37 Search Results for "M�nch, Lars"

Document
DOI: 10.4230/DagRep.13.9.69
Decision-Making Techniques for Smart Semiconductor Manufacturing (Dagstuhl Seminar 23362)

Authors: Hans Ehm, John Fowler, Lars Mönch, and Daniel Schorn

Published in: Dagstuhl Reports, Volume 13, Issue 9 (2024)

Abstract
In September 2023 the Dagstuhl Seminar 23362 explored the needs of the semiconductor industry for novel decision-making techniques and the related information systems to empower flexible decisions for smart production. The seminar participants also spent time identifying requirements for a simulation testbed which allows for assessing smart planning and control decisions in the semiconductor industry. The Executive Summary describes the process of the seminar and discusses key findings and areas for future research regarding these topics. Abstracts of presentations given during the seminar and the output of breakout sessions are collected in further sections.
Cite as

Hans Ehm, John Fowler, Lars Mönch, and Daniel Schorn. Decision-Making Techniques for Smart Semiconductor Manufacturing (Dagstuhl Seminar 23362). In Dagstuhl Reports, Volume 13, Issue 9, pp. 69-102, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{ehm_et_al:DagRep.13.9.69,
  author =	{Ehm, Hans and Fowler, John and M\"{o}nch, Lars and Schorn, Daniel},
  title =	{{Decision-Making Techniques for Smart Semiconductor Manufacturing (Dagstuhl Seminar 23362)}},
  pages =	{69--102},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2024},
  volume =	{13},
  number =	{9},
  editor =	{Ehm, Hans and Fowler, John and M\"{o}nch, Lars and Schorn, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.13.9.69},
  URN =		{urn:nbn:de:0030-drops-198216},
  doi =		{10.4230/DagRep.13.9.69},
  annote =	{Keywords: analytics, modeling, semiconductor manufacturing, simulation, smart manufacturing}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2023.7
Treewidth Is NP-Complete on Cubic Graphs

Authors: Hans L. Bodlaender, Édouard Bonnet, Lars Jaffke, Dušan Knop, Paloma T. Lima, Martin Milanič, Sebastian Ordyniak, Sukanya Pandey, and Ondřej Suchý

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

Abstract
In this paper, we show that Treewidth is NP-complete for cubic graphs, thereby improving the result by Bodlaender and Thilikos from 1997 that Treewidth is NP-complete on graphs with maximum degree at most 9. We add a new and simpler proof of the NP-completeness of treewidth, and show that Treewidth remains NP-complete on subcubic induced subgraphs of the infinite 3-dimensional grid.
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Hans L. Bodlaender, Édouard Bonnet, Lars Jaffke, Dušan Knop, Paloma T. Lima, Martin Milanič, Sebastian Ordyniak, Sukanya Pandey, and Ondřej Suchý. Treewidth Is NP-Complete on Cubic Graphs. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 7:1-7:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bodlaender_et_al:LIPIcs.IPEC.2023.7,
  author =	{Bodlaender, Hans L. and Bonnet, \'{E}douard and Jaffke, Lars and Knop, Du\v{s}an and Lima, Paloma T. and Milani\v{c}, Martin and Ordyniak, Sebastian and Pandey, Sukanya and Such\'{y}, Ond\v{r}ej},
  title =	{{Treewidth Is NP-Complete on Cubic Graphs}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{7:1--7:13},
  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.2023.7},
  URN =		{urn:nbn:de:0030-drops-194263},
  doi =		{10.4230/LIPIcs.IPEC.2023.7},
  annote =	{Keywords: Treewidth, cubic graphs, degree, NP-completeness}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2023.26
Dynamic Programming on Bipartite Tree Decompositions

