72 Search Results for "H�bner, Michael"

Document
DOI: 10.4230/DagRep.13.8.1
Recent Trends in Graph Decomposition (Dagstuhl Seminar 23331)

Authors: George Karypis, Christian Schulz, Darren Strash, Deepak Ajwani, Rob H. Bisseling, Katrin Casel, Ümit V. Çatalyürek, Cédric Chevalier, Florian Chudigiewitsch, Marcelo Fonseca Faraj, Michael Fellows, Lars Gottesbüren, Tobias Heuer, Kamer Kaya, Jakub Lacki, Johannes Langguth, Xiaoye Sherry Li, Ruben Mayer, Johannes Meintrup, Yosuke Mizutani, François Pellegrini, Fabrizio Petrini, Frances Rosamond, Ilya Safro, Sebastian Schlag, Roohani Sharma, Blair D. Sullivan, Bora Uçar, and Albert-Jan Yzelman

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

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 23331 "Recent Trends in Graph Decomposition", which took place from 13. August to 18. August, 2023. The seminar brought together 33 experts from academia and industry to discuss graph decomposition, a pivotal technique for handling massive graphs in applications such as social networks and scientific simulations. The seminar addressed the challenges posed by contemporary hardware designs, the potential of deep neural networks and reinforcement learning in developing heuristics, the unique optimization requirements of large sparse data, and the need for scalable algorithms suitable for emerging architectures. Through presentations, discussions, and collaborative sessions, the event fostered an exchange of innovative ideas, leading to the creation of community notes highlighting key open problems in the field.
Cite as

George Karypis, Christian Schulz, Darren Strash, Deepak Ajwani, Rob H. Bisseling, Katrin Casel, Ümit V. Çatalyürek, Cédric Chevalier, Florian Chudigiewitsch, Marcelo Fonseca Faraj, Michael Fellows, Lars Gottesbüren, Tobias Heuer, Kamer Kaya, Jakub Lacki, Johannes Langguth, Xiaoye Sherry Li, Ruben Mayer, Johannes Meintrup, Yosuke Mizutani, François Pellegrini, Fabrizio Petrini, Frances Rosamond, Ilya Safro, Sebastian Schlag, Roohani Sharma, Blair D. Sullivan, Bora Uçar, and Albert-Jan Yzelman. Recent Trends in Graph Decomposition (Dagstuhl Seminar 23331). In Dagstuhl Reports, Volume 13, Issue 8, pp. 1-45, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{karypis_et_al:DagRep.13.8.1,
  author =	{Karypis, George and Schulz, Christian and Strash, Darren and Ajwani, Deepak and Bisseling, Rob H. and Casel, Katrin and \c{C}ataly\"{u}rek, \"{U}mit V. and Chevalier, C\'{e}dric and Chudigiewitsch, Florian and Faraj, Marcelo Fonseca and Fellows, Michael and Gottesb\"{u}ren, Lars and Heuer, Tobias and Kaya, Kamer and Lacki, Jakub and Langguth, Johannes and Li, Xiaoye Sherry and Mayer, Ruben and Meintrup, Johannes and Mizutani, Yosuke and Pellegrini, Fran\c{c}ois and Petrini, Fabrizio and Rosamond, Frances and Safro, Ilya and Schlag, Sebastian and Sharma, Roohani and Sullivan, Blair D. and U\c{c}ar, Bora and Yzelman, Albert-Jan},
  title =	{{Recent Trends in Graph Decomposition (Dagstuhl Seminar 23331)}},
  pages =	{1--45},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2024},
  volume =	{13},
  number =	{8},
  editor =	{Karypis, George and Schulz, Christian and Strash, Darren},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.13.8.1},
  URN =		{urn:nbn:de:0030-drops-198114},
  doi =		{10.4230/DagRep.13.8.1},
  annote =	{Keywords: combinatorial optimization, experimental algorithmics, parallel algorithms}
}
Document
DOI: 10.4230/LIPIcs.CP.2023.21
Exploring Hydrogen Supply/Demand Networks: Modeller and Domain Expert Views

Authors: Matthias Klapperstueck, Frits de Nijs, Ilankaikone Senthooran, Jack Lee-Kopij, Maria Garcia de la Banda, and Michael Wybrow

