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Complexity Inside NP - A Computational Geometry Perspective

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Publications

Long plane trees

Author(s): Cabello, Sergio; Hoffmann, Michael; Klost, Katharina; Mulzer, Wolfgang; Tkadlec, Josef
Published in: EuroCG 2021, 2021

Weak Unit Disk Contact Representations for Graphs without Embedding

Author(s): Jonas Cleve
Published in: EuroCG 2020, 2020, Page(s) 28:1-28:9

Recognizing embedded caterpillars with weak unit disk contact representations is NP-hard

Author(s): Man-Kwun Chiu, Jonas Cleve, Martin Nöllenburg
Published in: EuroCG 2019, 2019, Page(s) 47:1-47:9

Asymmetric Convex Intersection Testing

Author(s): Barba, Luis; Mulzer, Wolfgang
Published in: SOSA 2019, Issue 69, 2019, Page(s) 9:1-9:14
DOI: 10.4230/oasics.sosa.2019.9

Approximate Minimum-Weight Matching with Outliers under Translation

Author(s): Agarwal, Pankaj K.; Kaplan, Haim; Kipper, Geva; Mulzer, Wolfgang; Rote, Günter; Sharir, Micha; Xiao, Allen
Published in: ISAAC 2018, Issue 123, 2018, Page(s) 26:1--26:13
DOI: 10.4230/lipics.isaac.2018.26

Maintaining the Union of Unit Discs under Insertions with Near-Optimal Overhead

Author(s): Agarwal, Pankaj K.; Cohen, Ravid; Halperin, Dan; Mulzer, Wolfgang
Published in: SoCG 2019, Issue 129, 2019, Page(s) 26:1-26:15
DOI: 10.4230/lipics.socg.2019.26

Combinatorics of Beacon-Based Routing in Three Dimensions

Author(s): Jonas Cleve, Wolfgang Mulzer
Published in: LATIN 2018: Theoretical Informatics, Issue 10807, 2018, Page(s) 346-360
DOI: 10.1007/978-3-319-77404-6_26

Recognizing Generalized Transmission Graphs of Line Segments and Circular Sectors

Author(s): Katharina Klost, Wolfgang Mulzer
Published in: LATIN 2018: Theoretical Informatics, Issue 10807, 2018, Page(s) 683-696
DOI: 10.1007/978-3-319-77404-6_50

Improved Topological Approximations by Digitization

Author(s): Aruni Choudhary, Michael Kerber, Sharath Raghvendra
Published in: Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, 2019, Page(s) 2675-2688
DOI: 10.1137/1.9781611975482.166

On the Stretch Factor of Polygonal Chains

Author(s): Chen, Ke; Dumitrescu, Adrian; Mulzer, Wolfgang; Tóth, Csaba D.
Published in: MFCS 2019, Issue 138, 2019, Page(s) 56:1–56:14
DOI: 10.4230/lipics.mfcs.2019.56

An Experimental Study of Algorithms for Geodesic Shortest Paths in the Constant-Workspace Model

Author(s): Jonas Cleve, Wolfgang Mulzer
Published in: Analysis of Experimental Algorithms - Special Event, SEA² 2019, Kalamata, Greece, June 24-29, 2019, Revised Selected Papers, Issue 11544, 2019, Page(s) 317-331
DOI: 10.1007/978-3-030-34029-2_21

Triangles and Girth in Disk Graphs and Transmission Graphs

Author(s): Haim Kaplan, Katharina Klost, Wolfgang Mulzer, Liam Roditty, Paul Seiferth, Micha Sharir
Published in: ESA 2019, Issue 144, 2019, Page(s) 64:1-64:14
DOI: 10.4230/lipics.esa.2019.64

Long Alternating Paths Exist

Author(s): Mulzer, Wolfgang; Valtr, Pavel
Published in: SoCG 2020, Issue 164, 2020, Page(s) 57:1-57:16
DOI: 10.4230/lipics.socg.2020.57

A Generalization of Self-Improving Algorithms

Author(s): Cheng, Siu-Wing; Chiu, Man-Kwun; Jin, Kai; Wong, Man Ting
Published in: SoCG 2020, Issue 164, 2020, Page(s) 29:1-29:13
DOI: 10.4230/lipics.socg.2020.29

No-Dimensional Tverberg Theorems and Algorithms

Author(s): Choudhary, Aruni; Mulzer, Wolfgang
Published in: SoCG 2020, Issue 164, 2020, Page(s) 31:1-31:17
DOI: 10.4230/lipics.socg.2020.31