Authors: Lars Jaffke, Laure Morelle, Ignasi Sau, and Dimitrios M. Thilikos

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

Abstract
We revisit a graph width parameter that we dub bipartite treewidth, along with its associated graph decomposition that we call bipartite tree decomposition. Bipartite treewidth can be seen as a common generalization of treewidth and the odd cycle transversal number. Intuitively, a bipartite tree decomposition is a tree decomposition whose bags induce almost bipartite graphs and whose adhesions contain at most one vertex from the bipartite part of any other bag, while the width of such decomposition measures how far the bags are from being bipartite. Adapted from a tree decomposition originally defined by Demaine, Hajiaghayi, and Kawarabayashi [SODA 2010] and explicitly defined by Tazari [Theor. Comput. Sci. 2012], bipartite treewidth appears to play a crucial role for solving problems related to odd-minors, which have recently attracted considerable attention. As a first step toward a theory for solving these problems efficiently, the main goal of this paper is to develop dynamic programming techniques to solve problems on graphs of small bipartite treewidth. For such graphs, we provide a number of para-NP-completeness results, FPT-algorithms, and XP-algorithms, as well as several open problems. In particular, we show that K_t-Subgraph-Cover, Weighted Vertex Cover/Independent Set, Odd Cycle Transversal, and Maximum Weighted Cut are FPT parameterized by bipartite treewidth. We also provide the following complexity dichotomy when H is a 2-connected graph, for each of the H-Subgraph-Packing, H-Induced-Packing, H-Scattered-Packing, and H-Odd-Minor-Packing problems: if H is bipartite, then the problem is para-NP-complete parameterized by bipartite treewidth while, if H is non-bipartite, then the problem is solvable in XP-time. Beyond bipartite treewidth, we define 1-ℋ-treewidth by replacing the bipartite graph class by any graph class ℋ. Most of the technology developed here also works for this more general parameter.
Cite as

Lars Jaffke, Laure Morelle, Ignasi Sau, and Dimitrios M. Thilikos. Dynamic Programming on Bipartite Tree Decompositions. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 26:1-26:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{jaffke_et_al:LIPIcs.IPEC.2023.26,
  author =	{Jaffke, Lars and Morelle, Laure and Sau, Ignasi and Thilikos, Dimitrios M.},
  title =	{{Dynamic Programming on Bipartite Tree Decompositions}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{26:1--26:22},
  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.2023.26},
  URN =		{urn:nbn:de:0030-drops-194455},
  doi =		{10.4230/LIPIcs.IPEC.2023.26},
  annote =	{Keywords: tree decomposition, bipartite graphs, dynamic programming, odd-minors, packing, maximum cut, vertex cover, independent set, odd cycle transversal}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2021.22
The Submodular Santa Claus Problem in the Restricted Assignment Case

Authors: Etienne Bamas, Paritosh Garg, and Lars Rohwedder

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
The submodular Santa Claus problem was introduced in a seminal work by Goemans, Harvey, Iwata, and Mirrokni (SODA'09) as an application of their structural result. In the mentioned problem n unsplittable resources have to be assigned to m players, each with a monotone submodular utility function f_i. The goal is to maximize min_i f_i(S_i) where S₁,...,S_m is a partition of the resources. The result by Goemans et al. implies a polynomial time O(n^{1/2 +ε})-approximation algorithm. Since then progress on this problem was limited to the linear case, that is, all f_i are linear functions. In particular, a line of research has shown that there is a polynomial time constant approximation algorithm for linear valuation functions in the restricted assignment case. This is the special case where each player is given a set of desired resources Γ_i and the individual valuation functions are defined as f_i(S) = f(S ∩ Γ_i) for a global linear function f. This can also be interpreted as maximizing min_i f(S_i) with additional assignment restrictions, i.e., resources can only be assigned to certain players. In this paper we make comparable progress for the submodular variant: If f is a monotone submodular function, we can in polynomial time compute an O(log log(n))-approximate solution.
Cite as