Published in: LIPIcs, Volume 280, 29th International Conference on Principles and Practice of Constraint Programming (CP 2023)

Abstract
Energy companies are considering producing renewable fuels such as hydrogen/ammonia. Setting up a production network means deciding where to build production plants, and how to operate them at minimum electricity and transport costs. These decisions are complicated by many factors including the difficulty in obtaining accurate current data (e.g., electricity price and transport costs) for potential supply locations, the accuracy of data predictions (e.g., for demand and costs), and the need for some decisions to be made due to external (not modelled) factors. Thus, decision-makers need access to a user-centric decision system that helps them visualise, explore, interact and compare the many possible solutions of many different scenarios. This paper describes the system we have built to support our energy partner in making such decisions, and shows the advantages of having a graphical user-focused interactive tool, and of using a high-level constraint modelling language (MiniZinc) to implement the underlying model.
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Matthias Klapperstueck, Frits de Nijs, Ilankaikone Senthooran, Jack Lee-Kopij, Maria Garcia de la Banda, and Michael Wybrow. Exploring Hydrogen Supply/Demand Networks: Modeller and Domain Expert Views. In 29th International Conference on Principles and Practice of Constraint Programming (CP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 280, pp. 21:1-21:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{klapperstueck_et_al:LIPIcs.CP.2023.21,
  author =	{Klapperstueck, Matthias and de Nijs, Frits and Senthooran, Ilankaikone and Lee-Kopij, Jack and Garcia de la Banda, Maria and Wybrow, Michael},
  title =	{{Exploring Hydrogen Supply/Demand Networks: Modeller and Domain Expert Views}},
  booktitle =	{29th International Conference on Principles and Practice of Constraint Programming (CP 2023)},
  pages =	{21:1--21:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-300-3},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{280},
  editor =	{Yap, Roland H. C.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2023.21},
  URN =		{urn:nbn:de:0030-drops-190584},
  doi =		{10.4230/LIPIcs.CP.2023.21},
  annote =	{Keywords: Facility Location, Hydrogen Supply Chain, Human-Centric Optimisation}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.29
Giant Components in Random Temporal Graphs

Authors: Ruben Becker, Arnaud Casteigts, Pierluigi Crescenzi, Bojana Kodric, Malte Renken, Michael Raskin, and Viktor Zamaraev

Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)

Abstract
A temporal graph is a graph whose edges appear only at certain points in time. In these graphs, reachability among nodes relies on paths that traverse edges in chronological order (temporal paths). Unlike standard paths, temporal paths may not be composable, thus the reachability relation is not transitive and connected components (i.e., sets of pairwise temporally connected nodes) do not form equivalence classes, a fact with far-reaching consequences. Recently, Casteigts et al. [FOCS 2021] proposed a natural temporal analog of the seminal Erdős-Rényi random graph model, based on the same parameters n and p. The proposed model is obtained by randomly permuting the edges of an Erdős-Rényi random graph and interpreting this permutation as an ordering of presence times. Casteigts et al. showed that the well-known single threshold for connectivity in the Erdős-Rényi model fans out into multiple phase transitions for several distinct notions of reachability in the temporal setting. The second most basic phenomenon studied by Erdős and Rényi in static (i.e., non-temporal) random graphs is the emergence of a giant connected component. However, the existence of a similar phase transition in the temporal model was left open until now. In this paper, we settle this question. We identify a sharp threshold at p = log n/n, where the size of the largest temporally connected component increases from o(n) to n-o(n) nodes. This transition occurs significantly later than in the static setting, where a giant component of size n-o(n) already exists for any p ∈ ω(1/n) (i.e., as soon as p is larger than a constant fraction of n). Interestingly, the threshold that we obtain holds for both open and closed connected components, i.e., components that allow, respectively forbid, their connecting paths to use external nodes - a distinction arising from the absence of transitivity. We achieve these results by strengthening the tools from Casteigts et al. and developing new techniques that provide means to decouple dependencies between past and future events in temporal Erdős-Rényi graphs, which could be of general interest in future investigations of these objects.
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Ruben Becker, Arnaud Casteigts, Pierluigi Crescenzi, Bojana Kodric, Malte Renken, Michael Raskin, and Viktor Zamaraev. Giant Components in Random Temporal Graphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 29:1-29:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{becker_et_al:LIPIcs.APPROX/RANDOM.2023.29,
  author =	{Becker, Ruben and Casteigts, Arnaud and Crescenzi, Pierluigi and Kodric, Bojana and Renken, Malte and Raskin, Michael and Zamaraev, Viktor},
  title =	{{Giant Components in Random Temporal Graphs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{29:1--29:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.29},
  URN =		{urn:nbn:de:0030-drops-188542},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.29},
  annote =	{Keywords: random temporal graph, Erd\H{o}s–R\'{e}nyi random graph, sharp threshold, temporal connectivity, temporal connected component, edge-ordered graph}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.65
A Weyl Criterion for Finite-State Dimension and Applications