Routing in Unit Disk Graphs without Dynamic Headers

Author(s): Mulzer, Wolfgang; Willert, Max
Published in: ISAAC 2020, 2020, Page(s) 16:1--16:14
DOI: 10.4230/lipics.isaac.2020.16

The Tree Stabbing Number is not Monotone

Author(s): Mulzer, Wolfgang; Obenaus, Johannes
Published in: EuroCG 2020, 2020, Page(s) 78:1-78:8

Maximum Matchings in Geometric Intersection Graphs

Author(s): Bonnet, Édouard; Cabello, Sergio; Mulzer, Wolfgang
Published in: STACS 2020, Issue 154, 2020, Page(s) 31:1-31:17
DOI: 10.4230/lipics.stacs.2020.31

Routing in Histograms

Author(s): Man-Kwun Chiu, Jonas Cleve, Katharina Klost, Matias Korman, Wolfgang Mulzer, André van Renssen, Marcel Roeloffzen, Max Willert
Published in: WALCOM: Algorithms and Computation - 14th International Conference, WALCOM 2020, Singapore, Singapore, March 31 – April 2, 2020, Proceedings, Issue 12049, 2020, Page(s) 43-54
DOI: 10.1007/978-3-030-39881-1_5

Minimal Representations of Order Types by Geometric Graphs

Author(s): Oswin Aichholzer, Martin Balko, Michael Hoffmann, Jan Kynčl, Wolfgang Mulzer, Irene Parada, Alexander Pilz, Manfred Scheucher, Pavel Valtr, Birgit Vogtenhuber, Emo Welzl
Published in: Graph Drawing and Network Visualization - 27th International Symposium, GD 2019, Prague, Czech Republic, September 17–20, 2019, Proceedings, Issue 11904, 2019, Page(s) 101-113
DOI: 10.1007/978-3-030-35802-0_8

Computational Complexity of the $\alpha$-Ham-Sandwich Problem

Author(s): Chiu, Man-Kwun; Choudhary, Aruni; Mulzer, Wolfgang
Published in: ICALP 2020, Issue 168, 2020, Page(s) 31:1-31:18
DOI: 10.4230/lipics.icalp.2020.31

Plane Spanning Trees in Edge-Colored Simple Drawings of $$K_{n}$$

Author(s): Oswin Aichholzer, Michael Hoffmann, Johannes Obenaus, Rosna Paul, Daniel Perz, Nadja Seiferth, Birgit Vogtenhuber, Alexandra Weinberger
Published in: Graph Drawing and Network Visualization - 28th International Symposium, GD 2020, Vancouver, BC, Canada, September 16–18, 2020, Revised Selected Papers, Issue 12590, 2020, Page(s) 482-489
DOI: 10.1007/978-3-030-68766-3_37

Stabbing pairwise intersecting disks by five points

Author(s): Sariel Har-Peled, Haim Kaplan, Wolfgang Mulzer, Liam Roditty, Paul Seiferth, Micha Sharir, Max Willert:
Published in: ISAAC 2018, 2018
DOI: 10.4230/lipics.isaac.2018.50

Time-Space Trade-Offs for Computing Euclidean Minimum Spanning Trees

Author(s): Bahareh Banyassady, Luis Barba, Wolfgang Mulzer
Published in: LATIN 2018: Theoretical Informatics, Issue 10807, 2018, Page(s) 108-119
DOI: 10.1007/978-3-319-77404-6_9

Delaunay simplices in diagonally distorted lattices

Author(s): Aruni Choudhary, Arijit Ghosh
Published in: Computational Geometry, Issue 81, 2019, Page(s) 33-44, ISSN 0925-7721
DOI: 10.1016/j.comgeo.2019.01.010

Time-space trade-offs for computing Euclidean minimum spanning trees

Author(s): Bahareh Banyassady, Luis Barba, Wolfgang Mulzer
Published in: Journal of Computational Geometry, Issue 11(1), 2020, Page(s) 525–547, ISSN 1920-180X
DOI: 10.20382/jocg.v11i1a21

The dual diameter of triangulations

Author(s): Matias Korman, Stefan Langerman, Wolfgang Mulzer, Alexander Pilz, Maria Saumell, Birgit Vogtenhuber
Published in: Computational Geometry, Issue 68, 2018, Page(s) 243-252, ISSN 0925-7721
DOI: 10.1016/j.comgeo.2017.06.008

Improved time-space trade-offs for computing Voronoi diagrams

Author(s): Bahareh Banyassady, Matias Korman, Wolfgang Mulzer, André van Renssen, Marcel Roeloffzen, Paul Seiferth, Yannik Stein
Published in: Journal of Computational Geometry, Issue 9(1), 2018, Page(s) 191-212, ISSN 1920-180X
DOI: 10.20382/jocg.v9i1a6

