28 Search Results for "Bl�sius, Thomas"


Document
On the Giant Component of Geometric Inhomogeneous Random Graphs

Authors: Thomas Bläsius, Tobias Friedrich, Maximilian Katzmann, Janosch Ruff, and Ziena Zeif

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)


Abstract
In this paper we study the threshold model of geometric inhomogeneous random graphs (GIRGs); a generative random graph model that is closely related to hyperbolic random graphs (HRGs). These models have been observed to capture complex real-world networks well with respect to the structural and algorithmic properties. Following comprehensive studies regarding their connectivity, i.e., which parts of the graphs are connected, we have a good understanding under which circumstances a giant component (containing a constant fraction of the graph) emerges. While previous results are rather technical and challenging to work with, the goal of this paper is to provide more accessible proofs. At the same time we significantly improve the previously known probabilistic guarantees, showing that GIRGs contain a giant component with probability 1 - exp(-Ω(n^{(3-τ)/2})) for graph size n and a degree distribution with power-law exponent τ ∈ (2, 3). Based on that we additionally derive insights about the connectivity of certain induced subgraphs of GIRGs.

Cite as

Thomas Bläsius, Tobias Friedrich, Maximilian Katzmann, Janosch Ruff, and Ziena Zeif. On the Giant Component of Geometric Inhomogeneous Random Graphs. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 20:1-20:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{blasius_et_al:LIPIcs.ESA.2023.20,
  author =	{Bl\"{a}sius, Thomas and Friedrich, Tobias and Katzmann, Maximilian and Ruff, Janosch and Zeif, Ziena},
  title =	{{On the Giant Component of Geometric Inhomogeneous Random Graphs}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{20:1--20:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.20},
  URN =		{urn:nbn:de:0030-drops-186737},
  doi =		{10.4230/LIPIcs.ESA.2023.20},
  annote =	{Keywords: geometric inhomogeneous random graphs, connectivity, giant component}
}
Document
An Efficient Algorithm for Power Dominating Set

Authors: Thomas Bläsius and Max Göttlicher

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)


Abstract
The problem Power Dominating Set (PDS) is motivated by the placement of phasor measurement units to monitor electrical networks. It asks for a minimum set of vertices in a graph that observes all remaining vertices by exhaustively applying two observation rules. Our contribution is twofold. First, we determine the parameterized complexity of PDS by proving it is W[P]-complete when parameterized with respect to the solution size. We note that it was only known to be W[2]-hard before. Our second and main contribution is a new algorithm for PDS that efficiently solves practical instances. Our algorithm consists of two complementary parts. The first is a set of reduction rules for PDS that can also be used in conjunction with previously existing algorithms. The second is an algorithm for solving the remaining kernel based on the implicit hitting set approach. Our evaluation on a set of power grid instances from the literature shows that our solver outperforms previous state-of-the-art solvers for PDS by more than one order of magnitude on average. Furthermore, our algorithm can solve previously unsolved instances of continental scale within a few minutes.

Cite as

Thomas Bläsius and Max Göttlicher. An Efficient Algorithm for Power Dominating Set. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 21:1-21:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{blasius_et_al:LIPIcs.ESA.2023.21,
  author =	{Bl\"{a}sius, Thomas and G\"{o}ttlicher, Max},
  title =	{{An Efficient Algorithm for Power Dominating Set}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{21:1--21:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.21},
  URN =		{urn:nbn:de:0030-drops-186743},
  doi =		{10.4230/LIPIcs.ESA.2023.21},
  annote =	{Keywords: Power Dominating Set, Implicit Hitting Set, Parameterized Complexity, Reduction Rules}
}
Document
Partitioning the Bags of a Tree Decomposition into Cliques