Authors: Jack H. Lutz, Satyadev Nandakumar, and Subin Pulari

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

Abstract
Finite-state dimension, introduced early in this century as a finite-state version of classical Hausdorff dimension, is a quantitative measure of the lower asymptotic density of information in an infinite sequence over a finite alphabet, as perceived by finite automata. Finite-state dimension is a robust concept that now has equivalent formulations in terms of finite-state gambling, lossless finite-state data compression, finite-state prediction, entropy rates, and automatic Kolmogorov complexity. The 1972 Schnorr-Stimm dichotomy theorem gave the first automata-theoretic characterization of normal sequences, which had been studied in analytic number theory since Borel defined them in 1909. This theorem implies, in present-day terminology, that a sequence (or a real number having this sequence as its base-b expansion) is normal if and only if it has finite-state dimension 1. One of the most powerful classical tools for investigating normal numbers is the 1916 Weyl’s criterion, which characterizes normality in terms of exponential sums. Such sums are well studied objects with many connections to other aspects of analytic number theory, and this has made use of Weyl’s criterion especially fruitful. This raises the question whether Weyl’s criterion can be generalized from finite-state dimension 1 to arbitrary finite-state dimensions, thereby making it a quantitative tool for studying data compression, prediction, etc. i.e., Can we characterize all compression ratios using exponential sums?. This paper does exactly this. We extend Weyl’s criterion from a characterization of sequences with finite-state dimension 1 to a criterion that characterizes every finite-state dimension. This turns out not to be a routine generalization of the original Weyl criterion. Even though exponential sums may diverge for non-normal numbers, finite-state dimension can be characterized in terms of the dimensions of the subsequence limits of the exponential sums. In case the exponential sums are convergent, they converge to the Fourier coefficients of a probability measure whose dimension is precisely the finite-state dimension of the sequence. This new and surprising connection helps us bring Fourier analytic techniques to bear in proofs in finite-state dimension, yielding a new perspective. We demonstrate the utility of our criterion by substantially improving known results about preservation of finite-state dimension under arithmetic. We strictly generalize the results by Aistleitner and Doty, Lutz and Nandakumar for finite-state dimensions under arithmetic operations. We use the method of exponential sums and our Weyl criterion to obtain the following new result: If y is a number having finite-state strong dimension 0, then dim_FS(x+qy) = dim_FS(x) and Dim_FS(x+qy) = Dim_FS(x) for any x ∈ ℝ and q ∈ ℚ. This generalization uses recent estimates obtained in the work of Hochman [Hochman, 2014] regarding the entropy of convolutions of probability measures.
Cite as

Jack H. Lutz, Satyadev Nandakumar, and Subin Pulari. A Weyl Criterion for Finite-State Dimension and Applications. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 65:1-65:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{lutz_et_al:LIPIcs.MFCS.2023.65,
  author =	{Lutz, Jack H. and Nandakumar, Satyadev and Pulari, Subin},
  title =	{{A Weyl Criterion for Finite-State Dimension and Applications}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{65:1--65:16},
  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.2023.65},
  URN =		{urn:nbn:de:0030-drops-185997},
  doi =		{10.4230/LIPIcs.MFCS.2023.65},
  annote =	{Keywords: Finite-state dimension, Finite-state compression, Weyl’s criterion, Exponential sums, Normal numbers}
}
Document
Media Exposition
DOI: 10.4230/LIPIcs.SoCG.2023.62
Godzilla Onions: A Skit and Applet to Explain Euclidean Half-Plane Fractional Cascading (Media Exposition)

Authors: Richard Berger, Vincent Ha, David Kratz, Michael Lin, Jeremy Moyer, and Christopher J. Tralie

