95 Search Results for "Chen, Danny Z."

Volume

LIPIcs, Volume 164

36th International Symposium on Computational Geometry (SoCG 2020)

SoCG 2020, June 23-26, 2020, Zürich, Switzerland

Editors: Sergio Cabello and Danny Z. Chen

Document
DOI: 10.4230/LIPIcs.AFT.2024.15
Privacy Comparison for Bitcoin Light Client Implementations

Authors: Arad Kotzer and Ori Rottenstreich

Published in: LIPIcs, Volume 316, 6th Conference on Advances in Financial Technologies (AFT 2024)

Abstract
Light clients implement a simple solution for Bitcoin’s scalability problem, as they do not store the entire blockchain but only the state of particular addresses of interest. To be able to keep track of the updated state of their addresses, light clients rely on full nodes to provide them with the required information. To do so, they must reveal information about the addresses they are interested in. This paper studies the two most common light client implementations, SPV and Neutrino with regards to their privacy. We define privacy metrics for comparing the privacy of the different implementations. We evaluate and compare the privacy of the implementations over time on real Bitcoin data and discuss the inherent privacy-communication tradeoff. In addition, we propose general techniques to enhance light client privacy in the existing implementations. Finally, we propose a new SPV-based light client model, the aggregation model, evaluate it, and show it can achieve enhanced privacy than in the existing light client implementations.
Cite as

Arad Kotzer and Ori Rottenstreich. Privacy Comparison for Bitcoin Light Client Implementations. In 6th Conference on Advances in Financial Technologies (AFT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 316, pp. 15:1-15:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kotzer_et_al:LIPIcs.AFT.2024.15,
  author =	{Kotzer, Arad and Rottenstreich, Ori},
  title =	{{Privacy Comparison for Bitcoin Light Client Implementations}},
  booktitle =	{6th Conference on Advances in Financial Technologies (AFT 2024)},
  pages =	{15:1--15:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-345-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{316},
  editor =	{B\"{o}hme, Rainer and Kiffer, Lucianna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2024.15},
  URN =		{urn:nbn:de:0030-drops-209510},
  doi =		{10.4230/LIPIcs.AFT.2024.15},
  annote =	{Keywords: Blockchain, Privacy, Light Clients, Bloom filter}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2024.15
RobTL: Robustness Temporal Logic for CPS

Authors: Valentina Castiglioni, Michele Loreti, and Simone Tini

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
We propose Robustness Temporal Logic (RobTL), a novel temporal logic for the specification and analysis of distances between the behaviours of Cyber-Physical Systems (CPS) over a finite time horizon. RobTL specifications allow us to measure the differences in the behaviours of systems with respect to various objectives and temporal constraints, and to study how those differences evolve in time. Specifically, the unique features of RobTL allow us to specify robustness properties of CPS against uncertainty and perturbations. As an example, we use RobTL to analyse the robustness of an engine system that is subject to attacks aimed at inflicting overstress of equipment.
Cite as

Valentina Castiglioni, Michele Loreti, and Simone Tini. RobTL: Robustness Temporal Logic for CPS. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 15:1-15:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{castiglioni_et_al:LIPIcs.CONCUR.2024.15,
  author =	{Castiglioni, Valentina and Loreti, Michele and Tini, Simone},
  title =	{{RobTL: Robustness Temporal Logic for CPS}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{15:1--15:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2024.15},
  URN =		{urn:nbn:de:0030-drops-207870},
  doi =		{10.4230/LIPIcs.CONCUR.2024.15},
  annote =	{Keywords: Cyber-physical systems, robustness, temporal logic, uncertainty}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.26
Capturing the Shape of a Point Set with a Line Segment

Authors: Nathan van Beusekom, Marc van Kreveld, Max van Mulken, Marcel Roeloffzen, Bettina Speckmann, and Jules Wulms

