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Documents authored by Heinrich C. Mayr

Found 5 Possible Name Variants:

Mayr, Heinrich C.

Document
DOI: 10.4230/DagRep.8.11.63
Next Generation Domain Specific Conceptual Modeling: Principles and Methods (Dagstuhl Seminar 18471)

Authors: Heinrich C. Mayr, Sudha Ram, Wolfgang Reisig, and Markus Stumptner

Published in: Dagstuhl Reports, Volume 8, Issue 11 (2019)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 18471 "Next Genera-tion Domain Specific Conceptual Modeling: Principles and Methods". It summarizes the resultsof the seminar and shows in which direction (Domain Specific) Conceptual Modeling shoulddevelop in the opinion of the participants. In addition, the report contains abstracts of thenumerous talks presented during the seminar as well as a summary of the discussions held inworking groups during the seminar. In particular, some open questions will be touched upon,which will be dealt with before a follow-up seminar.
Cite as

Heinrich C. Mayr, Sudha Ram, Wolfgang Reisig, and Markus Stumptner. Next Generation Domain Specific Conceptual Modeling: Principles and Methods (Dagstuhl Seminar 18471). In Dagstuhl Reports, Volume 8, Issue 11, pp. 63-90, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@Article{mayr_et_al:DagRep.8.11.63,
  author =	{Mayr, Heinrich C. and Ram, Sudha and Reisig, Wolfgang and Stumptner, Markus},
  title =	{{Next Generation Domain Specific Conceptual Modeling: Principles and Methods (Dagstuhl Seminar 18471)}},
  pages =	{63--90},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2019},
  volume =	{8},
  number =	{11},
  editor =	{Mayr, Heinrich C. and Ram, Sudha and Reisig, Wolfgang and Stumptner, Markus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.8.11.63},
  URN =		{urn:nbn:de:0030-drops-103560},
  doi =		{10.4230/DagRep.8.11.63},
  annote =	{Keywords: DSML, Meta Model, Modeling, Modeling Method, Semantics}
}
Document
DOI: 10.4230/DagSemProc.08181.2
08181 Report – The Evolution of Conceptual Modeling

Authors: Lois Delcambre, Roland H. Kaschek, and Heinrich C. Mayr

Published in: Dagstuhl Seminar Proceedings, Volume 8181, The Evolution of Conceptual Modeling (2008)

Abstract
The seminar took place at Dagstuhl from 27 – 30 April 2008. It was organized by Roland Kaschek, Lois Delcambre and Heinrich C. Mayr. The seminar’s purpose was looking into conceptual modeling from different perspectives, and along different dimensions: we wanted to achieve a better understanding of conceptual modeling issues in various domains of discourse, from a historical perspective and from a view beyond individual (modeling) projects. Consequently we did not focus on a particular application area or development project.
Cite as

Lois Delcambre, Roland H. Kaschek, and Heinrich C. Mayr. 08181 Report – The Evolution of Conceptual Modeling. In The Evolution of Conceptual Modeling. Dagstuhl Seminar Proceedings, Volume 8181, pp. 1-3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{delcambre_et_al:DagSemProc.08181.2,
  author =	{Delcambre, Lois and Kaschek, Roland H. and Mayr, Heinrich C.},
  title =	{{08181 Report – The Evolution of Conceptual Modeling}},
  booktitle =	{The Evolution of Conceptual Modeling},
  pages =	{1--3},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8181},
  editor =	{Lois Delcambre and Roland H. Kaschek and Heinrich C. Mayr},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08181.2},
  URN =		{urn:nbn:de:0030-drops-15986},
  doi =		{10.4230/DagSemProc.08181.2},
  annote =	{Keywords: Matrix analytic methods, markov processes, queuing theory, numerical methods, structured matrices, telecommunication modeling, performance evaluation}
}

Heinrich, Robert

Document
DOI: 10.4230/DagRep.9.11.97
Composing Model-Based Analysis Tools (Dagstuhl Seminar 19481)

Authors: Francisco Durán, Robert Heinrich, Diego Pérez-Palacín, Carolyn L. Talcott, and Steffen Zschaler

Published in: Dagstuhl Reports, Volume 9, Issue 11 (2020)

Abstract
This report documents the program and the outcomes of the Dagstuhl Seminar 19481 "Composing Model-Based Analysis Tools". The key objective of the seminar was to provide more flexibility in model-driven engineering by bringing together representatives from industry and researchers in the formal methods and software engineering communities to establishing the foundations for a common understanding on the modularity and composition of modeling languages and model-based analyses.
Cite as