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

Abstract
We provide a skit and an applet to illustrate fractional cascading in the context of half-plane range search for points in the Euclidean plane, which takes O(log N + h) output-sensitive time. In the video, a group of news anchors struggles to find the correct data structure to efficiently send out an early warning to the residents of Philadelphia who will be overtaken by a marching line of Godzillas. After exploring several options, the group eventually settles on onions and fractional cascading, only to discover that they themselves are in the line of fire! In the applet, we show step by step details of preprocessing to build the onions with fractional cascading and the subsequent query of the "Godzilla line" against the onion layers. Our video skit and applet can be found at https://ctralie.github.io/GodzillaOnions/
Cite as

Richard Berger, Vincent Ha, David Kratz, Michael Lin, Jeremy Moyer, and Christopher J. Tralie. Godzilla Onions: A Skit and Applet to Explain Euclidean Half-Plane Fractional Cascading (Media Exposition). In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 62:1-62:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{berger_et_al:LIPIcs.SoCG.2023.62,
  author =	{Berger, Richard and Ha, Vincent and Kratz, David and Lin, Michael and Moyer, Jeremy and Tralie, Christopher J.},
  title =	{{Godzilla Onions: A Skit and Applet to Explain Euclidean Half-Plane Fractional Cascading}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{62:1--62:3},
  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.2023.62},
  URN =		{urn:nbn:de:0030-drops-179129},
  doi =		{10.4230/LIPIcs.SoCG.2023.62},
  annote =	{Keywords: convex hulls, onions, fractional cascading, visualization, d3}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.20
Epic Fail: Emulators Can Tolerate Polynomially Many Edge Faults for Free

Authors: Greg Bodwin, Michael Dinitz, and Yasamin Nazari

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

Abstract
A t-emulator of a graph G is a graph H that approximates its pairwise shortest path distances up to multiplicative t error. We study fault tolerant t-emulators, under the model recently introduced by Bodwin, Dinitz, and Nazari [ITCS 2022] for vertex failures. In this paper we consider the version for edge failures, and show that they exhibit surprisingly different behavior. In particular, our main result is that, for (2k-1)-emulators with k odd, we can tolerate a polynomial number of edge faults for free. For example: for any n-node input graph, we construct a 5-emulator (k = 3) on O(n^{4/3}) edges that is robust to f = O(n^{2/9}) edge faults. It is well known that Ω(n^{4/3}) edges are necessary even if the 5-emulator does not need to tolerate any faults. Thus we pay no extra cost in the size to gain this fault tolerance. We leave open the precise range of free fault tolerance for odd k, and whether a similar phenomenon can be proved for even k.
Cite as

Greg Bodwin, Michael Dinitz, and Yasamin Nazari. Epic Fail: Emulators Can Tolerate Polynomially Many Edge Faults for Free. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 20:1-20:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bodwin_et_al:LIPIcs.ITCS.2023.20,
  author =	{Bodwin, Greg and Dinitz, Michael and Nazari, Yasamin},
  title =	{{Epic Fail: Emulators Can Tolerate Polynomially Many Edge Faults for Free}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{20:1--20:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.20},
  URN =		{urn:nbn:de:0030-drops-175231},
  doi =		{10.4230/LIPIcs.ITCS.2023.20},
  annote =	{Keywords: Emulators, Fault Tolerance, Girth Conjecture}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.23
Graph Product Structure for h-Framed Graphs

