121 Search Results for "M�nnich, Jan"

Volume

LIPIcs, Volume 223

33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)

CPM 2022, June 27-29, 2022, Prague, Czech Republic

Editors: Hideo Bannai and Jan Holub

Volume

LIPIcs, Volume 148

14th International Symposium on Parameterized and Exact Computation (IPEC 2019)

IPEC 2019, September 11-13, 2019, Munich, Germany

Editors: Bart M. P. Jansen and Jan Arne Telle

Document
DOI: 10.4230/DagRep.13.8.106
Algorithms and Complexity for Continuous Problems (Dagstuhl Seminar 23351)

Authors: Dmitriy Bilyk, Michael Gnewuch, Jan Vybíral, Larisa Yaroslavtseva, and Kumar Harsha

Published in: Dagstuhl Reports, Volume 13, Issue 8 (2024)

Abstract
The Dagstuhl Seminar 23351 was held at the Leibniz Center for Informatics, Schloss Dagstuhl, from August 27 to September 1, 2023. This event was the 14th in a series of Dagstuhl Seminars, starting in 1991. During the seminar, researchers presented overview talks, recent research results, work in progress and open problems. The first section of this report describes the goal of the seminar, the main seminar topics, and the general structure of the seminar. The third section contains the abstracts of the talks given during the seminar and the forth section the problems presented at the problem session.
Cite as

Dmitriy Bilyk, Michael Gnewuch, Jan Vybíral, Larisa Yaroslavtseva, and Kumar Harsha. Algorithms and Complexity for Continuous Problems (Dagstuhl Seminar 23351). In Dagstuhl Reports, Volume 13, Issue 8, pp. 106-128, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{bilyk_et_al:DagRep.13.8.106,
  author =	{Bilyk, Dmitriy and Gnewuch, Michael and Vyb{\'\i}ral, Jan and Yaroslavtseva, Larisa and Harsha, Kumar},
  title =	{{Algorithms and Complexity for Continuous Problems (Dagstuhl Seminar 23351)}},
  pages =	{106--128},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2024},
  volume =	{13},
  number =	{8},
  editor =	{Bilyk, Dmitriy and Gnewuch, Michael and Vyb{\'\i}ral, Jan and Yaroslavtseva, Larisa and Harsha, Kumar},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.13.8.106},
  URN =		{urn:nbn:de:0030-drops-198152},
  doi =		{10.4230/DagRep.13.8.106},
  annote =	{Keywords: computational stochastics, infinite-variate problems, quasi-\{M\}onte \{C\}arlo, sampling, tractability analysis}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2024.93
Training Multi-Layer Over-Parametrized Neural Network in Subquadratic Time

Authors: Zhao Song, Lichen Zhang, and Ruizhe Zhang

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract
We consider the problem of training a multi-layer over-parametrized neural network to minimize the empirical risk induced by a loss function. In the typical setting of over-parametrization, the network width m is much larger than the data dimension d and the number of training samples n (m = poly(n,d)), which induces a prohibitive large weight matrix W ∈ ℝ^{m× m} per layer. Naively, one has to pay O(m²) time to read the weight matrix and evaluate the neural network function in both forward and backward computation. In this work, we show how to reduce the training cost per iteration. Specifically, we propose a framework that uses m² cost only in the initialization phase and achieves a truly subquadratic cost per iteration in terms of m, i.e., m^{2-Ω(1)} per iteration. Our result has implications beyond standard over-parametrization theory, as it can be viewed as designing an efficient data structure on top of a pre-trained large model to further speed up the fine-tuning process, a core procedure to deploy large language models (LLM).
Cite as

Zhao Song, Lichen Zhang, and Ruizhe Zhang. Training Multi-Layer Over-Parametrized Neural Network in Subquadratic Time. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 93:1-93:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{song_et_al:LIPIcs.ITCS.2024.93,
  author =	{Song, Zhao and Zhang, Lichen and Zhang, Ruizhe},
  title =	{{Training Multi-Layer Over-Parametrized Neural Network in Subquadratic Time}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{93:1--93:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.93},
  URN =		{urn:nbn:de:0030-drops-196212},
  doi =		{10.4230/LIPIcs.ITCS.2024.93},
  annote =	{Keywords: Deep learning theory, Nonconvex optimization}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2023.6
The Parameterised Complexity Of Integer Multicommodity Flow