Etienne Bamas, Paritosh Garg, and Lars Rohwedder. The Submodular Santa Claus Problem in the Restricted Assignment Case. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 22:1-22:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bamas_et_al:LIPIcs.ICALP.2021.22,
  author =	{Bamas, Etienne and Garg, Paritosh and Rohwedder, Lars},
  title =	{{The Submodular Santa Claus Problem in the Restricted Assignment Case}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{22:1--22:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.22},
  URN =		{urn:nbn:de:0030-drops-140912},
  doi =		{10.4230/LIPIcs.ICALP.2021.22},
  annote =	{Keywords: Scheduling, submodularity, approximation algorithm, hypergraph matching}
}
Document
DOI: 10.4230/DagRep.10.5.1
Decision-Making Modeling and Solutions for Smart Semiconductor Manufacturing (Dagstuhl Seminar 20452)

Authors: Chen-Fu Chien, Hans Ehm, John W. Fowler, and Lars Mönch

Published in: Dagstuhl Reports, Volume 10, Issue 5 (2021)

Abstract
In November 2020 the Dagstuhl Seminar 20452 explored the needs of the semiconductor industry for making smart semiconductor manufacturing decisions and the information systems to empower flexible decisions for smart production. The seminar participants also spent time identifying the core elements for a simulation testbed which allows for assessing smart planning and control decisions in the semiconductor industry. This Executive Summary describes the process of the seminar and discusses key findings and areas for future research regarding these topics. Abstracts of presentations given during the seminar and the output of breakout sessions are collected in appendices.
Cite as

Chen-Fu Chien, Hans Ehm, John W. Fowler, and Lars Mönch. Decision-Making Modeling and Solutions for Smart Semiconductor Manufacturing (Dagstuhl Seminar 20452). In Dagstuhl Reports, Volume 10, Issue 5, pp. 1-18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@Article{chien_et_al:DagRep.10.5.1,
  author =	{Chien, Chen-Fu and Ehm, Hans and Fowler, John W. and M\"{o}nch, Lars},
  title =	{{Decision-Making Modeling and Solutions for Smart Semiconductor Manufacturing (Dagstuhl Seminar 20452)}},
  pages =	{1--18},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2021},
  volume =	{10},
  number =	{5},
  editor =	{Chien, Chen-Fu and Ehm, Hans and Fowler, John W. and M\"{o}nch, Lars},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.10.5.1},
  URN =		{urn:nbn:de:0030-drops-137410},
  doi =		{10.4230/DagRep.10.5.1},
  annote =	{Keywords: Modeling, Simulation, Smart Manufacturing, Analytics, Semiconductor Manufacturing}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2020.26
Diverse Pairs of Matchings

Authors: Fedor V. Fomin, Petr A. Golovach, Lars Jaffke, Geevarghese Philip, and Danil Sagunov

Published in: LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)

Abstract
We initiate the study of the Diverse Pair of (Maximum/ Perfect) Matchings problems which given a graph G and an integer k, ask whether G has two (maximum/perfect) matchings whose symmetric difference is at least k. Diverse Pair of Matchings (asking for two not necessarily maximum or perfect matchings) is NP-complete on general graphs if k is part of the input, and we consider two restricted variants. First, we show that on bipartite graphs, the problem is polynomial-time solvable, and second we show that Diverse Pair of Maximum Matchings is FPT parameterized by k. We round off the work by showing that Diverse Pair of Matchings has a kernel on 𝒪(k²) vertices.
Cite as

Fedor V. Fomin, Petr A. Golovach, Lars Jaffke, Geevarghese Philip, and Danil Sagunov. Diverse Pairs of Matchings. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 26:1-26:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{fomin_et_al:LIPIcs.ISAAC.2020.26,
  author =	{Fomin, Fedor V. and Golovach, Petr A. and Jaffke, Lars and Philip, Geevarghese and Sagunov, Danil},
  title =	{{Diverse Pairs of Matchings}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{26:1--26:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Cao, Yixin and Cheng, Siu-Wing and Li, Minming},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.26},
  URN =		{urn:nbn:de:0030-drops-133706},
  doi =		{10.4230/LIPIcs.ISAAC.2020.26},
  annote =	{Keywords: Matching, Solution Diversity, Fixed-Parameter Tractability}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2020.50
Compressing Permutation Groups into Grammars and Polytopes. A Graph Embedding Approach