Authors: Michael A. Bekos, Giordano Da Lozzo, Petr Hliněný, and Michael Kaufmann

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

Abstract
Graph product structure theory expresses certain graphs as subgraphs of the strong product of much simpler graphs. In particular, an elegant formulation for the corresponding structural theorems involves the strong product of a path and of a bounded treewidth graph, and allows to lift combinatorial results for bounded treewidth graphs to graph classes for which the product structure holds, such as to planar graphs [Dujmović et al., J. ACM, 67(4), 22:1-38, 2020]. In this paper, we join the search for extensions of this powerful tool beyond planarity by considering the h-framed graphs, a graph class that includes 1-planar, optimal 2-planar, and k-map graphs (for appropriate values of h). We establish a graph product structure theorem for h-framed graphs stating that the graphs in this class are subgraphs of the strong product of a path, of a planar graph of treewidth at most 3, and of a clique of size 3⌊ h/2 ⌋+⌊ h/3 ⌋-1. This allows us to improve over the previous structural theorems for 1-planar and k-map graphs. Our results constitute significant progress over the previous bounds on the queue number, non-repetitive chromatic number, and p-centered chromatic number of these graph classes, e.g., we lower the currently best upper bound on the queue number of 1-planar graphs and k-map graphs from 115 to 82 and from ⌊ 33/2(k+3 ⌊ k/2⌋ -3)⌋ to ⌊ 33/2 (3⌊ k/2 ⌋+⌊ k/3 ⌋-1) ⌋, respectively. We also employ the product structure machinery to improve the current upper bounds on the twin-width of 1-planar graphs from O(1) to 80. All our structural results are constructive and yield efficient algorithms to obtain the corresponding decompositions.
Cite as

Michael A. Bekos, Giordano Da Lozzo, Petr Hliněný, and Michael Kaufmann. Graph Product Structure for h-Framed Graphs. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 23:1-23:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bekos_et_al:LIPIcs.ISAAC.2022.23,
  author =	{Bekos, Michael A. and Da Lozzo, Giordano and Hlin\v{e}n\'{y}, Petr and Kaufmann, Michael},
  title =	{{Graph Product Structure for h-Framed Graphs}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{23:1--23:15},
  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.2022.23},
  URN =		{urn:nbn:de:0030-drops-173086},
  doi =		{10.4230/LIPIcs.ISAAC.2022.23},
  annote =	{Keywords: Graph product structure theory, h-framed graphs, k-map graphs, queue number, twin-width}
}
Document
Short Paper
DOI: 10.4230/LIPIcs.COSIT.2022.25
Collaborative Wayfinding Under Distributed Spatial Knowledge (Short Paper)

Authors: Panagiotis Mavros, Saskia Kuliga, Ed Manley, Hilal Rohaidi Fitri, Michael Joos, and Christoph Hölscher

Published in: LIPIcs, Volume 240, 15th International Conference on Spatial Information Theory (COSIT 2022)

Abstract
In many everyday situations, two or more people navigate collaboratively but their spatial knowledge does not necessarily overlap. However, most research to date, has investigated social wayfinding under either 1-sided or fully shared spatial information. Here, we present the pilot experiment of a novel, computerised, non-verbal experimental paradigm to study collaborative wayfinding under the face of spatial information uncertainty. Participants (N=32) learned two different neighbourhoods individually, and then navigated together as dyads (D=16), from one neighbourhood to the other. Our pilot results reveal that overall participants share navigational control, but are in control more when the task leads them to a familiar destination. We discuss the effects of spatial ability and motivation to lead, as well as the outlook of the paradigm.
Cite as

Panagiotis Mavros, Saskia Kuliga, Ed Manley, Hilal Rohaidi Fitri, Michael Joos, and Christoph Hölscher. Collaborative Wayfinding Under Distributed Spatial Knowledge (Short Paper). In 15th International Conference on Spatial Information Theory (COSIT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 240, pp. 25:1-25:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{mavros_et_al:LIPIcs.COSIT.2022.25,
  author =	{Mavros, Panagiotis and Kuliga, Saskia and Manley, Ed and Fitri, Hilal Rohaidi and Joos, Michael and H\"{o}lscher, Christoph},
  title =	{{Collaborative Wayfinding Under Distributed Spatial Knowledge}},
  booktitle =	{15th International Conference on Spatial Information Theory (COSIT 2022)},
  pages =	{25:1--25:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-257-0},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{240},
  editor =	{Ishikawa, Toru and Fabrikant, Sara Irina and Winter, Stephan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.COSIT.2022.25},
  URN =		{urn:nbn:de:0030-drops-169105},
  doi =		{10.4230/LIPIcs.COSIT.2022.25},
  annote =	{Keywords: navigation, wayfinding, collaboration, dyad, online}
}
Document
DOI: 10.4230/LIPIcs.SAT.2022.27
Migrating Solver State

Authors: Armin Biere, Md Solimul Chowdhury, Marijn J. H. Heule, Benjamin Kiesl, and Michael W. Whalen

Published in: LIPIcs, Volume 236, 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)