Francisco Durán, Robert Heinrich, Diego Pérez-Palacín, Carolyn L. Talcott, and Steffen Zschaler. Composing Model-Based Analysis Tools (Dagstuhl Seminar 19481). In Dagstuhl Reports, Volume 9, Issue 11, pp. 97-116, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@Article{duran_et_al:DagRep.9.11.97,
  author =	{Dur\'{a}n, Francisco and Heinrich, Robert and P\'{e}rez-Palac{\'\i}n, Diego and Talcott, Carolyn L. and Zschaler, Steffen},
  title =	{{Composing Model-Based Analysis Tools (Dagstuhl Seminar 19481)}},
  pages =	{97--116},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2020},
  volume =	{9},
  number =	{11},
  editor =	{Dur\'{a}n, Francisco and Heinrich, Robert and P\'{e}rez-Palac{\'\i}n, Diego and Talcott, Carolyn L. and Zschaler, Steffen},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.9.11.97},
  URN =		{urn:nbn:de:0030-drops-119853},
  doi =		{10.4230/DagRep.9.11.97},
  annote =	{Keywords: Modelling, Simulation, Semantics, Formal Methods, Software Engineering}
}

Heinrich, Stefan

Document
DOI: 10.4230/DagSemRep.287
Algorithms and Complexity for Continuous Problems (Dagstuhl Seminar 00391)

Authors: Stefan Heinrich, Sergei Pereverzev, Joseph Traub, and Grzegorz Wasilkowski

Published in: Dagstuhl Seminar Reports. Dagstuhl Seminar Reports, Volume 1 (2021)

Abstract
Cite as

Stefan Heinrich, Sergei Pereverzev, Joseph Traub, and Grzegorz Wasilkowski. Algorithms and Complexity for Continuous Problems (Dagstuhl Seminar 00391). Dagstuhl Seminar Report 287, pp. 1-15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2001)

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@TechReport{heinrich_et_al:DagSemRep.287,
  author =	{Heinrich, Stefan and Pereverzev, Sergei and Traub, Joseph and Wasilkowski, Grzegorz},
  title =	{{Algorithms and Complexity for Continuous Problems (Dagstuhl Seminar 00391)}},
  pages =	{1--15},
  ISSN =	{1619-0203},
  year =	{2001},
  type = 	{Dagstuhl Seminar Report},
  number =	{287},
  institution =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemRep.287},
  URN =		{urn:nbn:de:0030-drops-151719},
  doi =		{10.4230/DagSemRep.287},
}
Document
DOI: 10.4230/DagSemRep.101
Algorithms and Complexity for Continuous Problems (Dagstuhl Seminar 9442)

Authors: Stefan Heinrich, Joseph F. Traub, and Henryk Wozniakowski

Published in: Dagstuhl Seminar Reports. Dagstuhl Seminar Reports, Volume 1 (2021)

Abstract
Cite as

Stefan Heinrich, Joseph F. Traub, and Henryk Wozniakowski. Algorithms and Complexity for Continuous Problems (Dagstuhl Seminar 9442). Dagstuhl Seminar Report 101, pp. 1-22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (1994)

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@TechReport{heinrich_et_al:DagSemRep.101,
  author =	{Heinrich, Stefan and Traub, Joseph F. and Wozniakowski, Henryk},
  title =	{{Algorithms and Complexity for Continuous Problems (Dagstuhl Seminar 9442)}},
  pages =	{1--22},
  ISSN =	{1619-0203},
  year =	{1994},
  type = 	{Dagstuhl Seminar Report},
  number =	{101},
  institution =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemRep.101},
  URN =		{urn:nbn:de:0030-drops-149891},
  doi =		{10.4230/DagSemRep.101},
}

Heinrich, Marc

Document
DOI: 10.4230/LIPIcs.OPODIS.2021.19
Distributed Recoloring of Interval and Chordal Graphs

Authors: Nicolas Bousquet, Laurent Feuilloley, Marc Heinrich, and Mikaël Rabie

Published in: LIPIcs, Volume 217, 25th International Conference on Principles of Distributed Systems (OPODIS 2021)