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
Detecting location-correlated groups in point sets is an important task in a wide variety of applications areas. In addition to merely detecting such groups, the group’s shape carries meaning as well. In this paper, we represent a group’s shape using a simple geometric object, a line segment. Specifically, given a radius r, we say a line segment is representative of a point set P of n points if it is within distance r of each point p ∈ P. We aim to find the shortest such line segment. This problem is equivalent to stabbing a set of circles of radius r using the shortest line segment. We describe an algorithm to find the shortest representative segment in O(n log h + h log³h) time, where h is the size of the convex hull of P. Additionally, we show how to maintain a stable approximation of the shortest representative segment when the points in P move.
Cite as

Nathan van Beusekom, Marc van Kreveld, Max van Mulken, Marcel Roeloffzen, Bettina Speckmann, and Jules Wulms. Capturing the Shape of a Point Set with a Line Segment. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 26:1-26:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{vanbeusekom_et_al:LIPIcs.MFCS.2024.26,
  author =	{van Beusekom, Nathan and van Kreveld, Marc and van Mulken, Max and Roeloffzen, Marcel and Speckmann, Bettina and Wulms, Jules},
  title =	{{Capturing the Shape of a Point Set with a Line Segment}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{26:1--26:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.26},
  URN =		{urn:nbn:de:0030-drops-205820},
  doi =		{10.4230/LIPIcs.MFCS.2024.26},
  annote =	{Keywords: Shape descriptor, Stabbing, Rotating calipers}
}
Document
DOI: 10.4230/LIPIcs.SEA.2024.5
Buffered Streaming Edge Partitioning

Authors: Adil Chhabra, Marcelo Fonseca Faraj, Christian Schulz, and Daniel Seemaier

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
Addressing the challenges of processing massive graphs, which are prevalent in diverse fields such as social, biological, and technical networks, we introduce HeiStreamE and FreightE, two innovative (buffered) streaming algorithms designed for efficient edge partitioning of large-scale graphs. HeiStreamE utilizes an adapted Split-and-Connect graph model and a Fennel-based multilevel partitioning scheme, while FreightE partitions a hypergraph representation of the input graph. Besides ensuring superior solution quality, these approaches also overcome the limitations of existing algorithms by maintaining linear dependency on the graph size in both time and memory complexity with no dependence on the number of blocks of partition. Our comprehensive experimental analysis demonstrates that HeiStreamE outperforms current streaming algorithms and the re-streaming algorithm 2PS in partitioning quality (replication factor), and is more memory-efficient for real-world networks where the number of edges is far greater than the number of vertices. Further, FreightE is shown to produce fast and efficient partitions, particularly for higher numbers of partition blocks.
Cite as

Adil Chhabra, Marcelo Fonseca Faraj, Christian Schulz, and Daniel Seemaier. Buffered Streaming Edge Partitioning. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 5:1-5:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chhabra_et_al:LIPIcs.SEA.2024.5,
  author =	{Chhabra, Adil and Fonseca Faraj, Marcelo and Schulz, Christian and Seemaier, Daniel},
  title =	{{Buffered Streaming Edge Partitioning}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{5:1--5:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.5},
  URN =		{urn:nbn:de:0030-drops-203701},
  doi =		{10.4230/LIPIcs.SEA.2024.5},
  annote =	{Keywords: graph partitioning, edge partitioning, streaming, online, buffered partitioning}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.34
Fundamental Problems on Bounded-Treewidth Graphs: The Real Source of Hardness