Authors: Lars Jaffke, Mateus de Oliveira Oliveira, and Hans Raj Tiwary

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract
It can be shown that each permutation group G ⊑ 𝕊_n can be embedded, in a well defined sense, in a connected graph with O(n+|G|) vertices. Some groups, however, require much fewer vertices. For instance, 𝕊_n itself can be embedded in the n-clique K_n, a connected graph with n vertices. In this work, we show that the minimum size of a context-free grammar generating a finite permutation group G⊑ 𝕊_n can be upper bounded by three structural parameters of connected graphs embedding G: the number of vertices, the treewidth, and the maximum degree. More precisely, we show that any permutation group G ⊑ 𝕊_n that can be embedded into a connected graph with m vertices, treewidth k, and maximum degree Δ, can also be generated by a context-free grammar of size 2^{O(kΔlogΔ)}⋅ m^{O(k)}. By combining our upper bound with a connection established by Pesant, Quimper, Rousseau and Sellmann [Gilles Pesant et al., 2009] between the extension complexity of a permutation group and the grammar complexity of a formal language, we also get that these permutation groups can be represented by polytopes of extension complexity 2^{O(kΔlogΔ)}⋅ m^{O(k)}. The above upper bounds can be used to provide trade-offs between the index of permutation groups, and the number of vertices, treewidth and maximum degree of connected graphs embedding these groups. In particular, by combining our main result with a celebrated 2^{Ω(n)} lower bound on the grammar complexity of the symmetric group 𝕊_n due to Glaister and Shallit [Glaister and Shallit, 1996] we have that connected graphs of treewidth o(n/log n) and maximum degree o(n/log n) embedding subgroups of 𝕊_n of index 2^{cn} for some small constant c must have n^{ω(1)} vertices. This lower bound can be improved to exponential on graphs of treewidth n^{ε} for ε < 1 and maximum degree o(n/log n).
Cite as

Lars Jaffke, Mateus de Oliveira Oliveira, and Hans Raj Tiwary. Compressing Permutation Groups into Grammars and Polytopes. A Graph Embedding Approach. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 50:1-50:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{jaffke_et_al:LIPIcs.MFCS.2020.50,
  author =	{Jaffke, Lars and de Oliveira Oliveira, Mateus and Tiwary, Hans Raj},
  title =	{{Compressing Permutation Groups into Grammars and Polytopes. A Graph Embedding Approach}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{50:1--50:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.50},
  URN =		{urn:nbn:de:0030-drops-127161},
  doi =		{10.4230/LIPIcs.MFCS.2020.50},
  annote =	{Keywords: Permutation Groups, Context Free Grammars, Extension Complexity, Graph Embedding Complexity}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2020.6
Sea-Rise Flooding on Massive Dynamic Terrains

Authors: Lars Arge, Mathias Rav, Morten Revsbæk, Yujin Shin, and Jungwoo Yang

Published in: LIPIcs, Volume 162, 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)

Abstract
Predicting floods caused by storm surges is a crucial task. Since the rise of ocean water can create floods that extend far onto land, the flood damage can be severe. By developing efficient flood prediction algorithms that use very detailed terrain models and accurate sea-level forecasts, users can plan mitigations such as flood walls and gates to minimize the damage from storm surge flooding. In this paper we present a data structure for predicting floods from dynamic sea-level forecast data on dynamic massive terrains. The forecast data is dynamic in the sense that new forecasts are released several times per day; the terrain is dynamic in the sense that the terrain model may be updated to plan flood mitigations. Since accurate flood risk computations require using very detailed terrain models, and such terrain models can easily exceed the size of the main memory in a regular computer, our data structure is I/O-efficient, that is, it minimizes the number of I/Os (i.e. block transfers) between main memory and disk. For a terrain represented as a raster of N cells, it can be constructed using O(N/B log_M/B N/B) I/Os, it can compute the flood risk in a given small region using O(log_B N) I/Os, and it can handle updating the terrain elevation in a given small region using O(log²_B N) I/Os, where B is the block size and M is the capacity of main memory.
Cite as