Authors: Hans L. Bodlaender, Isja Mannens, Jelle J. Oostveen, Sukanya Pandey, and Erik Jan van Leeuwen

Published in: LIPIcs, Volume 285, 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)

Abstract
The Integer Multicommodity Flow problem has been studied extensively in the literature. However, from a parameterised perspective, mostly special cases, such as the Disjoint Path problem, have been considered. Therefore, we investigate the parameterised complexity of the general Integer Multicommodity Flow problem. We show that the decision version of this problem on directed graphs for a constant number of commodities, when the capacities are given in unary, is XNLP-complete with pathwidth as parameter and XALP-complete with treewidth as parameter. When the capacities are given in binary, the problem is NP-complete even for graphs of pathwidth at most 13. We give related results for undirected graphs. These results imply that the problem is unlikely to be fixed-parameter tractable by these parameters. In contrast, we show that the problem does become fixed-parameter tractable when weighted tree partition width (a variant of tree partition width for edge weighted graphs) is used as parameter.
Cite as

Hans L. Bodlaender, Isja Mannens, Jelle J. Oostveen, Sukanya Pandey, and Erik Jan van Leeuwen. The Parameterised Complexity Of Integer Multicommodity Flow. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bodlaender_et_al:LIPIcs.IPEC.2023.6,
  author =	{Bodlaender, Hans L. and Mannens, Isja and Oostveen, Jelle J. and Pandey, Sukanya and van Leeuwen, Erik Jan},
  title =	{{The Parameterised Complexity Of Integer Multicommodity Flow}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-305-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{285},
  editor =	{Misra, Neeldhara and Wahlstr\"{o}m, Magnus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.6},
  URN =		{urn:nbn:de:0030-drops-194250},
  doi =		{10.4230/LIPIcs.IPEC.2023.6},
  annote =	{Keywords: multicommodity flow, parameterised complexity, XNLP-completeness, XALP-completeness}
}
Document
PACE Solver Description
DOI: 10.4230/LIPIcs.IPEC.2023.35
PACE Solver Description: The PACE 2023 Parameterized Algorithms and Computational Experiments Challenge: Twinwidth

Authors: Max Bannach and Sebastian Berndt

Published in: LIPIcs, Volume 285, 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)

Abstract
This article is a report by the challenge organizers on the 8th Parameterized Algorithms and Computational Experiments Challenge (PACE 2023). As was common in previous iterations of the competition, this year’s iteration implemented an exact and heuristic track for a parameterized problem that has gained attention in the theory community. This year, the problem was to compute the twinwidth of a graph, a recently introduced width parameter that measures the similarity of a graph to a cograph. In the exact track, the competition participants were asked to develop an exact algorithm that can solve as many instances as possible from a benchmark set of 100 instances - with a time limit of 30 minutes per instance. The same task must be accomplished within 5 minutes in the heuristic track. However, the result in this track is not required to be optimal. As in previous iterations, the organizers handed out awards to the best solutions in both tracks and to the best student submissions. New this year is a dedicated theory award that appreciates new theoretical insights found by the participants during the development of their tools.
Cite as

Max Bannach and Sebastian Berndt. PACE Solver Description: The PACE 2023 Parameterized Algorithms and Computational Experiments Challenge: Twinwidth. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 35:1-35:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bannach_et_al:LIPIcs.IPEC.2023.35,
  author =	{Bannach, Max and Berndt, Sebastian},
  title =	{{PACE Solver Description: The PACE 2023 Parameterized Algorithms and Computational Experiments Challenge: Twinwidth}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{35:1--35:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-305-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{285},
  editor =	{Misra, Neeldhara and Wahlstr\"{o}m, Magnus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.35},
  URN =		{urn:nbn:de:0030-drops-194548},
  doi =		{10.4230/LIPIcs.IPEC.2023.35},
  annote =	{Keywords: Twinwidth, Algorithm Engineering, FPT, Kernelization}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2023.4
The Best of Both Worlds: Model-Driven Engineering Meets Model-Based Testing

Authors: P. H. M. van Spaendonck and Tim A. C. Willemse

Published in: LIPIcs, Volume 279, 34th International Conference on Concurrency Theory (CONCUR 2023)