Authors: Barış Can Esmer, Jacob Focke, Dániel Marx, and Paweł Rzążewski

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
It is known for many algorithmic problems that if a tree decomposition of width t is given in the input, then the problem can be solved with exponential dependence on t. A line of research initiated by Lokshtanov, Marx, and Saurabh [SODA 2011] produced lower bounds showing that in many cases known algorithms already achieve the best possible exponential dependence on t, assuming the Strong Exponential-Time Hypothesis (SETH). The main message of this paper is showing that the same lower bounds can already be obtained in a much more restricted setting: informally, a graph consisting of a block of t vertices connected to components of constant size already has the same hardness as a general tree decomposition of width t. Formally, a (σ,δ)-hub is a set Q of vertices such that every component of Q has size at most σ and is adjacent to at most δ vertices of Q. We explore if the known tight lower bounds parameterized by the width of the given tree decomposition remain valid if we parameterize by the size of the given hub. - For every ε > 0, there are σ,δ > 0 such that Independent Set (equivalently Vertex Cover) cannot be solved in time (2-ε)^p⋅ n, even if a (σ, δ)-hub of size p is given in the input, assuming the SETH. This matches the earlier tight lower bounds parameterized by width of the tree decomposition. Similar tight bounds are obtained for Odd Cycle Transversal, Max Cut, q-Coloring, and edge/vertex deletions versions of q-Coloring. - For every ε > 0, there are σ,δ > 0 such that △-Partition cannot be solved in time (2-ε)^p ⋅ n, even if a (σ, δ)-hub of size p is given in the input, assuming the Set Cover Conjecture (SCC). In fact, we prove that this statement is equivalent to the SCC, thus it is unlikely that this could be proved assuming the SETH. - For Dominating Set, we can prove a non-tight lower bound ruling out (2-ε)^p ⋅ n^𝒪(1) algorithms, assuming either the SETH or the SCC, but this does not match the 3^p⋅ n^{𝒪(1)} upper bound. Thus our results reveal that, for many problems, the research on lower bounds on the dependence on tree width was never really about tree decompositions, but the real source of hardness comes from a much simpler structure. Additionally, we study if the same lower bounds can be obtained if σ and δ are fixed universal constants (not depending on ε). We show that lower bounds of this form are possible for Max Cut and the edge-deletion version of q-Coloring, under the Max 3-Sat Hypothesis (M3SH). However, no such lower bounds are possible for Independent Set, Odd Cycle Transversal, and the vertex-deletion version of q-Coloring: better than brute force algorithms are possible for every fixed (σ,δ).
Cite as

Barış Can Esmer, Jacob Focke, Dániel Marx, and Paweł Rzążewski. Fundamental Problems on Bounded-Treewidth Graphs: The Real Source of Hardness. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 34:1-34:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{canesmer_et_al:LIPIcs.ICALP.2024.34,
  author =	{Can Esmer, Bar{\i}\c{s} and Focke, Jacob and Marx, D\'{a}niel and Rz\k{a}\.{z}ewski, Pawe{\l}},
  title =	{{Fundamental Problems on Bounded-Treewidth Graphs: The Real Source of Hardness}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{34:1--34:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.34},
  URN =		{urn:nbn:de:0030-drops-201772},
  doi =		{10.4230/LIPIcs.ICALP.2024.34},
  annote =	{Keywords: Parameterized Complexity, Tight Bounds, Hub, Treewidth, Strong Exponential Time Hypothesis, Vertex Coloring, Vertex Deletion, Edge Deletion, Triangle Packing, Triangle Partition, Set Cover Hypothesis, Dominating Set}
}
Document
Position
DOI: 10.4230/TGDK.2.1.5
Standardizing Knowledge Engineering Practices with a Reference Architecture

Authors: Bradley P. Allen and Filip Ilievski

Published in: TGDK, Volume 2, Issue 1 (2024): Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge, Volume 2, Issue 1

