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Documents authored by Schmidt, Jonas


Document
Dynamic Constant Time Parallel Graph Algorithms with Sub-Linear Work

Authors: Jonas Schmidt and Thomas Schwentick

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


Abstract
The paper proposes dynamic parallel algorithms for connectivity and bipartiteness of undirected graphs that require constant time and 𝒪(n^{1/2+ε}) work on the CRCW PRAM model. The work of these algorithms almost matches the work of the 𝒪(log n) time algorithm for connectivity by Kopelowitz et al. (2018) on the EREW PRAM model and the time of the sequential algorithm for bipartiteness by Eppstein et al. (1997). In particular, we show that the sparsification technique, which has been used in both mentioned papers, can in principle also be used for constant time algorithms in the CRCW PRAM model, despite the logarithmic depth of sparsification trees.

Cite as

Jonas Schmidt and Thomas Schwentick. Dynamic Constant Time Parallel Graph Algorithms with Sub-Linear Work. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 80:1-80:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{schmidt_et_al:LIPIcs.MFCS.2023.80,
  author =	{Schmidt, Jonas and Schwentick, Thomas},
  title =	{{Dynamic Constant Time Parallel Graph Algorithms with Sub-Linear Work}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{80:1--80:15},
  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.2023.80},
  URN =		{urn:nbn:de:0030-drops-186140},
  doi =		{10.4230/LIPIcs.MFCS.2023.80},
  annote =	{Keywords: Dynamic parallel algorithms, Undirected connectivity, Bipartiteness}
}
Document
On the Work of Dynamic Constant-Time Parallel Algorithms for Regular Tree Languages and Context-Free Languages

Authors: Jonas Schmidt, Thomas Schwentick, and Jennifer Todtenhoefer

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


Abstract
Previous work on Dynamic Complexity has established that there exist dynamic constant-time parallel algorithms for regular tree languages and context-free languages under label or symbol changes. However, these algorithms were not developed with the goal to minimise work (or, equivalently, the number of processors). In fact, their inspection yields the work bounds 𝒪(n²) and 𝒪(n⁷) per change operation, respectively. In this paper, dynamic algorithms for regular tree languages are proposed that generalise the previous algorithms in that they allow unbounded node rank and leaf insertions, while improving the work bound from 𝒪(n²) to 𝒪(n^ε), for arbitrary ε > 0. For context-free languages, algorithms with better work bounds (compared with 𝒪(n⁷)) for restricted classes are proposed: for every ε > 0 there are such algorithms for deterministic context-free languages with work bound 𝒪(n^{3+ε}) and for visibly pushdown languages with work bound 𝒪(n^{2+ε}).

Cite as

Jonas Schmidt, Thomas Schwentick, and Jennifer Todtenhoefer. On the Work of Dynamic Constant-Time Parallel Algorithms for Regular Tree Languages and Context-Free Languages. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 81:1-81:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{schmidt_et_al:LIPIcs.MFCS.2023.81,
  author =	{Schmidt, Jonas and Schwentick, Thomas and Todtenhoefer, Jennifer},
  title =	{{On the Work of Dynamic Constant-Time Parallel Algorithms for Regular Tree Languages and Context-Free Languages}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{81:1--81:15},
  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.2023.81},
  URN =		{urn:nbn:de:0030-drops-186152},
  doi =		{10.4230/LIPIcs.MFCS.2023.81},
  annote =	{Keywords: Dynamic complexity, work, parallel constant time}
}
Document
Solving Directed Feedback Vertex Set by Iterative Reduction to Vertex Cover

Authors: Sebastian Angrick, Ben Bals, Katrin Casel, Sarel Cohen, Tobias Friedrich, Niko Hastrich, Theresa Hradilak, Davis Issac, Otto Kißig, Jonas Schmidt, and Leo Wendt

Published in: LIPIcs, Volume 265, 21st International Symposium on Experimental Algorithms (SEA 2023)


Abstract
In the Directed Feedback Vertex Set (DFVS) problem, one is given a directed graph G = (V,E) and wants to find a minimum cardinality set S ⊆ V such that G-S is acyclic. DFVS is a fundamental problem in computer science and finds applications in areas such as deadlock detection. The problem was the subject of the 2022 PACE coding challenge. We develop a novel exact algorithm for the problem that is tailored to perform well on instances that are mostly bi-directed. For such instances, we adapt techniques from the well-researched vertex cover problem. Our core idea is an iterative reduction to vertex cover. To this end, we also develop a new reduction rule that reduces the number of not bi-directed edges. With the resulting algorithm, we were able to win third place in the exact track of the PACE challenge. We perform computational experiments and compare the running time to other exact algorithms, in particular to the winning algorithm in PACE. Our experiments show that we outpace the other algorithms on instances that have a low density of uni-directed edges.