Abstract
We present approaches to store and restore the state of a SAT solver, allowing us to migrate the state between different compute resources, or even between different solvers. This can be used in many ways, e.g., to improve the fault tolerance of solvers, to schedule SAT problems on a restricted number of cores, or to use dedicated preprocessing tools for inprocessing. We identify a minimum viable subset of the solver state to migrate such that the loss of performance is small. We then present and implement two different approaches to state migration: one approach stores the state at the end of a solver run whereas the other approach stores the state continuously as part of the proof trace. We show that our approaches enable the generation of correct models and valid unsatisfiability proofs. Experimental results confirm that the overhead is reasonable and that in several cases solver performance actually improves.
Cite as

Armin Biere, Md Solimul Chowdhury, Marijn J. H. Heule, Benjamin Kiesl, and Michael W. Whalen. Migrating Solver State. In 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 236, pp. 27:1-27:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{biere_et_al:LIPIcs.SAT.2022.27,
  author =	{Biere, Armin and Chowdhury, Md Solimul and Heule, Marijn J. H. and Kiesl, Benjamin and Whalen, Michael W.},
  title =	{{Migrating Solver State}},
  booktitle =	{25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)},
  pages =	{27:1--27:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-242-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{236},
  editor =	{Meel, Kuldeep S. and Strichman, Ofer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2022.27},
  URN =		{urn:nbn:de:0030-drops-167015},
  doi =		{10.4230/LIPIcs.SAT.2022.27},
  annote =	{Keywords: SAT, SMT, Cloud Computing, Serverless Computing}
}
Document
DOI: 10.4230/OASIcs.WCET.2022.2
LLVMTA: An LLVM-Based WCET Analysis Tool

Authors: Sebastian Hahn, Michael Jacobs, Nils Hölscher, Kuan-Hsun Chen, Jian-Jia Chen, and Jan Reineke

Published in: OASIcs, Volume 103, 20th International Workshop on Worst-Case Execution Time Analysis (WCET 2022)

Abstract
We present llvmta, an academic WCET analysis tool based on the LLVM compiler infrastructure. It aims to enable the evaluation of novel WCET analysis approaches in a state-of-the-art analysis framework without dealing with the complexity of modeling real-world hardware architectures. We discuss the main design decisions and interfaces that allow to implement new analysis approaches. Finally, we highlight various existing research projects whose evaluation has been enabled by llvmta.
Cite as

Sebastian Hahn, Michael Jacobs, Nils Hölscher, Kuan-Hsun Chen, Jian-Jia Chen, and Jan Reineke. LLVMTA: An LLVM-Based WCET Analysis Tool. In 20th International Workshop on Worst-Case Execution Time Analysis (WCET 2022). Open Access Series in Informatics (OASIcs), Volume 103, pp. 2:1-2:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{hahn_et_al:OASIcs.WCET.2022.2,
  author =	{Hahn, Sebastian and Jacobs, Michael and H\"{o}lscher, Nils and Chen, Kuan-Hsun and Chen, Jian-Jia and Reineke, Jan},
  title =	{{LLVMTA: An LLVM-Based WCET Analysis Tool}},
  booktitle =	{20th International Workshop on Worst-Case Execution Time Analysis (WCET 2022)},
  pages =	{2:1--2:17},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-244-0},
  ISSN =	{2190-6807},
  year =	{2022},
  volume =	{103},
  editor =	{Ballabriga, Cl\'{e}ment},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.WCET.2022.2},
  URN =		{urn:nbn:de:0030-drops-166242},
  doi =		{10.4230/OASIcs.WCET.2022.2},
  annote =	{Keywords: WCET analysis, low-level analysis, LLVM}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.86
Near-Optimal Decremental Hopsets with Applications