Computational Aspects of the Colorful Carathéodory Theorem

Author(s): Wolfgang Mulzer, Yannik Stein
Published in: Discrete & Computational Geometry, Issue 60/3, 2018, Page(s) 720-755, ISSN 0179-5376
DOI: 10.1007/s00454-018-9979-y

Faster algorithms for growing prioritized disks and rectangles

Author(s): Hee-Kap Ahn, Sang Won Bae, Jongmin Choi, Matias Korman, Wolfgang Mulzer, Eunjin Oh, Ji-won Park, André van Renssen, Antoine Vigneron
Published in: Computational Geometry, Issue 80, 2019, Page(s) 23-39, ISSN 0925-7721
DOI: 10.1016/j.comgeo.2019.02.001

Routing in Unit Disk Graphs

Author(s): Haim Kaplan, Wolfgang Mulzer, Liam Roditty, Paul Seiferth
Published in: Algorithmica, Issue 80/3, 2018, Page(s) 830-848, ISSN 0178-4617
DOI: 10.1007/s00453-017-0308-2

Spanners for Directed Transmission Graphs

Author(s): Haim Kaplan, Wolfgang Mulzer, Liam Roditty, Paul Seiferth
Published in: SIAM Journal on Computing, Issue 47/4, 2018, Page(s) 1585-1609, ISSN 0097-5397
DOI: 10.1137/16m1059692

Time–space trade-offs for triangulations and Voronoi diagrams

Author(s): Matias Korman, Wolfgang Mulzer, André van Renssen, Marcel Roeloffzen, Paul Seiferth, Yannik Stein
Published in: Computational Geometry, Issue 73, 2018, Page(s) 35-45, ISSN 0925-7721
DOI: 10.1016/j.comgeo.2017.01.001

A constructive proof of a concentration bound for real-valued random variables

Author(s): Wolfgang Mulzer, Natalia Shenkman
Published in: Information Processing Letters, Issue 158, 2020, Page(s) 105942, ISSN 0020-0190
DOI: 10.1016/j.ipl.2020.105942

Implicit Manifold Reconstruction

Author(s): Siu-Wing Cheng, Man-Kwun Chiu
Published in: Discrete & Computational Geometry, Issue 62/3, 2019, Page(s) 700-742, ISSN 0179-5376
DOI: 10.1007/s00454-019-00095-w

Routing in polygonal domains

Author(s): Bahareh Banyassady, Man-Kwun Chiu, Matias Korman, Wolfgang Mulzer, André van Renssen, Marcel Roeloffzen, Paul Seiferth, Yannik Stein, Birgit Vogtenhuber, Max Willert
Published in: Computational Geometry, Issue 87, 2020, Page(s) 101593, ISSN 0925-7721
DOI: 10.1016/j.comgeo.2019.101593

Combinatorics of beacon-based routing in three dimensions

Author(s): Jonas Cleve, Wolfgang Mulzer
Published in: Computational Geometry, Issue 91, 2020, Page(s) 101667, ISSN 0925-7721
DOI: 10.1016/j.comgeo.2020.101667

Reachability Oracles for Directed Transmission Graphs

Author(s): Haim Kaplan, Wolfgang Mulzer, Liam Roditty, Paul Seiferth
Published in: Algorithmica, Issue 82/5, 2020, Page(s) 1259-1276, ISSN 0178-4617
DOI: 10.1007/s00453-019-00641-1

Balanced line separators of unit disk graphs

Author(s): Paz Carmi, Man Kwun Chiu, Matthew J. Katz, Matias Korman, Yoshio Okamoto, André van Renssen, Marcel Roeloffzen, Taichi Shiitada, Shakhar Smorodinsky
Published in: Computational Geometry, Issue 86, 2020, Page(s) 101575, ISSN 0925-7721
DOI: 10.1016/j.comgeo.2019.101575

A time–space trade-off for computing the k-visibility region of a point in a polygon

Author(s): Yeganeh Bahoo, Bahareh Banyassady, Prosenjit K. Bose, Stephane Durocher, Wolfgang Mulzer
Published in: Theoretical Computer Science, Issue 789, 2019, Page(s) 13-21, ISSN 0304-3975
DOI: 10.1016/j.tcs.2018.06.017