Abstract
One of the fundamental and most-studied algorithmic problems in distributed computing on networks is graph coloring, both in bounded-degree and in general graphs. Recently, the study of this problem has been extended in two directions. First, the problem of recoloring, that is computing an efficient transformation between two given colorings (instead of computing a new coloring), has been considered, both to model radio network updates, and as a useful subroutine for coloring. Second, as it appears that general graphs and bounded-degree graphs do not model real networks very well (with, respectively, pathological worst-case topologies and too strong assumptions), coloring has been studied in more specific graph classes. In this paper, we study the intersection of these two directions: distributed recoloring in two relevant graph classes, interval and chordal graphs. More formally, the question of recoloring a graph is as follows: we are given a network, an input coloring α and a target coloring β, and we want to find a schedule of colorings to reach β starting from α. In a distributed setting, the schedule needs to be found within the LOCAL model, where nodes communicate with their direct neighbors synchronously. The question we want to answer is: how many rounds of communication {are} needed to produce a schedule, and what is the length of this schedule? In the case of interval and chordal graphs, we prove that, if we have less than 2ω colors, ω being the size of the largest clique, extra colors will be needed in the intermediate colorings. For interval graphs, we produce a schedule after O(poly(Δ)log*n) rounds of communication, and for chordal graphs, we need O(ω²Δ²log n) rounds to get one. Our techniques also improve classic coloring algorithms. Namely, we get ω+1-colorings of interval graphs in O(ωlog*n) rounds and of chordal graphs in O(ωlog n) rounds, which improves on previous known algorithms that use ω+2 colors for the same running times.
Cite as

Nicolas Bousquet, Laurent Feuilloley, Marc Heinrich, and Mikaël Rabie. Distributed Recoloring of Interval and Chordal Graphs. In 25th International Conference on Principles of Distributed Systems (OPODIS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 217, pp. 19:1-19:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bousquet_et_al:LIPIcs.OPODIS.2021.19,
  author =	{Bousquet, Nicolas and Feuilloley, Laurent and Heinrich, Marc and Rabie, Mika\"{e}l},
  title =	{{Distributed Recoloring of Interval and Chordal Graphs}},
  booktitle =	{25th International Conference on Principles of Distributed Systems (OPODIS 2021)},
  pages =	{19:1--19:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-219-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{217},
  editor =	{Bramas, Quentin and Gramoli, Vincent and Milani, Alessia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2021.19},
  URN =		{urn:nbn:de:0030-drops-157941},
  doi =		{10.4230/LIPIcs.OPODIS.2021.19},
  annote =	{Keywords: Distributed coloring, distributed recoloring, interval graphs, chordal graphs, intersection graphs}
}
Document
PACE Solver Description
DOI: 10.4230/LIPIcs.IPEC.2021.29
PACE Solver Description: PaSTEC - PAths, Stars and Twins to Edit Towards Clusters

Authors: Valentin Bartier, Gabriel Bathie, Nicolas Bousquet, Marc Heinrich, Théo Pierron, and Ulysse Prieto

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

Abstract
This document describes our exact Cluster Editing solver, PaSTEC, which got the third place in the 2021 PACE Challenge.
Cite as

Valentin Bartier, Gabriel Bathie, Nicolas Bousquet, Marc Heinrich, Théo Pierron, and Ulysse Prieto. PACE Solver Description: PaSTEC - PAths, Stars and Twins to Edit Towards Clusters. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 29:1-29:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bartier_et_al:LIPIcs.IPEC.2021.29,
  author =	{Bartier, Valentin and Bathie, Gabriel and Bousquet, Nicolas and Heinrich, Marc and Pierron, Th\'{e}o and Prieto, Ulysse},
  title =	{{PACE Solver Description: PaSTEC - PAths, Stars and Twins to Edit Towards Clusters}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{29:1--29:4},
  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.2021.29},
  URN =		{urn:nbn:de:0030-drops-154129},
  doi =		{10.4230/LIPIcs.IPEC.2021.29},
  annote =	{Keywords: cluster editing, exact algorithm, star packing, twins}
}
Document
PACE Solver Description
DOI: 10.4230/LIPIcs.IPEC.2021.33
PACE Solver Description: μSolver - Heuristic Track

Authors: Valentin Bartier, Gabriel Bathie, Nicolas Bousquet, Marc Heinrich, Théo Pierron, and Ulysse Prieto

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

Abstract
This document describes our heuristic Cluster Editing solver, μSolver, which got the third place in the 2021 PACE Challenge. We present the local search and kernelization techniques for Cluster Editing that are implemented in the solver.
Cite as