Authors: Jakub Łącki and Yasamin Nazari

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

Abstract
Given a weighted undirected graph G = (V,E,w), a hopset H of hopbound β and stretch (1+ε) is a set of edges such that for any pair of nodes u, v ∈ V, there is a path in G ∪ H of at most β hops, whose length is within a (1+ε) factor from the distance between u and v in G. We show the first efficient decremental algorithm for maintaining hopsets with a polylogarithmic hopbound. The update time of our algorithm matches the best known static algorithm up to polylogarithmic factors. All the previous decremental hopset constructions had a superpolylogarithmic (but subpolynomial) hopbound of 2^{log^{Ω(1)} n} [Bernstein, FOCS'09; HKN, FOCS'14; Chechik, FOCS'18]. By applying our decremental hopset construction, we get improved or near optimal bounds for several distance problems. Most importantly, we show how to decrementally maintain (2k-1)(1+ε)-approximate all-pairs shortest paths (for any constant k ≥ 2), in Õ(n^{1/k}) amortized update time and O(k) query time. This improves (by a polynomial factor) over the update-time of the best previously known decremental algorithm in the constant query time regime. Moreover, it improves over the result of [Chechik, FOCS'18] that has a query time of O(log log(nW)), where W is the aspect ratio, and the amortized update time is n^{1/k}⋅(1/ε)^{Õ(√{log n})}). For sparse graphs our construction nearly matches the best known static running time / query time tradeoff. We also obtain near-optimal bounds for maintaining approximate multi-source shortest paths and distance sketches, and get improved bounds for approximate single-source shortest paths. Our algorithms are randomized and our bounds hold with high probability against an oblivious adversary.
Cite as

Jakub Łącki and Yasamin Nazari. Near-Optimal Decremental Hopsets with Applications. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 86:1-86:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{lacki_et_al:LIPIcs.ICALP.2022.86,
  author =	{{\L}\k{a}cki, Jakub and Nazari, Yasamin},
  title =	{{Near-Optimal Decremental Hopsets with Applications}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{86:1--86:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.86},
  URN =		{urn:nbn:de:0030-drops-164277},
  doi =		{10.4230/LIPIcs.ICALP.2022.86},
  annote =	{Keywords: Dynamic Algorithms, Data Structures, Shortest Paths, Hopsets}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2022.9
Tighter Bounds for Reconstruction from ε-Samples

Authors: Håvard Bakke Bjerkevik

Published in: LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022)

Abstract
We show that reconstructing a curve in ℝ^d for d ≥ 2 from a 0.66-sample is always possible using an algorithm similar to the classical NN-Crust algorithm. Previously, this was only known to be possible for 0.47-samples in ℝ² and 1/3-samples in ℝ^d for d ≥ 3. In addition, we show that there is not always a unique way to reconstruct a curve from a 0.72-sample; this was previously only known for 1-samples. We also extend this non-uniqueness result to hypersurfaces in all higher dimensions.
Cite as

Håvard Bakke Bjerkevik. Tighter Bounds for Reconstruction from ε-Samples. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bakkebjerkevik:LIPIcs.SoCG.2022.9,
  author =	{Bakke Bjerkevik, H\r{a}vard},
  title =	{{Tighter Bounds for Reconstruction from \epsilon-Samples}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{9:1--9:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.9},
  URN =		{urn:nbn:de:0030-drops-160170},
  doi =		{10.4230/LIPIcs.SoCG.2022.9},
  annote =	{Keywords: Curve reconstruction, surface reconstruction, \epsilon-sampling}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2022.10
Erdős-Szekeres-Type Problems in the Real Projective Plane

Authors: Martin Balko, Manfred Scheucher, and Pavel Valtr

Published in: LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022)

Abstract
We consider point sets in the real projective plane ℝ𝒫² and explore variants of classical extremal problems about planar point sets in this setting, with a main focus on Erdős-Szekeres-type problems. We provide asymptotically tight bounds for a variant of the Erdős-Szekeres theorem about point sets in convex position in ℝ𝒫², which was initiated by Harborth and Möller in 1994. The notion of convex position in ℝ𝒫² agrees with the definition of convex sets introduced by Steinitz in 1913. For k ≥ 3, an (affine) k-hole in a finite set S ⊆ ℝ² is a set of k points from S in convex position with no point of S in the interior of their convex hull. After introducing a new notion of k-holes for points sets from ℝ𝒫², called projective k-holes, we find arbitrarily large finite sets of points from ℝ𝒫² with no projective 8-holes, providing an analogue of a classical result by Horton from 1983. We also prove that they contain only quadratically many projective k-holes for k ≤ 7. On the other hand, we show that the number of k-holes can be substantially larger in ℝ𝒫² than in ℝ² by constructing, for every k ∈ {3,… ,6}, sets of n points from ℝ² ⊂ ℝ𝒫² with Ω(n^{3-3/5k}) projective k-holes and only O(n²) affine k-holes. Last but not least, we prove several other results, for example about projective holes in random point sets in ℝ𝒫² and about some algorithmic aspects. The study of extremal problems about point sets in ℝ𝒫² opens a new area of research, which we support by posing several open problems.
Cite as