Authors: Thomas Bläsius, Maximilian Katzmann, and Marcus Wilhelm

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


Abstract
We consider a variant of treewidth that we call clique-partitioned treewidth in which each bag is partitioned into cliques. This is motivated by the recent development of FPT-algorithms based on similar parameters for various problems. With this paper, we take a first step towards computing clique-partitioned tree decompositions. Our focus lies on the subproblem of computing clique partitions, i.e., for each bag of a given tree decomposition, we compute an optimal partition of the induced subgraph into cliques. The goal here is to minimize the product of the clique sizes (plus 1). We show that this problem is NP-hard. We also describe four heuristic approaches as well as an exact branch-and-bound algorithm. Our evaluation shows that the branch-and-bound solver is sufficiently efficient to serve as a good baseline. Moreover, our heuristics yield solutions close to the optimum. As a bonus, our algorithms allow us to compute first upper bounds for the clique-partitioned treewidth of real-world networks. A comparison to traditional treewidth indicates that clique-partitioned treewidth is a promising parameter for graphs with high clustering.

Cite as

Thomas Bläsius, Maximilian Katzmann, and Marcus Wilhelm. Partitioning the Bags of a Tree Decomposition into Cliques. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 3:1-3:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{blasius_et_al:LIPIcs.SEA.2023.3,
  author =	{Bl\"{a}sius, Thomas and Katzmann, Maximilian and Wilhelm, Marcus},
  title =	{{Partitioning the Bags of a Tree Decomposition into Cliques}},
  booktitle =	{21st International Symposium on Experimental Algorithms (SEA 2023)},
  pages =	{3:1--3:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-279-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{265},
  editor =	{Georgiadis, Loukas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.3},
  URN =		{urn:nbn:de:0030-drops-183533},
  doi =		{10.4230/LIPIcs.SEA.2023.3},
  annote =	{Keywords: treewidth, weighted treewidth, algorithm engineering, cliques, clustering, complex networks}
}
Document
Strongly Hyperbolic Unit Disk Graphs

Authors: Thomas Bläsius, Tobias Friedrich, Maximilian Katzmann, and Daniel Stephan

Published in: LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)


Abstract
The class of Euclidean unit disk graphs is one of the most fundamental and well-studied graph classes with underlying geometry. In this paper, we identify this class as a special case in the broader class of hyperbolic unit disk graphs and introduce strongly hyperbolic unit disk graphs as a natural counterpart to the Euclidean variant. In contrast to the grid-like structures exhibited by Euclidean unit disk graphs, strongly hyperbolic networks feature hierarchical structures, which are also observed in complex real-world networks. We investigate basic properties of strongly hyperbolic unit disk graphs, including adjacencies and the formation of cliques, and utilize the derived insights to demonstrate that the class is useful for the development and analysis of graph algorithms. Specifically, we develop a simple greedy routing scheme and analyze its performance on strongly hyperbolic unit disk graphs in order to prove that routing can be performed more efficiently on such networks than in general.

Cite as

Thomas Bläsius, Tobias Friedrich, Maximilian Katzmann, and Daniel Stephan. Strongly Hyperbolic Unit Disk Graphs. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{blasius_et_al:LIPIcs.STACS.2023.13,
  author =	{Bl\"{a}sius, Thomas and Friedrich, Tobias and Katzmann, Maximilian and Stephan, Daniel},
  title =	{{Strongly Hyperbolic Unit Disk Graphs}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{13:1--13:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.13},
  URN =		{urn:nbn:de:0030-drops-176652},
  doi =		{10.4230/LIPIcs.STACS.2023.13},
  annote =	{Keywords: hyperbolic geometry, unit disk graphs, greedy routing, hyperbolic random graphs, graph classes}
}
Document
On the External Validity of Average-Case Analyses of Graph Algorithms

Authors: Thomas Bläsius and Philipp Fischbeck

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)


Abstract
The number one criticism of average-case analysis is that we do not actually know the probability distribution of real-world inputs. Thus, analyzing an algorithm on some random model has no implications for practical performance. At its core, this criticism doubts the existence of external validity, i.e., it assumes that algorithmic behavior on the somewhat simple and clean models does not translate beyond the models to practical performance real-world input. With this paper, we provide a first step towards studying the question of external validity systematically. To this end, we evaluate the performance of six graph algorithms on a collection of 2751 sparse real-world networks depending on two properties; the heterogeneity (variance in the degree distribution) and locality (tendency of edges to connect vertices that are already close). We compare this with the performance on generated networks with varying locality and heterogeneity. We find that the performance in the idealized setting of network models translates surprisingly well to real-world networks. Moreover, heterogeneity and locality appear to be the core properties impacting the performance of many graph algorithms.