Lars Arge, Mathias Rav, Morten Revsbæk, Yujin Shin, and Jungwoo Yang. Sea-Rise Flooding on Massive Dynamic Terrains. In 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 162, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{arge_et_al:LIPIcs.SWAT.2020.6,
  author =	{Arge, Lars and Rav, Mathias and Revsb{\ae}k, Morten and Shin, Yujin and Yang, Jungwoo},
  title =	{{Sea-Rise Flooding on Massive Dynamic Terrains}},
  booktitle =	{17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-150-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{162},
  editor =	{Albers, Susanne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2020.6},
  URN =		{urn:nbn:de:0030-drops-122539},
  doi =		{10.4230/LIPIcs.SWAT.2020.6},
  annote =	{Keywords: Computational geometry, I/O-algorithms, merge tree, dynamic terrain}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2019.34
A Complexity Dichotomy for Critical Values of the b-Chromatic Number of Graphs

Authors: Lars Jaffke and Paloma T. Lima

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

Abstract
A b-coloring of a graph G is a proper coloring of its vertices such that each color class contains a vertex that has at least one neighbor in all the other color classes. The b-Coloring problem asks whether a graph G has a b-coloring with k colors. The b-chromatic number of a graph G, denoted by chi_b(G), is the maximum number k such that G admits a b-coloring with k colors. We consider the complexity of the b-Coloring problem, whenever the value of k is close to one of two upper bounds on chi_b(G): The maximum degree Delta(G) plus one, and the m-degree, denoted by m(G), which is defined as the maximum number i such that G has i vertices of degree at least i-1. We obtain a dichotomy result for all fixed k in N when k is close to one of the two above mentioned upper bounds. Concretely, we show that if k in {Delta(G) + 1 - p, m(G) - p}, the problem is polynomial-time solvable whenever p in {0, 1} and, even when k = 3, it is NP-complete whenever p >= 2. We furthermore consider parameterizations of the b-Coloring problem that involve the maximum degree Delta(G) of the input graph G and give two FPT-algorithms. First, we show that deciding whether a graph G has a b-coloring with m(G) colors is FPT parameterized by Delta(G). Second, we show that b-Coloring{} is FPT parameterized by Delta(G) + l_k(G), where l_k(G) denotes the number of vertices of degree at least k.
Cite as

Lars Jaffke and Paloma T. Lima. A Complexity Dichotomy for Critical Values of the b-Chromatic Number of Graphs. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 34:1-34:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{jaffke_et_al:LIPIcs.MFCS.2019.34,
  author =	{Jaffke, Lars and Lima, Paloma T.},
  title =	{{A Complexity Dichotomy for Critical Values of the b-Chromatic Number of Graphs}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{34:1--34:13},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.34},
  URN =		{urn:nbn:de:0030-drops-109784},
  doi =		{10.4230/LIPIcs.MFCS.2019.34},
  annote =	{Keywords: b-Coloring, b-Chromatic Number}
}
Document
DOI: 10.4230/LIPIcs.STACS.2019.44
Tight Complexity Lower Bounds for Integer Linear Programming with Few Constraints

