	{Gupta, Siddharth and Sa'ar, Guy and Zehavi, Meirav},
  title =	{{Grid Recognition: Classical and Parameterized Computational Perspectives}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{37:1--37:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.37},
  URN =		{urn:nbn:de:0030-drops-154703},
  doi =		{10.4230/LIPIcs.ISAAC.2021.37},
  annote =	{Keywords: Grid Recognition, Grid Graph, Parameterized Complexity}
}

Document

Complete Volume

DOI: 10.4230/LIPIcs.IPEC.2021

LIPIcs, Volume 214, IPEC 2021, Complete Volume

Authors: Petr A. Golovach and Meirav Zehavi

Published in: LIPIcs, Volume 214, 16th International Symposium on Parameterized and Exact Computation (IPEC 2021)

Abstract

LIPIcs, Volume 214, IPEC 2021, Complete Volume

Cite as

Petr A. Golovach and Meirav Zehavi. LIPIcs, Volume 214, IPEC 2021, Complete Volume. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 1-474, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@Proceedings{golovach_et_al:LIPIcs.IPEC.2021,
  title =	{{LIPIcs, Volume 214, IPEC 2021, Complete Volume}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{1--474},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-216-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{214},
  editor =	{Golovach, Petr A. and Zehavi, Meirav},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021},
  URN =		{urn:nbn:de:0030-drops-153828},
  doi =		{10.4230/LIPIcs.IPEC.2021},
  annote =	{Keywords: LIPIcs, Volume 214, IPEC 2021, Complete Volume}
}

Document

Front Matter

DOI: 10.4230/LIPIcs.IPEC.2021.0

Front Matter, Table of Contents, Preface, Conference Organization

Authors: Petr A. Golovach and Meirav Zehavi

Published in: LIPIcs, Volume 214, 16th International Symposium on Parameterized and Exact Computation (IPEC 2021)

Abstract

Front Matter, Table of Contents, Preface, Conference Organization

Cite as

Petr A. Golovach and Meirav Zehavi. Front Matter, Table of Contents, Preface, Conference Organization. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 0:i-0:xviii, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{golovach_et_al:LIPIcs.IPEC.2021.0,
  author =	{Golovach, Petr A. and Zehavi, Meirav},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{0:i--0:xviii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-216-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{214},
  editor =	{Golovach, Petr A. and Zehavi, Meirav},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.0},
  URN =		{urn:nbn:de:0030-drops-153834},
  doi =		{10.4230/LIPIcs.IPEC.2021.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}

Document

DOI: 10.4230/LIPIcs.IPEC.2021.1

A Polynomial Kernel for Deletion to Ptolemaic Graphs

Authors: Akanksha Agrawal, Aditya Anand, and Saket Saurabh

Published in: LIPIcs, Volume 214, 16th International Symposium on Parameterized and Exact Computation (IPEC 2021)

Abstract

For a family of graphs F, given a graph G and an integer k, the F-Deletion problem asks whether we can delete at most k vertices from G to obtain a graph in the family F. The F-Deletion problems for all non-trivial families F that satisfy the hereditary property on induced subgraphs are known to be NP-hard by a result of Yannakakis (STOC'78). Ptolemaic graphs are the graphs that satisfy the Ptolemy inequality, and they are the intersection of chordal graphs and distance-hereditary graphs. Equivalently, they form the set of graphs that do not contain any chordless cycles or a gem as an induced subgraph. (A gem is the graph on 5 vertices, where four vertices form an induced path, and the fifth vertex is adjacent to all the vertices of this induced path.) The Ptolemaic Deletion problem is the F-Deletion problem, where F is the family of Ptolemaic graphs. In this paper we study Ptolemaic Deletion from the viewpoint of Kernelization Complexity, and obtain a kernel with 𝒪(k⁶) vertices for the problem.

Cite as

Akanksha Agrawal, Aditya Anand, and Saket Saurabh. A Polynomial Kernel for Deletion to Ptolemaic Graphs. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 1:1-1:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{agrawal_et_al:LIPIcs.IPEC.2021.1,
  author =	{Agrawal, Akanksha and Anand, Aditya and Saurabh, Saket},
  title =	{{A Polynomial Kernel for Deletion to Ptolemaic Graphs}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{1:1--1:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-216-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{214},
  editor =	{Golovach, Petr A. and Zehavi, Meirav},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.1},
  URN =		{urn:nbn:de:0030-drops-153840},
  doi =		{10.4230/LIPIcs.IPEC.2021.1},
  annote =	{Keywords: Ptolemaic Deletion, Kernelization, Parameterized Complexity, Gem-free chordal graphs}
}

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