On the Average Complexity of the $k$-Level

Author(s): Steiner, Raphael; id_orcid0000-0001-8391-8949; Scheucher, Manfred; Felsner, Stefan; Valtr, Pavel; Chiu, Man-Kwun; Schnider, Patrick
Published in: Journal of Computational Geometry, Issue 11 (1), 2020, Page(s) 493-506, ISSN 1920-180X
DOI: 10.3929/ethz-b-000464326

Minimum cuts in geometric intersection graphs

Author(s): Sergio Cabello, Wolfgang Mulzer
Published in: Computational Geometry, Issue 94, 2021, Page(s) 101720, ISSN 0925-7721
DOI: 10.1016/j.comgeo.2020.101720

Rectilinear link diameter and radius in a rectilinear polygonal domain

Author(s): Elena Arseneva, Man-Kwun Chiu, Matias Korman, Aleksandar Markovic, Yoshio Okamoto, Aurélien Ooms, André van Renssen, Marcel Roeloffzen
Published in: Computational Geometry, Issue 92, 2021, Page(s) 101685, ISSN 0925-7721
DOI: 10.1016/j.comgeo.2020.101685

Dynamic Planar Voronoi Diagrams for General Distance Functions and Their Algorithmic Applications

Author(s): Haim Kaplan, Wolfgang Mulzer, Liam Roditty, Paul Seiferth, Micha Sharir
Published in: Discrete & Computational Geometry, Issue 64/3, 2020, Page(s) 838-904, ISSN 0179-5376
DOI: 10.1007/s00454-020-00243-7

Minimal Representations of Order Types by Geometric Graphs

Author(s): Oswin Aichholzer, Martin Balko, Michael Hoffmann, Jan Kynčl, Wolfgang Mulzer, Irene Parada, Alexander Pilz, Manfred Scheucher, Pavel Valtr, Birgit Vogtenhuber, Emo Welzl
Published in: Journal of Graph Algorithms and Applications, Issue 24/4, 2020, Page(s) 551-572, ISSN 1526-1719
DOI: 10.7155/jgaa.00545

Coxeter Triangulations Have Good Quality

Author(s): Aruni Choudhary, Siargey Kachanovich, Mathijs Wintraecken
Published in: Mathematics in Computer Science, Issue 14/1, 2020, Page(s) 141-176, ISSN 1661-8270
DOI: 10.1007/s11786-020-00461-5

Five Proofs of Chernoff's Bound with Applications

Author(s): Mulzer, Wolfgang
Published in: Bulletin of the EATCS, Issue 3, 2018, ISSN 0252-9742

Computational Geometry Column 67

Author(s): Bahareh Banyassady, Matias Korman, Wolfgang Mulzer
Published in: ACM SIGACT News, Issue 49/2, 2018, Page(s) 77-94, ISSN 0163-5700
DOI: 10.1145/3232679.3232692

A Simple Randomized $O(n \log n)$--Time Closest-Pair Algorithm in Doubling Metrics

Author(s): Maheshwari, Anil; Mulzer, Wolfgang; Smid, Michiel
Published in: Journal of Computational Geometry, Issue 11 (1), 2020, Page(s) 507–524, ISSN 1920-180X
DOI: 10.20382/jocg.v11i1a20

Dynamic Maintenance of the Lower Envelope of Pseudo-Lines

Author(s): Agarwal, Pankaj K.; Cohen, Ravid; Halperin, Dan; Mulzer, Wolfgang
Published in: Issue 1, 2019

On the Average Complexity of the $k$-Level

Author(s): Chiu, Man-Kwun; Felsner, Stefan; Scheucher, Manfred; Schnider, Patrick; Steiner, Raphael; Valtr, Pavel
Published in: 2020

Distance bounds for high dimensional consistent digital rays and 2-D partially-consistent digital rays

Author(s): Chiu, Man-Kwun; Korman, Matias; Suderland, Martin; Tokuyama, Takeshi
Published in: 2020

Minimum Cuts in Geometric Intersection Graphs

Author(s): Cabello, Sergio; Mulzer, Wolfgang
Published in: 2020

Special Issue on the 34th European Workshop on Computational Geometry, Guest Editors' Foreword

Author(s): Matias Korman, Wolfgang Mulzer
Published in: Computational Geometry, Issue 84, 2019, Page(s) 1-2, ISSN 0925-7721
DOI: 10.1016/j.comgeo.2019.07.001

New Results in Sona Drawing: Hardness and TSP Separation

Author(s): Man-Kwun Chiu, Erik D. Demaine, Yevhenii Diomidov, David Eppstein, Robert A. Hearn, Adam Hesterberg, Matias Korman, Irene Parada, Mikhail Rudoy
Published in: 2020