Abstract
Knowledge engineering is the process of creating and maintaining knowledge-producing systems. Throughout the history of computer science and AI, knowledge engineering workflows have been widely used given the importance of high-quality knowledge for reliable intelligent agents. Meanwhile, the scope of knowledge engineering, as apparent from its target tasks and use cases, has been shifting, together with its paradigms such as expert systems, semantic web, and language modeling. The intended use cases and supported user requirements between these paradigms have not been analyzed globally, as new paradigms often satisfy prior pain points while possibly introducing new ones. The recent abstraction of systemic patterns into a boxology provides an opening for aligning the requirements and use cases of knowledge engineering with the systems, components, and software that can satisfy them best, however, this direction has not been explored to date. This paper proposes a vision of harmonizing the best practices in the field of knowledge engineering by leveraging the software engineering methodology of creating reference architectures. We describe how a reference architecture can be iteratively designed and implemented to associate user needs with recurring systemic patterns, building on top of existing knowledge engineering workflows and boxologies. We provide a six-step roadmap that can enable the development of such an architecture, consisting of scope definition, selection of information sources, architectural analysis, synthesis of an architecture based on the information source analysis, evaluation through instantiation, and, ultimately, instantiation into a concrete software architecture. We provide an initial design and outcome of the definition of architectural scope, selection of information sources, and analysis. As the remaining steps of design, evaluation, and instantiation of the architecture are largely use-case specific, we provide a detailed description of their procedures and point to relevant examples. We expect that following through on this vision will lead to well-grounded reference architectures for knowledge engineering, will advance the ongoing initiatives of organizing the neurosymbolic knowledge engineering space, and will build new links to the software architectures and data science communities.
Cite as

Bradley P. Allen and Filip Ilievski. Standardizing Knowledge Engineering Practices with a Reference Architecture. In Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge (TGDK), Volume 2, Issue 1, pp. 5:1-5:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{allen_et_al:TGDK.2.1.5,
  author =	{Allen, Bradley P. and Ilievski, Filip},
  title =	{{Standardizing Knowledge Engineering Practices with a Reference Architecture}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{5:1--5:23},
  ISSN =	{2942-7517},
  year =	{2024},
  volume =	{2},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.2.1.5},
  URN =		{urn:nbn:de:0030-drops-198623},
  doi =		{10.4230/TGDK.2.1.5},
  annote =	{Keywords: knowledge engineering, knowledge graphs, quality attributes, software architectures, sociotechnical systems}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.SoCG.2020
LIPIcs, Volume 164, SoCG 2020, Complete Volume

Authors: Sergio Cabello and Danny Z. Chen

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)

Abstract
LIPIcs, Volume 164, SoCG 2020, Complete Volume
Cite as

36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 1-1222, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@Proceedings{cabello_et_al:LIPIcs.SoCG.2020,
  title =	{{LIPIcs, Volume 164, SoCG 2020, Complete Volume}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{1--1222},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020},
  URN =		{urn:nbn:de:0030-drops-121576},
  doi =		{10.4230/LIPIcs.SoCG.2020},
  annote =	{Keywords: LIPIcs, Volume 164, SoCG 2020, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.SoCG.2020.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Sergio Cabello and Danny Z. Chen

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 0:i-0:xx, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{cabello_et_al:LIPIcs.SoCG.2020.0,
  author =	{Cabello, Sergio and Chen, Danny Z.},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{0:i--0:xx},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.0},
  URN =		{urn:nbn:de:0030-drops-121587},
  doi =		{10.4230/LIPIcs.SoCG.2020.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2020.1
An Almost Optimal Bound on the Number of Intersections of Two Simple Polygons

Authors: Eyal Ackerman, Balázs Keszegh, and Günter Rote

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)

Abstract
What is the maximum number of intersections of the boundaries of a simple m-gon and a simple n-gon, assuming general position? This is a basic question in combinatorial geometry, and the answer is easy if at least one of m and n is even. If both m and n are odd, the best known construction has mn-(m+n)+3 intersections, and it is conjectured that this is the maximum. However, the best known upper bound is only mn-(m + ⌈ n/6 ⌉), for m ≥ n. We prove a new upper bound of mn-(m+n)+C for some constant C, which is optimal apart from the value of C.
Cite as