Abstract
We study the connection between stable-failures refinement and the ioco conformance relation. Both behavioural relations underlie methodologies that have gained traction in industry: stable-failures refinement is used in several commercial Model-Driven Engineering tool suites, whereas the ioco conformance relation is used in Model-Based Testing tools. Refinement-based Model-Driven Engineering approaches promise to generate executable code from high-level models, thus guaranteeing that the code upholds specified behavioural contracts. Manual testing, however, is still required to gain confidence that the model-to-code transformation and the execution platform do not lead to unexpected contract violations. We identify conditions under which also this last step in the design methodology can be automated using the ioco conformance relation and the associated tools.
Cite as

P. H. M. van Spaendonck and Tim A. C. Willemse. The Best of Both Worlds: Model-Driven Engineering Meets Model-Based Testing. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 4:1-4:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{vanspaendonck_et_al:LIPIcs.CONCUR.2023.4,
  author =	{van Spaendonck, P. H. M. and Willemse, Tim A. C.},
  title =	{{The Best of Both Worlds: Model-Driven Engineering Meets Model-Based Testing}},
  booktitle =	{34th International Conference on Concurrency Theory (CONCUR 2023)},
  pages =	{4:1--4:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-299-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{279},
  editor =	{P\'{e}rez, Guillermo A. and Raskin, Jean-Fran\c{c}ois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2023.4},
  URN =		{urn:nbn:de:0030-drops-189988},
  doi =		{10.4230/LIPIcs.CONCUR.2023.4},
  annote =	{Keywords: stable-failures refinement, Model-Driven Engineering, input output conformance, Input Output Labelled Transition Systems, internal choice}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.8
Recognizing H-Graphs - Beyond Circular-Arc Graphs

Authors: Deniz Ağaoğlu Çağırıcı, Onur Çağırıcı, Jan Derbisz, Tim A. Hartmann, Petr Hliněný, Jan Kratochvíl, Tomasz Krawczyk, and Peter Zeman

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

Abstract
In 1992 Biró, Hujter and Tuza introduced, for every fixed connected graph H, the class of H-graphs, defined as the intersection graphs of connected subgraphs of some subdivision of H. Such classes of graphs are related to many known graph classes: for example, K₂-graphs coincide with interval graphs, K₃-graphs with circular-arc graphs, the union of T-graphs, where T ranges over all trees, coincides with chordal graphs. Recently, quite a lot of research has been devoted to understanding the tractability border for various computational problems, such as recognition or isomorphism testing, in classes of H-graphs for different graphs H. In this work we undertake this research topic, focusing on the recognition problem. Chaplick, Töpfer, Voborník, and Zeman showed an XP-algorithm testing whether a given graph is a T-graph, where the parameter is the size of the tree T. In particular, for every fixed tree T the recognition of T-graphs can be solved in polynomial time. Tucker showed a polynomial time algorithm recognizing K₃-graphs (circular-arc graphs). On the other hand, Chaplick et al. showed also that for every fixed graph H containing two distinct cycles sharing an edge, the recognition of H-graphs is NP-hard. The main two results of this work narrow the gap between the NP-hard and 𝖯 cases of H-graph recognition. First, we show that the recognition of H-graphs is NP-hard when H contains two distinct cycles. On the other hand, we show a polynomial-time algorithm recognizing L-graphs, where L is a graph containing a cycle and an edge attached to it (which we call lollipop graphs). Our work leaves open the recognition problems of M-graphs for every unicyclic graph M different from a cycle and a lollipop.
Cite as

Deniz Ağaoğlu Çağırıcı, Onur Çağırıcı, Jan Derbisz, Tim A. Hartmann, Petr Hliněný, Jan Kratochvíl, Tomasz Krawczyk, and Peter Zeman. Recognizing H-Graphs - Beyond Circular-Arc Graphs. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 8:1-8:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{agaoglucagirici_et_al:LIPIcs.MFCS.2023.8,
  author =	{A\u{g}ao\u{g}lu \c{C}a\u{g}{\i}r{\i}c{\i}, Deniz and \c{C}a\u{g}{\i}r{\i}c{\i}, Onur and Derbisz, Jan and Hartmann, Tim A. and Hlin\v{e}n\'{y}, Petr and Kratochv{\'\i}l, Jan and Krawczyk, Tomasz and Zeman, Peter},
  title =	{{Recognizing H-Graphs - Beyond Circular-Arc Graphs}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{8:1--8:14},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.8},
  URN =		{urn:nbn:de:0030-drops-185420},
  doi =		{10.4230/LIPIcs.MFCS.2023.8},
  annote =	{Keywords: H-graphs, Intersection Graphs, Helly Property}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2023.125
Indiscernibles and Flatness in Monadically Stable and Monadically NIP Classes