Cite as

Sebastian Angrick, Ben Bals, Katrin Casel, Sarel Cohen, Tobias Friedrich, Niko Hastrich, Theresa Hradilak, Davis Issac, Otto Kißig, Jonas Schmidt, and Leo Wendt. Solving Directed Feedback Vertex Set by Iterative Reduction to Vertex Cover. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 10:1-10:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{angrick_et_al:LIPIcs.SEA.2023.10,
  author =	{Angrick, Sebastian and Bals, Ben and Casel, Katrin and Cohen, Sarel and Friedrich, Tobias and Hastrich, Niko and Hradilak, Theresa and Issac, Davis and Ki{\ss}ig, Otto and Schmidt, Jonas and Wendt, Leo},
  title =	{{Solving Directed Feedback Vertex Set by Iterative Reduction to Vertex Cover}},
  booktitle =	{21st International Symposium on Experimental Algorithms (SEA 2023)},
  pages =	{10:1--10:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-279-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{265},
  editor =	{Georgiadis, Loukas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.10},
  URN =		{urn:nbn:de:0030-drops-183602},
  doi =		{10.4230/LIPIcs.SEA.2023.10},
  annote =	{Keywords: directed feedback vertex set, vertex cover, reduction rules}
}
Document
PACE Solver Description
PACE Solver Description: Mount Doom - An Exact Solver for Directed Feedback Vertex Set

Authors: Sebastian Angrick, Ben Bals, Katrin Casel, Sarel Cohen, Tobias Friedrich, Niko Hastrich, Theresa Hradilak, Davis Issac, Otto Kißig, Jonas Schmidt, and Leo Wendt

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


Abstract
In this document we describe the techniques we used and implemented for our submission to the Parameterized Algorithms and Computational Experiments Challenge (PACE) 2022. The given problem is Directed Feedback Vertex Set (DFVS), where one is given a directed graph G = (V,E) and wants to find a minimum S ⊆ V such that G-S is acyclic. We approach this problem by first exhaustively applying a set of reduction rules. In order to find a minimum DFVS on the remaining instance, we create and solve a series of Vertex Cover instances.

Cite as

Sebastian Angrick, Ben Bals, Katrin Casel, Sarel Cohen, Tobias Friedrich, Niko Hastrich, Theresa Hradilak, Davis Issac, Otto Kißig, Jonas Schmidt, and Leo Wendt. PACE Solver Description: Mount Doom - An Exact Solver for Directed Feedback Vertex Set. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 28:1-28:4, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{angrick_et_al:LIPIcs.IPEC.2022.28,
  author =	{Angrick, Sebastian and Bals, Ben and Casel, Katrin and Cohen, Sarel and Friedrich, Tobias and Hastrich, Niko and Hradilak, Theresa and Issac, Davis and Ki{\ss}ig, Otto and Schmidt, Jonas and Wendt, Leo},
  title =	{{PACE Solver Description: Mount Doom - An Exact Solver for Directed Feedback Vertex Set}},
  booktitle =	{17th International Symposium on Parameterized and Exact Computation (IPEC 2022)},
  pages =	{28:1--28:4},
  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.2022.28},
  URN =		{urn:nbn:de:0030-drops-173847},
  doi =		{10.4230/LIPIcs.IPEC.2022.28},
  annote =	{Keywords: directed feedback vertex set, vertex cover, reduction rules}
}
Document
Dynamic Complexity Meets Parameterised Algorithms

Authors: Jonas Schmidt, Thomas Schwentick, Nils Vortmeier, Thomas Zeume, and Ioannis Kokkinis

Published in: LIPIcs, Volume 152, 28th EACSL Annual Conference on Computer Science Logic (CSL 2020)


Abstract
Dynamic Complexity studies the maintainability of queries with logical formulas in a setting where the underlying structure or database changes over time. Most often, these formulas are from first-order logic, giving rise to the dynamic complexity class DynFO. This paper investigates extensions of DynFO in the spirit of parameterised algorithms. In this setting structures come with a parameter k and the extensions allow additional "space" of size f(k) (in the form of an additional structure of this size) or additional time f(k) (in the form of iterations of formulas) or both. The resulting classes are compared with their non-dynamic counterparts and other classes. The main part of the paper explores the applicability of methods for parameterised algorithms to this setting through case studies for various well-known parameterised problems.

Cite as

Jonas Schmidt, Thomas Schwentick, Nils Vortmeier, Thomas Zeume, and Ioannis Kokkinis. Dynamic Complexity Meets Parameterised Algorithms. In 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 152, pp. 36:1-36:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


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@InProceedings{schmidt_et_al:LIPIcs.CSL.2020.36,
  author =	{Schmidt, Jonas and Schwentick, Thomas and Vortmeier, Nils and Zeume, Thomas and Kokkinis, Ioannis},
  title =	{{Dynamic Complexity Meets Parameterised Algorithms}},
  booktitle =	{28th EACSL Annual Conference on Computer Science Logic (CSL 2020)},
  pages =	{36:1--36:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-132-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{152},
  editor =	{Fern\'{a}ndez, Maribel and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2020.36},
  URN =		{urn:nbn:de:0030-drops-116792},
  doi =		{10.4230/LIPIcs.CSL.2020.36},
  annote =	{Keywords: Dynamic complexity, parameterised complexity}
}
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