Cite as

Thomas Bläsius and Philipp Fischbeck. On the External Validity of Average-Case Analyses of Graph Algorithms. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 21:1-21:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{blasius_et_al:LIPIcs.ESA.2022.21,
  author =	{Bl\"{a}sius, Thomas and Fischbeck, Philipp},
  title =	{{On the External Validity of Average-Case Analyses of Graph Algorithms}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{21:1--21:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.21},
  URN =		{urn:nbn:de:0030-drops-169590},
  doi =		{10.4230/LIPIcs.ESA.2022.21},
  annote =	{Keywords: Average Case, Network Models, Empirical Evaluation}
}
Document
A Branch-And-Bound Algorithm for Cluster Editing

Authors: Thomas Bläsius, Philipp Fischbeck, Lars Gottesbüren, Michael Hamann, Tobias Heuer, Jonas Spinner, Christopher Weyand, and Marcus Wilhelm

Published in: LIPIcs, Volume 233, 20th International Symposium on Experimental Algorithms (SEA 2022)


Abstract
The cluster editing problem asks to transform a given graph into a disjoint union of cliques by inserting and deleting as few edges as possible. We describe and evaluate an exact branch-and-bound algorithm for cluster editing. For this, we introduce new reduction rules and adapt existing ones. Moreover, we generalize a known packing technique to obtain lower bounds and experimentally show that it contributes significantly to the performance of the solver. Our experiments further evaluate the effectiveness of the different reduction rules and examine the effects of structural properties of the input graph on solver performance. Our solver won the exact track of the 2021 PACE challenge.

Cite as

Thomas Bläsius, Philipp Fischbeck, Lars Gottesbüren, Michael Hamann, Tobias Heuer, Jonas Spinner, Christopher Weyand, and Marcus Wilhelm. A Branch-And-Bound Algorithm for Cluster Editing. In 20th International Symposium on Experimental Algorithms (SEA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 233, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{blasius_et_al:LIPIcs.SEA.2022.13,
  author =	{Bl\"{a}sius, Thomas and Fischbeck, Philipp and Gottesb\"{u}ren, Lars and Hamann, Michael and Heuer, Tobias and Spinner, Jonas and Weyand, Christopher and Wilhelm, Marcus},
  title =	{{A Branch-And-Bound Algorithm for Cluster Editing}},
  booktitle =	{20th International Symposium on Experimental Algorithms (SEA 2022)},
  pages =	{13:1--13:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-251-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{233},
  editor =	{Schulz, Christian and U\c{c}ar, Bora},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2022.13},
  URN =		{urn:nbn:de:0030-drops-165473},
  doi =		{10.4230/LIPIcs.SEA.2022.13},
  annote =	{Keywords: cluster editing}
}
Document
The Impact of Geometry on Monochrome Regions in the Flip Schelling Process

Authors: Thomas Bläsius, Tobias Friedrich, Martin S. Krejca, and Louise Molitor

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)


Abstract
Schelling’s classical segregation model gives a coherent explanation for the wide-spread phenomenon of residential segregation. We introduce an agent-based saturated open-city variant, the Flip Schelling Process (FSP), in which agents, placed on a graph, have one out of two types and, based on the predominant type in their neighborhood, decide whether to change their types; similar to a new agent arriving as soon as another agent leaves the vertex. We investigate the probability that an edge {u,v} is monochrome, i.e., that both vertices u and v have the same type in the FSP, and we provide a general framework for analyzing the influence of the underlying graph topology on residential segregation. In particular, for two adjacent vertices, we show that a highly decisive common neighborhood, i.e., a common neighborhood where the absolute value of the difference between the number of vertices with different types is high, supports segregation and, moreover, that large common neighborhoods are more decisive. As an application, we study the expected behavior of the FSP on two common random graph models with and without geometry: (1) For random geometric graphs, we show that the existence of an edge {u,v} makes a highly decisive common neighborhood for u and v more likely. Based on this, we prove the existence of a constant c > 0 such that the expected fraction of monochrome edges after the FSP is at least 1/2 + c. (2) For Erdős-Rényi graphs we show that large common neighborhoods are unlikely and that the expected fraction of monochrome edges after the FSP is at most 1/2 + o(1). Our results indicate that the cluster structure of the underlying graph has a significant impact on the obtained segregation strength.