Authors: Jan Dreier, Nikolas Mählmann, Sebastian Siebertz, and Szymon Toruńczyk

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
Monadically stable and monadically NIP classes of structures were initially studied in the context of model theory and defined in logical terms. They have recently attracted attention in the area of structural graph theory, as they generalize notions such as nowhere denseness, bounded cliquewidth, and bounded twinwidth. Our main result is the - to the best of our knowledge first - purely combinatorial characterization of monadically stable classes of graphs, in terms of a property dubbed flip-flatness. A class C of graphs is flip-flat if for every fixed radius r, every sufficiently large set of vertices of a graph G ∈ C contains a large subset of vertices with mutual distance larger than r, where the distance is measured in some graph G' that can be obtained from G by performing a bounded number of flips that swap edges and non-edges within a subset of vertices. Flip-flatness generalizes the notion of uniform quasi-wideness, which characterizes nowhere dense classes and had a key impact on the combinatorial and algorithmic treatment of nowhere dense classes. To obtain this result, we develop tools that also apply to the more general monadically NIP classes, based on the notion of indiscernible sequences from model theory. We show that in monadically stable and monadically NIP classes indiscernible sequences impose a strong combinatorial structure on their definable neighborhoods. All our proofs are constructive and yield efficient algorithms.
Cite as

Jan Dreier, Nikolas Mählmann, Sebastian Siebertz, and Szymon Toruńczyk. Indiscernibles and Flatness in Monadically Stable and Monadically NIP Classes. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 125:1-125:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{dreier_et_al:LIPIcs.ICALP.2023.125,
  author =	{Dreier, Jan and M\"{a}hlmann, Nikolas and Siebertz, Sebastian and Toru\'{n}czyk, Szymon},
  title =	{{Indiscernibles and Flatness in Monadically Stable and Monadically NIP Classes}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{125:1--125:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.125},
  URN =		{urn:nbn:de:0030-drops-181779},
  doi =		{10.4230/LIPIcs.ICALP.2023.125},
  annote =	{Keywords: stability, NIP, combinatorial characterization, first-order model checking}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2023.6
Drawings of Complete Multipartite Graphs up to Triangle Flips

Authors: Oswin Aichholzer, Man-Kwun Chiu, Hung P. Hoang, Michael Hoffmann, Jan Kynčl, Yannic Maus, Birgit Vogtenhuber, and Alexandra Weinberger

Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)

Abstract
For a drawing of a labeled graph, the rotation of a vertex or crossing is the cyclic order of its incident edges, represented by the labels of their other endpoints. The extended rotation system (ERS) of the drawing is the collection of the rotations of all vertices and crossings. A drawing is simple if each pair of edges has at most one common point. Gioan’s Theorem states that for any two simple drawings of the complete graph K_n with the same crossing edge pairs, one drawing can be transformed into the other by a sequence of triangle flips (a.k.a. Reidemeister moves of Type 3). This operation refers to the act of moving one edge of a triangular cell formed by three pairwise crossing edges over the opposite crossing of the cell, via a local transformation. We investigate to what extent Gioan-type theorems can be obtained for wider classes of graphs. A necessary (but in general not sufficient) condition for two drawings of a graph to be transformable into each other by a sequence of triangle flips is that they have the same ERS. As our main result, we show that for the large class of complete multipartite graphs, this necessary condition is in fact also sufficient. We present two different proofs of this result, one of which is shorter, while the other one yields a polynomial time algorithm for which the number of needed triangle flips for graphs on n vertices is bounded by O(n^{16}). The latter proof uses a Carathéodory-type theorem for simple drawings of complete multipartite graphs, which we believe to be of independent interest. Moreover, we show that our Gioan-type theorem for complete multipartite graphs is essentially tight in the following sense: For the complete bipartite graph K_{m,n} minus two edges and K_{m,n} plus one edge for any m,n ≥ 4, as well as K_n minus a 4-cycle for any n ≥ 5, there exist two simple drawings with the same ERS that cannot be transformed into each other using triangle flips. So having the same ERS does not remain sufficient when removing or adding very few edges.
Cite as