Valentin Bartier, Gabriel Bathie, Nicolas Bousquet, Marc Heinrich, Théo Pierron, and Ulysse Prieto. PACE Solver Description: μSolver - Heuristic Track. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 33:1-33:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bartier_et_al:LIPIcs.IPEC.2021.33,
  author =	{Bartier, Valentin and Bathie, Gabriel and Bousquet, Nicolas and Heinrich, Marc and Pierron, Th\'{e}o and Prieto, Ulysse},
  title =	{{PACE Solver Description: \muSolver - Heuristic Track}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{33:1--33:3},
  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.2021.33},
  URN =		{urn:nbn:de:0030-drops-154161},
  doi =		{10.4230/LIPIcs.IPEC.2021.33},
  annote =	{Keywords: kernelization, graph editing, clustering, local search}
}
Document
DOI: 10.4230/LIPIcs.STACS.2020.35
Shortest Reconfiguration of Colorings Under Kempe Changes

Authors: Marthe Bonamy, Marc Heinrich, Takehiro Ito, Yusuke Kobayashi, Haruka Mizuta, Moritz Mühlenthaler, Akira Suzuki, and Kunihiro Wasa

Published in: LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)

Abstract
A k-coloring of a graph maps each vertex of the graph to a color in {1, 2, …, k}, such that no two adjacent vertices receive the same color. Given a k-coloring of a graph, a Kempe change produces a new k-coloring by swapping the colors in a bicolored connected component. We investigate the complexity of finding the smallest number of Kempe changes needed to transform a given k-coloring into another given k-coloring. We show that this problem admits a polynomial-time dynamic programming algorithm on path graphs, which turns out to be highly non-trivial. Furthermore, the problem is NP-hard even on star graphs and we show that on such graphs it admits a constant-factor approximation algorithm and is fixed-parameter tractable when parameterized by the number k of colors. The hardness result as well as the algorithmic results are based on the notion of a canonical transformation.
Cite as

Marthe Bonamy, Marc Heinrich, Takehiro Ito, Yusuke Kobayashi, Haruka Mizuta, Moritz Mühlenthaler, Akira Suzuki, and Kunihiro Wasa. Shortest Reconfiguration of Colorings Under Kempe Changes. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 35:1-35:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bonamy_et_al:LIPIcs.STACS.2020.35,
  author =	{Bonamy, Marthe and Heinrich, Marc and Ito, Takehiro and Kobayashi, Yusuke and Mizuta, Haruka and M\"{u}hlenthaler, Moritz and Suzuki, Akira and Wasa, Kunihiro},
  title =	{{Shortest Reconfiguration of Colorings Under Kempe Changes}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{35:1--35:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Paul, Christophe and Bl\"{a}ser, Markus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.35},
  URN =		{urn:nbn:de:0030-drops-118961},
  doi =		{10.4230/LIPIcs.STACS.2020.35},
  annote =	{Keywords: Combinatorial Reconfiguration, Graph Algorithms, Graph Coloring, Kempe Equivalence}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2019.80
The Perfect Matching Reconfiguration Problem

Authors: Marthe Bonamy, Nicolas Bousquet, Marc Heinrich, Takehiro Ito, Yusuke Kobayashi, Arnaud Mary, Moritz Mühlenthaler, and Kunihiro Wasa

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract
We study the perfect matching reconfiguration problem: Given two perfect matchings of a graph, is there a sequence of flip operations that transforms one into the other? Here, a flip operation exchanges the edges in an alternating cycle of length four. We are interested in the complexity of this decision problem from the viewpoint of graph classes. We first prove that the problem is PSPACE-complete even for split graphs and for bipartite graphs of bounded bandwidth with maximum degree five. We then investigate polynomial-time solvable cases. Specifically, we prove that the problem is solvable in polynomial time for strongly orderable graphs (that include interval graphs and strongly chordal graphs), for outerplanar graphs, and for cographs (also known as P_4-free graphs). Furthermore, for each yes-instance from these graph classes, we show that a linear number of flip operations is sufficient and we can exhibit a corresponding sequence of flip operations in polynomial time.
Cite as