Cite as

Thomas Bläsius, Tobias Friedrich, Martin S. Krejca, and Louise Molitor. The Impact of Geometry on Monochrome Regions in the Flip Schelling Process. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 29:1-29:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{blasius_et_al:LIPIcs.ISAAC.2021.29,
  author =	{Bl\"{a}sius, Thomas and Friedrich, Tobias and Krejca, Martin S. and Molitor, Louise},
  title =	{{The Impact of Geometry on Monochrome Regions in the Flip Schelling Process}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{29:1--29:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.29},
  URN =		{urn:nbn:de:0030-drops-154623},
  doi =		{10.4230/LIPIcs.ISAAC.2021.29},
  annote =	{Keywords: Agent-based Model, Schelling Segregation, Spin System}
}
Document
PACE Solver Description
PACE Solver Description: The KaPoCE Exact Cluster Editing Algorithm

Authors: Thomas Bläsius, Philipp Fischbeck, Lars Gottesbüren, Michael Hamann, Tobias Heuer, Jonas Spinner, Christopher Weyand, and Marcus Wilhelm

Published in: LIPIcs, Volume 214, 16th International Symposium on Parameterized and Exact Computation (IPEC 2021)


Abstract
The cluster editing problem is to transform an input graph into a cluster graph by performing a minimum number of edge editing operations. A cluster graph is a graph where each connected component is a clique. An edit operation can be either adding a new edge or removing an existing edge. In this write-up we outline the core techniques used in the exact cluster editing algorithm of the KaPoCE framework (contains also a heuristic solver), submitted to the exact track of the 2021 PACE challenge.

Cite as

Thomas Bläsius, Philipp Fischbeck, Lars Gottesbüren, Michael Hamann, Tobias Heuer, Jonas Spinner, Christopher Weyand, and Marcus Wilhelm. PACE Solver Description: The KaPoCE Exact Cluster Editing Algorithm. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 27:1-27:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{blasius_et_al:LIPIcs.IPEC.2021.27,
  author =	{Bl\"{a}sius, Thomas and Fischbeck, Philipp and Gottesb\"{u}ren, Lars and Hamann, Michael and Heuer, Tobias and Spinner, Jonas and Weyand, Christopher and Wilhelm, Marcus},
  title =	{{PACE Solver Description: The KaPoCE Exact Cluster Editing Algorithm}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{27:1--27:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-216-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{214},
  editor =	{Golovach, Petr A. and Zehavi, Meirav},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.27},
  URN =		{urn:nbn:de:0030-drops-154109},
  doi =		{10.4230/LIPIcs.IPEC.2021.27},
  annote =	{Keywords: cluster editing}
}
Document
PACE Solver Description
PACE Solver Description: KaPoCE: A Heuristic Cluster Editing Algorithm

Authors: Thomas Bläsius, Philipp Fischbeck, Lars Gottesbüren, Michael Hamann, Tobias Heuer, Jonas Spinner, Christopher Weyand, and Marcus Wilhelm

Published in: LIPIcs, Volume 214, 16th International Symposium on Parameterized and Exact Computation (IPEC 2021)


Abstract
The cluster editing problem is to transform an input graph into a cluster graph by performing a minimum number of edge editing operations. A cluster graph is a graph where each connected component is a clique. An edit operation can be either adding a new edge or removing an existing edge. In this write-up we outline the core techniques used in the heuristic cluster editing algorithm of the Karlsruhe and Potsdam Cluster Editing (KaPoCE) framework, submitted to the heuristic track of the 2021 PACE challenge.