Oswin Aichholzer, Man-Kwun Chiu, Hung P. Hoang, Michael Hoffmann, Jan Kynčl, Yannic Maus, Birgit Vogtenhuber, and Alexandra Weinberger. Drawings of Complete Multipartite Graphs up to Triangle Flips. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{aichholzer_et_al:LIPIcs.SoCG.2023.6,
  author =	{Aichholzer, Oswin and Chiu, Man-Kwun and Hoang, Hung P. and Hoffmann, Michael and Kyn\v{c}l, Jan and Maus, Yannic and Vogtenhuber, Birgit and Weinberger, Alexandra},
  title =	{{Drawings of Complete Multipartite Graphs up to Triangle Flips}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{6:1--6:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-273-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{258},
  editor =	{Chambers, Erin W. and Gudmundsson, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.6},
  URN =		{urn:nbn:de:0030-drops-178563},
  doi =		{10.4230/LIPIcs.SoCG.2023.6},
  annote =	{Keywords: Simple drawings, simple topological graphs, complete graphs, multipartite graphs, k-partite graphs, bipartite graphs, Gioan’s Theorem, triangle flips, Reidemeister moves}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2023.7
Decomposition of Zero-Dimensional Persistence Modules via Rooted Subsets

Authors: Ángel Javier Alonso and Michael Kerber

Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)

Abstract
We study the decomposition of zero-dimensional persistence modules, viewed as functors valued in the category of vector spaces factorizing through sets. Instead of working directly at the level of vector spaces, we take a step back and first study the decomposition problem at the level of sets. This approach allows us to define the combinatorial notion of rooted subsets. In the case of a filtered metric space M, rooted subsets relate the clustering behavior of the points of M with the decomposition of the associated persistence module. In particular, we can identify intervals in such a decomposition quickly. In addition, rooted subsets can be understood as a generalization of the elder rule, and are also related to the notion of constant conqueror of Cai, Kim, Mémoli and Wang. As an application, we give a lower bound on the number of intervals that we can expect in the decomposition of zero-dimensional persistence modules of a density-Rips filtration in Euclidean space: in the limit, and under very general circumstances, we can expect that at least 25% of the indecomposable summands are interval modules.
Cite as

Ángel Javier Alonso and Michael Kerber. Decomposition of Zero-Dimensional Persistence Modules via Rooted Subsets. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 7:1-7:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{alonso_et_al:LIPIcs.SoCG.2023.7,
  author =	{Alonso, \'{A}ngel Javier and Kerber, Michael},
  title =	{{Decomposition of Zero-Dimensional Persistence Modules via Rooted Subsets}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{7:1--7:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-273-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{258},
  editor =	{Chambers, Erin W. and Gudmundsson, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.7},
  URN =		{urn:nbn:de:0030-drops-178570},
  doi =		{10.4230/LIPIcs.SoCG.2023.7},
  annote =	{Keywords: Multiparameter persistent homology, Clustering, Decomposition of persistence modules, Elder Rule}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.11
Combinatorial and Algorithmic Aspects of Monadic Stability

Authors: Jan Dreier, Nikolas Mählmann, Amer E. Mouawad, Sebastian Siebertz, and Alexandre Vigny