Authors: Dušan Knop, Michał Pilipczuk, and Marcin Wrochna

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

Abstract
We consider the standard ILP Feasibility problem: given an integer linear program of the form {Ax = b, x >= 0}, where A is an integer matrix with k rows and l columns, x is a vector of l variables, and b is a vector of k integers, we ask whether there exists x in N^l that satisfies Ax = b. Each row of A specifies one linear constraint on x; our goal is to study the complexity of ILP Feasibility when both k, the number of constraints, and |A|_infty, the largest absolute value of an entry in A, are small. Papadimitriou [Christos H. Papadimitriou, 1981] was the first to give a fixed-parameter algorithm for ILP Feasibility under parameterization by the number of constraints that runs in time ((|A |_infty + |b|_infty) * k)^O(k^2). This was very recently improved by Eisenbrand and Weismantel [Friedrich Eisenbrand and Robert Weismantel, 2018], who used the Steinitz lemma to design an algorithm with running time (k |A|_infty)^{O(k)}* |b|_infty^2, which was subsequently improved by Jansen and Rohwedder [Klaus Jansen and Lars Rohwedder, 2019] to O(k |A |_infty)^k* log |b|_infty. We prove that for {0,1}-matrices A, the running time of the algorithm of Eisenbrand and Weismantel is probably optimal: an algorithm with running time 2^{o(k log k)}* (l+|{b}|_infty)^{o(k)} would contradict the Exponential Time Hypothesis (ETH). This improves previous non-tight lower bounds of Fomin et al. [Fedor V. Fomin et al., 2018]. We then consider integer linear programs that may have many constraints, but they need to be structured in a "shallow" way. Precisely, we consider the parameter {dual treedepth} of the matrix A, denoted td_D(A), which is the treedepth of the graph over the rows of A, where two rows are adjacent if in some column they simultaneously contain a non-zero entry. It was recently shown by Koutecký et al. [Martin Koutecký et al., 2018] that {ILP Feasibility} can be solved in time |A |_infty^{2^O(td_D(A))} * (k+l+log |b|_infty)^O(1). We present a streamlined proof of this fact and prove that, again, this running time is probably optimal: even assuming that all entries of A and {b} are in {-1,0,1}, the existence of an algorithm with running time 2^{2^o(td_D(A))} * (k+l)^O(1) would contradict the ETH.
Cite as

Dušan Knop, Michał Pilipczuk, and Marcin Wrochna. Tight Complexity Lower Bounds for Integer Linear Programming with Few Constraints. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 44:1-44:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{knop_et_al:LIPIcs.STACS.2019.44,
  author =	{Knop, Du\v{s}an and Pilipczuk, Micha{\l} and Wrochna, Marcin},
  title =	{{Tight Complexity Lower Bounds for Integer Linear Programming with Few Constraints}},
  booktitle =	{36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
  pages =	{44:1--44:15},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.44},
  URN =		{urn:nbn:de:0030-drops-102831},
  doi =		{10.4230/LIPIcs.STACS.2019.44},
  annote =	{Keywords: integer linear programming, fixed-parameter tractability, ETH}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2018.4
Improved Dynamic Geodesic Nearest Neighbor Searching in a Simple Polygon

Authors: Pankaj K. Agarwal, Lars Arge, and Frank Staals

Published in: LIPIcs, Volume 99, 34th International Symposium on Computational Geometry (SoCG 2018)

Abstract
We present an efficient dynamic data structure that supports geodesic nearest neighbor queries for a set S of point sites in a static simple polygon P. Our data structure allows us to insert a new site in S, delete a site from S, and ask for the site in S closest to an arbitrary query point q in P. All distances are measured using the geodesic distance, that is, the length of the shortest path that is completely contained in P. Our data structure achieves polylogarithmic update and query times, and uses O(n log^3n log m + m) space, where n is the number of sites in S and m is the number of vertices in P. The crucial ingredient in our data structure is an implicit representation of a vertical shallow cutting of the geodesic distance functions. We show that such an implicit representation exists, and that we can compute it efficiently.
Cite as

Pankaj K. Agarwal, Lars Arge, and Frank Staals. Improved Dynamic Geodesic Nearest Neighbor Searching in a Simple Polygon. In 34th International Symposium on Computational Geometry (SoCG 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 99, pp. 4:1-4:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{agarwal_et_al:LIPIcs.SoCG.2018.4,
  author =	{Agarwal, Pankaj K. and Arge, Lars and Staals, Frank},
  title =	{{Improved Dynamic Geodesic Nearest Neighbor Searching in a Simple Polygon}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{4:1--4:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Speckmann, Bettina and T\'{o}th, Csaba D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2018.4},
  URN =		{urn:nbn:de:0030-drops-87175},
  doi =		{10.4230/LIPIcs.SoCG.2018.4},
  annote =	{Keywords: data structure, simple polygon, geodesic distance, nearest neighbor searching, shallow cutting}
}
Document
DOI: 10.4230/DagRep.6.2.28
Modeling and Analysis of Semiconductor Supply Chains (Dagstuhl Seminar 16062)