Cite as

Thomas Bläsius, Philipp Fischbeck, Lars Gottesbüren, Michael Hamann, Tobias Heuer, Jonas Spinner, Christopher Weyand, and Marcus Wilhelm. PACE Solver Description: KaPoCE: A Heuristic Cluster Editing Algorithm. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 31:1-31:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{blasius_et_al:LIPIcs.IPEC.2021.31,
  author =	{Bl\"{a}sius, Thomas and Fischbeck, Philipp and Gottesb\"{u}ren, Lars and Hamann, Michael and Heuer, Tobias and Spinner, Jonas and Weyand, Christopher and Wilhelm, Marcus},
  title =	{{PACE Solver Description: KaPoCE: A Heuristic Cluster Editing Algorithm}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{31:1--31:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-216-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{214},
  editor =	{Golovach, Petr A. and Zehavi, Meirav},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.31},
  URN =		{urn:nbn:de:0030-drops-154147},
  doi =		{10.4230/LIPIcs.IPEC.2021.31},
  annote =	{Keywords: cluster editing, local search, variable neighborhood search}
}
Document
Synchronized Planarity with Applications to Constrained Planarity Problems

Authors: Thomas Bläsius, Simon D. Fink, and Ignaz Rutter

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)


Abstract
We introduce the problem Synchronized Planarity. Roughly speaking, its input is a loop-free multi-graph together with synchronization constraints that, e.g., match pairs of vertices of equal degree by providing a bijection between their edges. Synchronized Planarity then asks whether the graph admits a crossing-free embedding into the plane such that the orders of edges around synchronized vertices are consistent. We show, on the one hand, that Synchronized Planarity can be solved in quadratic time, and, on the other hand, that it serves as a powerful modeling language that lets us easily formulate several constrained planarity problems as instances of Synchronized Planarity. In particular, this lets us solve Clustered Planarity in quadratic time, where the most efficient previously known algorithm has an upper bound of O(n⁸).

Cite as

Thomas Bläsius, Simon D. Fink, and Ignaz Rutter. Synchronized Planarity with Applications to Constrained Planarity Problems. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 19:1-19:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{blasius_et_al:LIPIcs.ESA.2021.19,
  author =	{Bl\"{a}sius, Thomas and Fink, Simon D. and Rutter, Ignaz},
  title =	{{Synchronized Planarity with Applications to Constrained Planarity Problems}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{19:1--19:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.19},
  URN =		{urn:nbn:de:0030-drops-146009},
  doi =		{10.4230/LIPIcs.ESA.2021.19},
  annote =	{Keywords: Planarity Testing, Constrained Planarity, Cluster Planarity, Atomic Embeddability}
}
Document
Efficiently Approximating Vertex Cover on Scale-Free Networks with Underlying Hyperbolic Geometry

Authors: Thomas Bläsius, Tobias Friedrich, and Maximilian Katzmann

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)


Abstract
Finding a minimum vertex cover in a network is a fundamental NP-complete graph problem. One way to deal with its computational hardness, is to trade the qualitative performance of an algorithm (allowing non-optimal outputs) for an improved running time. For the vertex cover problem, there is a gap between theory and practice when it comes to understanding this tradeoff. On the one hand, it is known that it is NP-hard to approximate a minimum vertex cover within a factor of √2. On the other hand, a simple greedy algorithm yields close to optimal approximations in practice. A promising approach towards understanding this discrepancy is to recognize the differences between theoretical worst-case instances and real-world networks. Following this direction, we close the gap between theory and practice by providing an algorithm that efficiently computes nearly optimal vertex cover approximations on hyperbolic random graphs; a network model that closely resembles real-world networks in terms of degree distribution, clustering, and the small-world property. More precisely, our algorithm computes a (1 + o(1))-approximation, asymptotically almost surely, and has a running time of 𝒪(m log(n)). The proposed algorithm is an adaption of the successful greedy approach, enhanced with a procedure that improves on parts of the graph where greedy is not optimal. This makes it possible to introduce a parameter that can be used to tune the tradeoff between approximation performance and running time. Our empirical evaluation on real-world networks shows that this allows for improving over the near-optimal results of the greedy approach.