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract
Nowhere dense classes of graphs are classes of sparse graphs with rich structural and algorithmic properties, however, they fail to capture even simple classes of dense graphs. Monadically stable classes, originating from model theory, generalize nowhere dense classes and close them under transductions, i.e. transformations defined by colorings and simple first-order interpretations. In this work we aim to extend some combinatorial and algorithmic properties of nowhere dense classes to monadically stable classes of finite graphs. We prove the following results. - For every monadically stable class C and fixed integer s ≥ 3, the Ramsey numbers R_C(s,t) are bounded from above by 𝒪(t^{s-1-δ}) for some δ > 0, improving the bound R(s,t) ∈ 𝒪(t^{s-1}/(log t)^{s-1}) known for the class of all graphs and the bounds known for k-stable graphs when s ≤ k. - For every monadically stable class C and every integer r, there exists δ > 0 such that every graph G ∈ C that contains an r-subdivision of the biclique K_{t,t} as a subgraph also contains K_{t^δ,t^δ} as a subgraph. This generalizes earlier results for nowhere dense graph classes. - We obtain a stronger regularity lemma for monadically stable classes of graphs. - Finally, we show that we can compute polynomial kernels for the independent set and dominating set problems in powers of nowhere dense classes. Formerly, only fixed-parameter tractable algorithms were known for these problems on powers of nowhere dense classes.
Cite as

Jan Dreier, Nikolas Mählmann, Amer E. Mouawad, Sebastian Siebertz, and Alexandre Vigny. Combinatorial and Algorithmic Aspects of Monadic Stability. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 11:1-11:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dreier_et_al:LIPIcs.ISAAC.2022.11,
  author =	{Dreier, Jan and M\"{a}hlmann, Nikolas and Mouawad, Amer E. and Siebertz, Sebastian and Vigny, Alexandre},
  title =	{{Combinatorial and Algorithmic Aspects of Monadic Stability}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{11:1--11:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.11},
  URN =		{urn:nbn:de:0030-drops-172961},
  doi =		{10.4230/LIPIcs.ISAAC.2022.11},
  annote =	{Keywords: Monadic Stability, Structural Graph Theory, Ramsey Numbers, Regularity, Kernels}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2022.29
Algorithms and Hardness Results for Computing Cores of Markov Chains

Authors: Ali Ahmadi, Krishnendu Chatterjee, Amir Kafshdar Goharshady, Tobias Meggendorfer, Roodabeh Safavi, and Ðorđe Žikelić

Published in: LIPIcs, Volume 250, 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)

Abstract
Given a Markov chain M = (V, v_0, δ), with state space V and a starting state v_0, and a probability threshold ε, an ε-core is a subset C of states that is left with probability at most ε. More formally, C ⊆ V is an ε-core, iff ℙ[reach (V\C)] ≤ ε. Cores have been applied in a wide variety of verification problems over Markov chains, Markov decision processes, and probabilistic programs, as a means of discarding uninteresting and low-probability parts of a probabilistic system and instead being able to focus on the states that are likely to be encountered in a real-world run. In this work, we focus on the problem of computing a minimal ε-core in a Markov chain. Our contributions include both negative and positive results: (i) We show that the decision problem on the existence of an ε-core of a given size is NP-complete. This solves an open problem posed in [Jan Kretínský and Tobias Meggendorfer, 2020]. We additionally show that the problem remains NP-complete even when limited to acyclic Markov chains with bounded maximal vertex degree; (ii) We provide a polynomial time algorithm for computing a minimal ε-core on Markov chains over control-flow graphs of structured programs. A straightforward combination of our algorithm with standard branch prediction techniques allows one to apply the idea of cores to find a subset of program lines that are left with low probability and then focus any desired static analysis on this core subset.
Cite as

Ali Ahmadi, Krishnendu Chatterjee, Amir Kafshdar Goharshady, Tobias Meggendorfer, Roodabeh Safavi, and Ðorđe Žikelić. Algorithms and Hardness Results for Computing Cores of Markov Chains. In 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 250, pp. 29:1-29:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{ahmadi_et_al:LIPIcs.FSTTCS.2022.29,
  author =	{Ahmadi, Ali and Chatterjee, Krishnendu and Goharshady, Amir Kafshdar and Meggendorfer, Tobias and Safavi, Roodabeh and \v{Z}ikeli\'{c}, Ðor{\d}e},
  title =	{{Algorithms and Hardness Results for Computing Cores of Markov Chains}},
  booktitle =	{42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)},
  pages =	{29:1--29:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-261-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{250},
  editor =	{Dawar, Anuj and Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2022.29},
  URN =		{urn:nbn:de:0030-drops-174216},
  doi =		{10.4230/LIPIcs.FSTTCS.2022.29},
  annote =	{Keywords: Markov Chains, Cores, Complexity}
}
Document
DOI: 10.4230/LIPIcs.CCC.2022.17
Nisan-Wigderson Generators in Proof Complexity: New Lower Bounds