Authors: Chen-Fu Chien, Hans Ehm, John Fowler, and Lars Mönch

Published in: Dagstuhl Reports, Volume 6, Issue 2 (2016)

Abstract
In February 2016 the Dagstuhl Seminar 16062 explored the needs of the semiconductor industry for better planning and scheduling approaches at the supply chain level and the requirements for information systems to support the approaches. The seminar participants also spent time identifying the core elements of a conceptual reference model for planning and control of semiconductor manufacturing supply chains. This Executive Summary describes the process of the seminar and discusses key findings and areas for future research regarding these topics. Abstracts of presentations given during the seminar and the output of breakout sessions are collected in appendices.
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Chen-Fu Chien, Hans Ehm, John Fowler, and Lars Mönch. Modeling and Analysis of Semiconductor Supply Chains (Dagstuhl Seminar 16062). In Dagstuhl Reports, Volume 6, Issue 2, pp. 28-64, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@Article{chien_et_al:DagRep.6.2.28,
  author =	{Chien, Chen-Fu and Ehm, Hans and Fowler, John and M\"{o}nch, Lars},
  title =	{{Modeling and Analysis of Semiconductor Supply Chains (Dagstuhl Seminar 16062)}},
  pages =	{28--64},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2016},
  volume =	{6},
  number =	{2},
  editor =	{Chien, Chen-Fu and Ehm, Hans and Fowler, John and M\"{o}nch, Lars},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.6.2.28},
  URN =		{urn:nbn:de:0030-drops-58606},
  doi =		{10.4230/DagRep.6.2.28},
  annote =	{Keywords: Modeling, Simulation, Supply Chain Management, Semiconductor Manufacturing}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2015.198
Modal Logics for Nominal Transition Systems

Authors: Joachim Parrow, Johannes Borgström, Lars-Henrik Eriksson, Ramunas Gutkovas, and Tjark Weber

Published in: LIPIcs, Volume 42, 26th International Conference on Concurrency Theory (CONCUR 2015)

Abstract
We define a uniform semantic substrate for a wide variety of process calculi where states and action labels can be from arbitrary nominal sets. A Hennessy-Milner logic for these systems is introduced, and proved adequate for bisimulation equivalence. A main novelty is the use of finitely supported infinite conjunctions. We show how to treat different bisimulation variants such as early, late and open in a systematic way, and make substantial comparisons with related work. The main definitions and theorems have been formalized in Nominal Isabelle.
Cite as

Joachim Parrow, Johannes Borgström, Lars-Henrik Eriksson, Ramunas Gutkovas, and Tjark Weber. Modal Logics for Nominal Transition Systems. In 26th International Conference on Concurrency Theory (CONCUR 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 42, pp. 198-211, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{parrow_et_al:LIPIcs.CONCUR.2015.198,
  author =	{Parrow, Joachim and Borgstr\"{o}m, Johannes and Eriksson, Lars-Henrik and Gutkovas, Ramunas and Weber, Tjark},
  title =	{{Modal Logics for Nominal Transition Systems}},
  booktitle =	{26th International Conference on Concurrency Theory (CONCUR 2015)},
  pages =	{198--211},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-91-0},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{42},
  editor =	{Aceto, Luca and de Frutos Escrig, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2015.198},
  URN =		{urn:nbn:de:0030-drops-53823},
  doi =		{10.4230/LIPIcs.CONCUR.2015.198},
  annote =	{Keywords: Process algebra, nominal sets, bisimulation, modal logic}
}
Document
DOI: 10.4230/LIPIcs.RTA.2015.194
Network Rewriting II: Bi- and Hopf Algebras