Cite as

Thomas Bläsius, Tobias Friedrich, and Maximilian Katzmann. Efficiently Approximating Vertex Cover on Scale-Free Networks with Underlying Hyperbolic Geometry. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 20:1-20:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{blasius_et_al:LIPIcs.ESA.2021.20,
  author =	{Bl\"{a}sius, Thomas and Friedrich, Tobias and Katzmann, Maximilian},
  title =	{{Efficiently Approximating Vertex Cover on Scale-Free Networks with Underlying Hyperbolic Geometry}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{20:1--20:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.20},
  URN =		{urn:nbn:de:0030-drops-146012},
  doi =		{10.4230/LIPIcs.ESA.2021.20},
  annote =	{Keywords: vertex cover, approximation, random graphs, hyperbolic geometry, efficient algorithm}
}
Document
Efficiently Computing Maximum Flows in Scale-Free Networks

Authors: Thomas Bläsius, Tobias Friedrich, and Christopher Weyand

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)


Abstract
We study the maximum-flow/minimum-cut problem on scale-free networks, i.e., graphs whose degree distribution follows a power-law. We propose a simple algorithm that capitalizes on the fact that often only a small fraction of such a network is relevant for the flow. At its core, our algorithm augments Dinitz’s algorithm with a balanced bidirectional search. Our experiments on a scale-free random network model indicate sublinear run time. On scale-free real-world networks, we outperform the commonly used highest-label Push-Relabel implementation by up to two orders of magnitude. Compared to Dinitz’s original algorithm, our modifications reduce the search space, e.g., by a factor of 275 on an autonomous systems graph. Beyond these good run times, our algorithm has an additional advantage compared to Push-Relabel. The latter computes a preflow, which makes the extraction of a minimum cut potentially more difficult. This is relevant, for example, for the computation of Gomory-Hu trees. On a social network with 70000 nodes, our algorithm computes the Gomory-Hu tree in 3 seconds compared to 12 minutes when using Push-Relabel.

Cite as

Thomas Bläsius, Tobias Friedrich, and Christopher Weyand. Efficiently Computing Maximum Flows in Scale-Free Networks. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 21:1-21:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{blasius_et_al:LIPIcs.ESA.2021.21,
  author =	{Bl\"{a}sius, Thomas and Friedrich, Tobias and Weyand, Christopher},
  title =	{{Efficiently Computing Maximum Flows in Scale-Free Networks}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{21:1--21:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.21},
  URN =		{urn:nbn:de:0030-drops-146029},
  doi =		{10.4230/LIPIcs.ESA.2021.21},
  annote =	{Keywords: graphs, flow, network, scale-free}
}
Document
Force-Directed Embedding of Scale-Free Networks in the Hyperbolic Plane

Authors: Thomas Bläsius, Tobias Friedrich, and Maximilian Katzmann

Published in: LIPIcs, Volume 190, 19th International Symposium on Experimental Algorithms (SEA 2021)


Abstract
Force-directed drawing algorithms are the most commonly used approach to visualize networks. While they are usually very robust, the performance of Euclidean spring embedders decreases if the graph exhibits the high level of heterogeneity that typically occurs in scale-free real-world networks. As heterogeneity naturally emerges from hyperbolic geometry (in fact, scale-free networks are often perceived to have an underlying hyperbolic geometry), it is natural to embed them into the hyperbolic plane instead. Previous techniques that produce hyperbolic embeddings usually make assumptions about the given network, which (if not met) impairs the quality of the embedding. It is still an open problem to adapt force-directed embedding algorithms to make use of the heterogeneity of the hyperbolic plane, while also preserving their robustness. We identify fundamental differences between the behavior of spring embedders in Euclidean and hyperbolic space, and adapt the technique to take advantage of the heterogeneity of the hyperbolic plane.