Authors: Erfan Khaniki

Published in: LIPIcs, Volume 234, 37th Computational Complexity Conference (CCC 2022)

Abstract
A map g:{0,1}ⁿ → {0,1}^m (m > n) is a hard proof complexity generator for a proof system P iff for every string b ∈ {0,1}^m ⧵ Rng(g), formula τ_b(g) naturally expressing b ∉ Rng(g) requires superpolynomial size P-proofs. One of the well-studied maps in the theory of proof complexity generators is Nisan-Wigderson generator. Razborov [A. A. {Razborov}, 2015] conjectured that if A is a suitable matrix and f is a NP∩CoNP function hard-on-average for 𝖯/poly, then NW_{f, A} is a hard proof complexity generator for Extended Frege. In this paper, we prove a form of Razborov’s conjecture for AC⁰-Frege. We show that for any symmetric NP∩CoNP function f that is exponentially hard for depth two AC⁰ circuits, NW_{f,A} is a hard proof complexity generator for AC⁰-Frege in a natural setting. As direct applications of this theorem, we show that: 1) For any f with the specified properties, τ_b(NW_{f,A}) (for a natural formalization) based on a random b and a random matrix A with probability 1-o(1) is a tautology and requires superpolynomial (or even exponential) AC⁰-Frege proofs. 2) Certain formalizations of the principle f_n ∉ (NP∩CoNP)/poly requires superpolynomial AC⁰-Frege proofs. These applications relate to two questions that were asked by Krajíček [J. {Krajíček}, 2019].
Cite as

Erfan Khaniki. Nisan-Wigderson Generators in Proof Complexity: New Lower Bounds. In 37th Computational Complexity Conference (CCC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 234, pp. 17:1-17:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{khaniki:LIPIcs.CCC.2022.17,
  author =	{Khaniki, Erfan},
  title =	{{Nisan-Wigderson Generators in Proof Complexity: New Lower Bounds}},
  booktitle =	{37th Computational Complexity Conference (CCC 2022)},
  pages =	{17:1--17:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-241-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{234},
  editor =	{Lovett, Shachar},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2022.17},
  URN =		{urn:nbn:de:0030-drops-165799},
  doi =		{10.4230/LIPIcs.CCC.2022.17},
  annote =	{Keywords: Proof complexity, Bounded arithmetic, Bounded depth Frege, Nisan-Wigderson generators, Meta-complexity, Lower bounds}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2022.24
JavaScript Sealed Classes

Authors: Manuel Serrano

Published in: LIPIcs, Volume 222, 36th European Conference on Object-Oriented Programming (ECOOP 2022)

Abstract
In this work, we study the JavaScript Sealed Classes, which differ from regular classes in a few ways that allow ahead-of-time (AoT) compilers to implement them more efficiently. Sealed classes are compatible with the rest of the language so that they can be combined with all other structures, including regular classes, and can be gradually integrated into existing code bases. We present the design of the sealed classes and study their implementation in the hopc AoT compiler. We present an in-depth analysis of the speed of sealed classes compared to regular classes. To do so, we assembled a new suite of benchmarks that focuses on the efficiency of the class implementations. On this suite, we found that sealed classes provide an average speedup of 19%. The more classes and methods programs use, the greater the speedup. For the most favorable test that uses them intensively, we measured a speedup of 56%.
Cite as

Manuel Serrano. JavaScript Sealed Classes. In 36th European Conference on Object-Oriented Programming (ECOOP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 222, pp. 24:1-24:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{serrano:LIPIcs.ECOOP.2022.24,
  author =	{Serrano, Manuel},
  title =	{{JavaScript Sealed Classes}},
  booktitle =	{36th European Conference on Object-Oriented Programming (ECOOP 2022)},
  pages =	{24:1--24:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-225-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{222},
  editor =	{Ali, Karim and Vitek, Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2022.24},
  URN =		{urn:nbn:de:0030-drops-162523},
  doi =		{10.4230/LIPIcs.ECOOP.2022.24},
  annote =	{Keywords: JavaScript, Compiler, Dynamic Languages, Classes, Inline Caches}
}
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