Authors: Lars Hellström

Published in: LIPIcs, Volume 36, 26th International Conference on Rewriting Techniques and Applications (RTA 2015)

Abstract
Bialgebras and their specialisation Hopf algebras are algebraic structures that challenge traditional mathematical notation, in that they sport two core operations that defy the basic functional paradigm of taking zero or more operands as input and producing one result as output. On the other hand, these peculiarities do not prevent studying them using rewriting techniques, if one works within an appropriate network formalism rather than the traditional term formalism. This paper restates the traditional axioms as rewriting systems, demonstrating confluence in the case of bialgebras and finding the (infinite) completion in the case of Hopf algebras. A noteworthy minor problem solved along the way is that of constructing a quasi-order with respect to which the rules are compatible.
Cite as

Lars Hellström. Network Rewriting II: Bi- and Hopf Algebras. In 26th International Conference on Rewriting Techniques and Applications (RTA 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 36, pp. 194-208, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{hellstrom:LIPIcs.RTA.2015.194,
  author =	{Hellstr\"{o}m, Lars},
  title =	{{Network Rewriting II: Bi- and Hopf Algebras}},
  booktitle =	{26th International Conference on Rewriting Techniques and Applications (RTA 2015)},
  pages =	{194--208},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-85-9},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{36},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2015.194},
  URN =		{urn:nbn:de:0030-drops-51975},
  doi =		{10.4230/LIPIcs.RTA.2015.194},
  annote =	{Keywords: confluence, network, PROP, Hopf algebra}
}
Document
DOI: 10.4230/LIPIcs.SOCG.2015.1
Combinatorial Discrepancy for Boxes via the gamma_2 Norm

Authors: Jirí Matoušek and Aleksandar Nikolov

Published in: LIPIcs, Volume 34, 31st International Symposium on Computational Geometry (SoCG 2015)

Abstract
The gamma_2 norm of a real m by n matrix A is the minimum number t such that the column vectors of A are contained in a 0-centered ellipsoid E that in turn is contained in the hypercube [-t, t]^m. This classical quantity is polynomial-time computable and was proved by the second author and Talwar to approximate the hereditary discrepancy: it bounds the hereditary discrepancy from above and from below, up to logarithmic factors. Here we provided a simplified proof of the upper bound and show that both the upper and the lower bound are asymptotically tight in the worst case. We then demonstrate on several examples the power of the gamma_2 norm as a tool for proving lower and upper bounds in discrepancy theory. Most notably, we prove a new lower bound of log(n)^(d-1) (up to constant factors) for the d-dimensional Tusnady problem, asking for the combinatorial discrepancy of an n-point set in d-dimensional space with respect to axis-parallel boxes. For d>2, this improves the previous best lower bound, which was of order approximately log(n)^((d-1)/2), and it comes close to the best known upper bound of O(log(n)^(d+1/2)), for which we also obtain a new, very simple proof. Applications to lower bounds for dynamic range searching and lower bounds in differential privacy are given.
Cite as

Jirí Matoušek and Aleksandar Nikolov. Combinatorial Discrepancy for Boxes via the gamma_2 Norm. In 31st International Symposium on Computational Geometry (SoCG 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 34, pp. 1-15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{matousek_et_al:LIPIcs.SOCG.2015.1,
  author =	{Matou\v{s}ek, Jir{\'\i} and Nikolov, Aleksandar},
  title =	{{Combinatorial Discrepancy for Boxes via the gamma\underline2 Norm}},
  booktitle =	{31st International Symposium on Computational Geometry (SoCG 2015)},
  pages =	{1--15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-83-5},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{34},
  editor =	{Arge, Lars and Pach, J\'{a}nos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SOCG.2015.1},
  URN =		{urn:nbn:de:0030-drops-51091},
  doi =		{10.4230/LIPIcs.SOCG.2015.1},
  annote =	{Keywords: discrepancy theory, range counting, factorization norms}
}
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