Cite as

Thomas Bläsius, Tobias Friedrich, and Maximilian Katzmann. Force-Directed Embedding of Scale-Free Networks in the Hyperbolic Plane. In 19th International Symposium on Experimental Algorithms (SEA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 190, pp. 22:1-22:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{blasius_et_al:LIPIcs.SEA.2021.22,
  author =	{Bl\"{a}sius, Thomas and Friedrich, Tobias and Katzmann, Maximilian},
  title =	{{Force-Directed Embedding of Scale-Free Networks in the Hyperbolic Plane}},
  booktitle =	{19th International Symposium on Experimental Algorithms (SEA 2021)},
  pages =	{22:1--22:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-185-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{190},
  editor =	{Coudert, David and Natale, Emanuele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2021.22},
  URN =		{urn:nbn:de:0030-drops-137944},
  doi =		{10.4230/LIPIcs.SEA.2021.22},
  annote =	{Keywords: force-directed drawing algorithms, spring embedding, hyperbolic space}
}
Document
Round-Competitive Algorithms for Uncertainty Problems with Parallel Queries

Authors: Thomas Erlebach, Michael Hoffmann, and Murilo Santos de Lima

Published in: LIPIcs, Volume 187, 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)


Abstract
The area of computing with uncertainty considers problems where some information about the input elements is uncertain, but can be obtained using queries. For example, instead of the weight of an element, we may be given an interval that is guaranteed to contain the weight, and a query can be performed to reveal the weight. While previous work has considered models where queries are asked either sequentially (adaptive model) or all at once (non-adaptive model), and the goal is to minimize the number of queries that are needed to solve the given problem, we propose and study a new model where k queries can be made in parallel in each round, and the goal is to minimize the number of query rounds. We use competitive analysis and present upper and lower bounds on the number of query rounds required by any algorithm in comparison with the optimal number of query rounds. Given a set of uncertain elements and a family of m subsets of that set, we present an algorithm for determining the value of the minimum of each of the subsets that requires at most (2+ε) ⋅ opt_k+O(1/(ε) ⋅ lg m) rounds for every 0 < ε < 1, where opt_k is the optimal number of rounds, as well as nearly matching lower bounds. For the problem of determining the i-th smallest value and identifying all elements with that value in a set of uncertain elements, we give a 2-round-competitive algorithm. We also show that the problem of sorting a family of sets of uncertain elements admits a 2-round-competitive algorithm and this is the best possible.

Cite as

Thomas Erlebach, Michael Hoffmann, and Murilo Santos de Lima. Round-Competitive Algorithms for Uncertainty Problems with Parallel Queries. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 27:1-27:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{erlebach_et_al:LIPIcs.STACS.2021.27,
  author =	{Erlebach, Thomas and Hoffmann, Michael and de Lima, Murilo Santos},
  title =	{{Round-Competitive Algorithms for Uncertainty Problems with Parallel Queries}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{27:1--27:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2021.27},
  URN =		{urn:nbn:de:0030-drops-136728},
  doi =		{10.4230/LIPIcs.STACS.2021.27},
  annote =	{Keywords: online algorithms, competitive analysis, explorable uncertainty, parallel algorithms, minimum problem, selection problem}
}
Document
A Faster Algorithm for Finding Tarski Fixed Points

Authors: John Fearnley and Rahul Savani

Published in: LIPIcs, Volume 187, 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)


Abstract
Dang et al. have given an algorithm that can find a Tarski fixed point in a k-dimensional lattice of width n using O(log^k n) queries [Chuangyin Dang et al., 2020]. Multiple authors have conjectured that this algorithm is optimal [Chuangyin Dang et al., 2020; Kousha Etessami et al., 2020], and indeed this has been proven for two-dimensional instances [Kousha Etessami et al., 2020]. We show that these conjectures are false in dimension three or higher by giving an O(log² n) query algorithm for the three-dimensional Tarski problem, which generalises to give an O(log^{k-1} n) query algorithm for the k-dimensional problem when k ≥ 3.

Cite as

John Fearnley and Rahul Savani. A Faster Algorithm for Finding Tarski Fixed Points. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 29:1-29:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{fearnley_et_al:LIPIcs.STACS.2021.29,
  author =	{Fearnley, John and Savani, Rahul},
  title =	{{A Faster Algorithm for Finding Tarski Fixed Points}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{29:1--29:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2021.29},
  URN =		{urn:nbn:de:0030-drops-136741},
  doi =		{10.4230/LIPIcs.STACS.2021.29},
  annote =	{Keywords: query complexity, Tarski fixed points, total function problem}
}
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