Eyal Ackerman, Balázs Keszegh, and Günter Rote. An Almost Optimal Bound on the Number of Intersections of Two Simple Polygons. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 1:1-1:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{ackerman_et_al:LIPIcs.SoCG.2020.1,
  author =	{Ackerman, Eyal and Keszegh, Bal\'{a}zs and Rote, G\"{u}nter},
  title =	{{An Almost Optimal Bound on the Number of Intersections of Two Simple Polygons}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{1:1--1:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.1},
  URN =		{urn:nbn:de:0030-drops-121591},
  doi =		{10.4230/LIPIcs.SoCG.2020.1},
  annote =	{Keywords: Simple polygon, Ramsey theory, combinatorial geometry}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2020.2
Dynamic Geometric Set Cover and Hitting Set

Authors: Pankaj K. Agarwal, Hsien-Chih Chang, Subhash Suri, Allen Xiao, and Jie Xue

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)

Abstract
We investigate dynamic versions of geometric set cover and hitting set where points and ranges may be inserted or deleted, and we want to efficiently maintain an (approximately) optimal solution for the current problem instance. While their static versions have been extensively studied in the past, surprisingly little is known about dynamic geometric set cover and hitting set. For instance, even for the most basic case of one-dimensional interval set cover and hitting set, no nontrivial results were known. The main contribution of our paper are two frameworks that lead to efficient data structures for dynamically maintaining set covers and hitting sets in ℝ¹ and ℝ². The first framework uses bootstrapping and gives a (1+ε)-approximate data structure for dynamic interval set cover in ℝ¹ with O(n^α/ε) amortized update time for any constant α > 0; in ℝ², this method gives O(1)-approximate data structures for unit-square (and quadrant) set cover and hitting set with O(n^(1/2+α)) amortized update time. The second framework uses local modification, and leads to a (1+ε)-approximate data structure for dynamic interval hitting set in ℝ¹ with Õ(1/ε) amortized update time; in ℝ², it gives O(1)-approximate data structures for unit-square (and quadrant) set cover and hitting set in the partially dynamic settings with Õ(1) amortized update time.
Cite as

Pankaj K. Agarwal, Hsien-Chih Chang, Subhash Suri, Allen Xiao, and Jie Xue. Dynamic Geometric Set Cover and Hitting Set. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 2:1-2:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{agarwal_et_al:LIPIcs.SoCG.2020.2,
  author =	{Agarwal, Pankaj K. and Chang, Hsien-Chih and Suri, Subhash and Xiao, Allen and Xue, Jie},
  title =	{{Dynamic Geometric Set Cover and Hitting Set}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{2:1--2:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.2},
  URN =		{urn:nbn:de:0030-drops-121604},
  doi =		{10.4230/LIPIcs.SoCG.2020.2},
  annote =	{Keywords: Geometric set cover, Geometric hitting set, Dynamic data structures}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2020.3
The Parameterized Complexity of Guarding Almost Convex Polygons

Authors: Akanksha Agrawal, Kristine V. K. Knudsen, Daniel Lokshtanov, Saket Saurabh, and Meirav Zehavi

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)