Marthe Bonamy, Nicolas Bousquet, Marc Heinrich, Takehiro Ito, Yusuke Kobayashi, Arnaud Mary, Moritz Mühlenthaler, and Kunihiro Wasa. The Perfect Matching Reconfiguration Problem. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 80:1-80:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bonamy_et_al:LIPIcs.MFCS.2019.80,
  author =	{Bonamy, Marthe and Bousquet, Nicolas and Heinrich, Marc and Ito, Takehiro and Kobayashi, Yusuke and Mary, Arnaud and M\"{u}hlenthaler, Moritz and Wasa, Kunihiro},
  title =	{{The Perfect Matching Reconfiguration Problem}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{80:1--80:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.80},
  URN =		{urn:nbn:de:0030-drops-110248},
  doi =		{10.4230/LIPIcs.MFCS.2019.80},
  annote =	{Keywords: Combinatorial Reconfiguration, Graph Algorithms, Perfect Matching}
}
Document
DOI: 10.4230/LIPIcs.STACS.2019.16
Enumerating Minimal Dominating Sets in Triangle-Free Graphs

Authors: Marthe Bonamy, Oscar Defrain, Marc Heinrich, and Jean-Florent Raymond

Published in: LIPIcs, Volume 126, 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)

Abstract
It is a long-standing open problem whether the minimal dominating sets of a graph can be enumerated in output-polynomial time. In this paper we prove that this is the case in triangle-free graphs. This answers a question of Kanté et al. Additionally, we show that deciding if a set of vertices of a bipartite graph can be completed into a minimal dominating set is a NP-complete problem.
Cite as

Marthe Bonamy, Oscar Defrain, Marc Heinrich, and Jean-Florent Raymond. Enumerating Minimal Dominating Sets in Triangle-Free Graphs. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 16:1-16:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bonamy_et_al:LIPIcs.STACS.2019.16,
  author =	{Bonamy, Marthe and Defrain, Oscar and Heinrich, Marc and Raymond, Jean-Florent},
  title =	{{Enumerating Minimal Dominating Sets in Triangle-Free Graphs}},
  booktitle =	{36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
  pages =	{16:1--16:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-100-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{126},
  editor =	{Niedermeier, Rolf and Paul, Christophe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.16},
  URN =		{urn:nbn:de:0030-drops-102557},
  doi =		{10.4230/LIPIcs.STACS.2019.16},
  annote =	{Keywords: Enumeration algorithms, output-polynomial algorithms, minimal dominating set, triangle-free graphs, split graphs}
}

Heinrich, Zacharias

Document
DOI: 10.4230/LIPIcs.IPEC.2021.7
Dynamic Kernels for Hitting Sets and Set Packing

Authors: Max Bannach, Zacharias Heinrich, Rüdiger Reischuk, and Till Tantau

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

Abstract
Computing small kernels for the hitting set problem is a well-studied computational problem where we are given a hypergraph with n vertices and m hyperedges, each of size d for some small constant d, and a parameter k. The task is to compute a new hypergraph, called a kernel, whose size is polynomial with respect to the parameter k and which has a size-k hitting set if, and only if, the original hypergraph has one. State-of-the-art algorithms compute kernels of size k^d (which is a polynomial kernel size as d is a constant), and they do so in time m⋅ 2^d poly(d) for a small polynomial poly(d) (which is a linear runtime as d is again a constant). We generalize this task to the dynamic setting where hyperedges may continuously be added or deleted and one constantly has to keep track of a size-k^d hitting set kernel in memory (including moments when no size-k hitting set exists). This paper presents a deterministic solution with worst-case time 3^d poly(d) for updating the kernel upon hyperedge inserts and time 5^d poly(d) for updates upon deletions. These bounds nearly match the time 2^d poly(d) needed by the best static algorithm per hyperedge. Let us stress that for constant d our algorithm maintains a dynamic hitting set kernel with constant, deterministic, worst-case update time that is independent of n, m, and the parameter k. As a consequence, we also get a deterministic dynamic algorithm for keeping track of size-k hitting sets in d-hypergraphs with update times O(1) and query times O(c^k) where c = d - 1 + O(1/d) equals the best base known for the static setting.
Cite as

Max Bannach, Zacharias Heinrich, Rüdiger Reischuk, and Till Tantau. Dynamic Kernels for Hitting Sets and Set Packing. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bannach_et_al:LIPIcs.IPEC.2021.7,
  author =	{Bannach, Max and Heinrich, Zacharias and Reischuk, R\"{u}diger and Tantau, Till},
  title =	{{Dynamic Kernels for Hitting Sets and Set Packing}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{7:1--7:18},
  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.2021.7},
  URN =		{urn:nbn:de:0030-drops-153900},
  doi =		{10.4230/LIPIcs.IPEC.2021.7},
  annote =	{Keywords: Kernelization, Dynamic Algorithms, Hitting Set, Set Packings}
}
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