Martin Balko, Manfred Scheucher, and Pavel Valtr. Erdős-Szekeres-Type Problems in the Real Projective Plane. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 10:1-10:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{balko_et_al:LIPIcs.SoCG.2022.10,
  author =	{Balko, Martin and Scheucher, Manfred and Valtr, Pavel},
  title =	{{Erd\H{o}s-Szekeres-Type Problems in the Real Projective Plane}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{10:1--10:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.10},
  URN =		{urn:nbn:de:0030-drops-160182},
  doi =		{10.4230/LIPIcs.SoCG.2022.10},
  annote =	{Keywords: real projective plane, point set, convex position, k-gon, k-hole, Erd\H{o}s-Szekeres theorem, Horton set, random point set}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2022.14
Quasi-Universality of Reeb Graph Distances

Authors: Ulrich Bauer, Håvard Bakke Bjerkevik, and Benedikt Fluhr

Published in: LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022)

Abstract
We establish bi-Lipschitz bounds certifying quasi-universality (universality up to a constant factor) for various distances between Reeb graphs: the interleaving distance, the functional distortion distance, and the functional contortion distance. The definition of the latter distance is a novel contribution, and for the special case of contour trees we also prove strict universality of this distance. Furthermore, we prove that for the special case of merge trees the functional contortion distance coincides with the interleaving distance, yielding universality of all four distances in this case.
Cite as

Ulrich Bauer, Håvard Bakke Bjerkevik, and Benedikt Fluhr. Quasi-Universality of Reeb Graph Distances. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bauer_et_al:LIPIcs.SoCG.2022.14,
  author =	{Bauer, Ulrich and Bjerkevik, H\r{a}vard Bakke and Fluhr, Benedikt},
  title =	{{Quasi-Universality of Reeb Graph Distances}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{14:1--14:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.14},
  URN =		{urn:nbn:de:0030-drops-160221},
  doi =		{10.4230/LIPIcs.SoCG.2022.14},
  annote =	{Keywords: Reeb graphs, contour trees, merge trees, distances, universality, interleaving distance, functional distortion distance, functional contortion distance}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2022.30
Hop-Spanners for Geometric Intersection Graphs

Authors: Jonathan B. Conroy and Csaba D. Tóth

Published in: LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022)

Abstract
A t-spanner of a graph G = (V,E) is a subgraph H = (V,E') that contains a uv-path of length at most t for every uv ∈ E. It is known that every n-vertex graph admits a (2k-1)-spanner with O(n^{1+1/k}) edges for k ≥ 1. This bound is the best possible for 1 ≤ k ≤ 9 and is conjectured to be optimal due to Erdős' girth conjecture. We study t-spanners for t ∈ {2,3} for geometric intersection graphs in the plane. These spanners are also known as t-hop spanners to emphasize the use of graph-theoretic distances (as opposed to Euclidean distances between the geometric objects or their centers). We obtain the following results: (1) Every n-vertex unit disk graph (UDG) admits a 2-hop spanner with O(n) edges; improving upon the previous bound of O(nlog n). (2) The intersection graph of n axis-aligned fat rectangles admits a 2-hop spanner with O(nlog n) edges, and this bound is the best possible. (3) The intersection graph of n fat convex bodies in the plane admits a 3-hop spanner with O(nlog n) edges. (4) The intersection graph of n axis-aligned rectangles admits a 3-hop spanner with O(nlog² n) edges.
Cite as

Jonathan B. Conroy and Csaba D. Tóth. Hop-Spanners for Geometric Intersection Graphs. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 30:1-30:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{conroy_et_al:LIPIcs.SoCG.2022.30,
  author =	{Conroy, Jonathan B. and T\'{o}th, Csaba D.},
  title =	{{Hop-Spanners for Geometric Intersection Graphs}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{30:1--30:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.30},
  URN =		{urn:nbn:de:0030-drops-160381},
  doi =		{10.4230/LIPIcs.SoCG.2022.30},
  annote =	{Keywords: geometric intersection graph, unit disk graph, hop-spanner}
}
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