Abstract
The Art Gallery problem is a fundamental visibility problem in Computational Geometry. The input consists of a simple polygon P, (possibly infinite) sets G and C of points within P, and an integer k; the task is to decide if at most k guards can be placed on points in G so that every point in C is visible to at least one guard. In the classic formulation of Art Gallery, G and C consist of all the points within P. Other well-known variants restrict G and C to consist either of all the points on the boundary of P or of all the vertices of P. Recently, three new important discoveries were made: the above mentioned variants of Art Gallery are all W[1]-hard with respect to k [Bonnet and Miltzow, ESA'16], the classic variant has an O(log k)-approximation algorithm [Bonnet and Miltzow, SoCG'17], and it may require irrational guards [Abrahamsen et al., SoCG'17]. Building upon the third result, the classic variant and the case where G consists only of all the points on the boundary of P were both shown to be ∃ℝ-complete [Abrahamsen et al., STOC'18]. Even when both G and C consist only of all the points on the boundary of P, the problem is not known to be in NP. Given the first discovery, the following question was posed by Giannopoulos [Lorentz Center Workshop, 2016]: Is Art Gallery FPT with respect to r, the number of reflex vertices? In light of the developments above, we focus on the variant where G and C consist of all the vertices of P, called Vertex-Vertex Art Gallery. Apart from being a variant of Art Gallery, this case can also be viewed as the classic Dominating Set problem in the visibility graph of a polygon. In this article, we show that the answer to the question by Giannopoulos is positive: Vertex-Vertex Art Gallery is solvable in time r^O(r²)n^O(1). Furthermore, our approach extends to assert that Vertex-Boundary Art Gallery and Boundary-Vertex Art Gallery are both FPT as well. To this end, we utilize structural properties of "almost convex polygons" to present a two-stage reduction from Vertex-Vertex Art Gallery to a new constraint satisfaction problem (whose solution is also provided in this paper) where constraints have arity 2 and involve monotone functions.
Cite as

Akanksha Agrawal, Kristine V. K. Knudsen, Daniel Lokshtanov, Saket Saurabh, and Meirav Zehavi. The Parameterized Complexity of Guarding Almost Convex Polygons. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 3:1-3:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{agrawal_et_al:LIPIcs.SoCG.2020.3,
  author =	{Agrawal, Akanksha and Knudsen, Kristine V. K. and Lokshtanov, Daniel and Saurabh, Saket and Zehavi, Meirav},
  title =	{{The Parameterized Complexity of Guarding Almost Convex Polygons}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{3:1--3:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.3},
  URN =		{urn:nbn:de:0030-drops-121614},
  doi =		{10.4230/LIPIcs.SoCG.2020.3},
  annote =	{Keywords: Art Gallery, Reflex vertices, Monotone 2-CSP, Parameterized Complexity, Fixed Parameter Tractability}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2020.4
Euclidean TSP in Narrow Strips

Authors: Henk Alkema, Mark de Berg, and Sándor Kisfaludi-Bak

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)

Abstract
We investigate how the complexity of {Euclidean TSP} for point sets P inside the strip (-∞,+∞)×[0,δ] depends on the strip width δ. We obtain two main results. - For the case where the points have distinct integer x-coordinates, we prove that a shortest bitonic tour (which can be computed in O(n log²n) time using an existing algorithm) is guaranteed to be a shortest tour overall when δ ⩽ 2√2, a bound which is best possible. - We present an algorithm that is fixed-parameter tractable with respect to δ. More precisely, our algorithm has running time 2^{O(√δ)} n² for sparse point sets, where each 1×δ rectangle inside the strip contains O(1) points. For random point sets, where the points are chosen uniformly at random from the rectangle [0,n]× [0,δ], it has an expected running time of 2^{O(√δ)} n² + O(n³).
Cite as

Henk Alkema, Mark de Berg, and Sándor Kisfaludi-Bak. Euclidean TSP in Narrow Strips. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 4:1-4:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{alkema_et_al:LIPIcs.SoCG.2020.4,
  author =	{Alkema, Henk and de Berg, Mark and Kisfaludi-Bak, S\'{a}ndor},
  title =	{{Euclidean TSP in Narrow Strips}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{4:1--4:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.4},
  URN =		{urn:nbn:de:0030-drops-121628},
  doi =		{10.4230/LIPIcs.SoCG.2020.4},
  annote =	{Keywords: Computational geometry, Euclidean TSP, bitonic TSP, fixed-parameter tractable algorithms}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2020.5
The ε-t-Net Problem

Authors: Noga Alon, Bruno Jartoux, Chaya Keller, Shakhar Smorodinsky, and Yelena Yuditsky

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)

Abstract
We study a natural generalization of the classical ε-net problem (Haussler - Welzl 1987), which we call the ε-t-net problem: Given a hypergraph on n vertices and parameters t and ε ≥ t/n, find a minimum-sized family S of t-element subsets of vertices such that each hyperedge of size at least ε n contains a set in S. When t=1, this corresponds to the ε-net problem. We prove that any sufficiently large hypergraph with VC-dimension d admits an ε-t-net of size O((1+log t)d/ε log 1/ε). For some families of geometrically-defined hypergraphs (such as the dual hypergraph of regions with linear union complexity), we prove the existence of O(1/ε)-sized ε-t-nets. We also present an explicit construction of ε-t-nets (including ε-nets) for hypergraphs with bounded VC-dimension. In comparison to previous constructions for the special case of ε-nets (i.e., for t=1), it does not rely on advanced derandomization techniques. To this end we introduce a variant of the notion of VC-dimension which is of independent interest.
Cite as

Noga Alon, Bruno Jartoux, Chaya Keller, Shakhar Smorodinsky, and Yelena Yuditsky. The ε-t-Net Problem. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 5:1-5:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{alon_et_al:LIPIcs.SoCG.2020.5,
  author =	{Alon, Noga and Jartoux, Bruno and Keller, Chaya and Smorodinsky, Shakhar and Yuditsky, Yelena},
  title =	{{The \epsilon-t-Net Problem}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{5:1--5:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.5},
  URN =		{urn:nbn:de:0030-drops-121639},
  doi =		{10.4230/LIPIcs.SoCG.2020.5},
  annote =	{Keywords: epsilon-nets, geometric hypergraphs, VC-dimension, linear union complexity}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2020.6
Terrain Visibility Graphs: Persistence Is Not Enough

Authors: Safwa Ameer, Matt Gibson-Lopez, Erik Krohn, Sean Soderman, and Qing Wang

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)

Abstract
In this paper, we consider the Visibility Graph Recognition and Reconstruction problems in the context of terrains. Here, we are given a graph G with labeled vertices v₀, v₁, …, v_{n-1} such that the labeling corresponds with a Hamiltonian path H. G also may contain other edges. We are interested in determining if there is a terrain T with vertices p₀, p₁, …, p_{n-1} such that G is the visibility graph of T and the boundary of T corresponds with H. G is said to be persistent if and only if it satisfies the so-called X-property and Bar-property. It is known that every "pseudo-terrain" has a persistent visibility graph and that every persistent graph is the visibility graph for some pseudo-terrain. The connection is not as clear for (geometric) terrains. It is known that the visibility graph of any terrain T is persistent, but it has been unclear whether every persistent graph G has a terrain T such that G is the visibility graph of T. There actually have been several papers that claim this to be the case (although no formal proof has ever been published), and recent works made steps towards building a terrain reconstruction algorithm for any persistent graph. In this paper, we show that there exists a persistent graph G that is not the visibility graph for any terrain T. This means persistence is not enough by itself to characterize the visibility graphs of terrains, and implies that pseudo-terrains are not stretchable.
Cite as

Safwa Ameer, Matt Gibson-Lopez, Erik Krohn, Sean Soderman, and Qing Wang. Terrain Visibility Graphs: Persistence Is Not Enough. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 6:1-6:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{ameer_et_al:LIPIcs.SoCG.2020.6,
  author =	{Ameer, Safwa and Gibson-Lopez, Matt and Krohn, Erik and Soderman, Sean and Wang, Qing},
  title =	{{Terrain Visibility Graphs: Persistence Is Not Enough}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{6:1--6:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.6},
  URN =		{urn:nbn:de:0030-drops-121640},
  doi =		{10.4230/LIPIcs.SoCG.2020.6},
  annote =	{Keywords: Terrains, Visibility Graph Characterization, Visibility Graph Recognition}
}
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