TU Graz Logo

Institute of Geometry
Contact   People   Courses & Exams   Events   Research   Lehramtsstudium  
In reverse chronological order:
  • Angel Javier Alonso, Michael Kerber, Primoz Skraba: Probabilistic Analysis of Multiparameter Persistence Decompositions. Accepted for the 40th Symposium on Computational Geometry (SOCG 2024). Available at arXiv:2403.11939
  • Angel Javier Alonso, Michael Kerber, Tung Lam, Michael Lesnick: Delaunay Bifiltrations of Functions on Point Clouds. Symposium on Discrete Algorithms (SODA 2024), pp.4872-4891. Available at arXiv:2310.15902
  • Ulrich Bauer, Michael Kerber, Fabian Roll, Alexander Rolle: A Unified View on the Functorial Nerve Theorem and its Variations. Expositiones Mathematicae 41, pp. 125503, 2023. Available at arXiv:2203.03571
  • Havard Bjerkevik, Michael Kerber: Asymptotic Improvements on the Exact Matching Distance for 2-parameter Persistence. Journal of Computational Geometry (JoCG) 14 (1), pp.309-342, 2023 (link).
  • Martin Uray, Barbara Giunti, Michael Kerber, Stefan Huber: Topological Data Analysis in smart manufacturing processes -- A survey on the state of the art. arXiv:2310.09319
  • Angel Javier Alonso, Michael Kerber: Decomposition of zero-dimensional persistence modules via rooted subsets. 39th Symposium on Computational Geometry (SoCG 2023), pp.7:1-7:16. Available at arXiv:2303.06118
  • Michael Kerber, Matthias Söls: The localized Union-of-Balls Bifiltration. 39th Symposium on Computational Geometry (SoCG 2023), pp.45:1-45:19. Available at arXiv:2303.07002
  • Mickael Buchet, Bianca Dornelas, Michael Kerber: Sparse higher order Cech filtrations. 39th Symposium on Computational Geometry (SoCG 2023), pp.20:1-20:17. Available at arXiv:2303.06666
  • Ulderico Fugacci, Michael Kerber, Alexander Rolle: Compression for 2-parameter persistent homology. Computational Geometry: Theory and Applications 109, 2023 - Special issue on Algorithmic aspects of computational and applied topology (link).
  • Angel Javier Alonso, Michael Kerber, Siddharth Pritam: Filtration-Domination in Bifiltered Graphs. SIAM Symposium on Algorithm Engineering and Experiments (ALENEX 2023) (link)
  • Ulrich Bauer, Talha Bin Masood, Barbara Giunti, Guillaume Houry, Michael Kerber, Abhishek Rathod: Keeping it sparse: Computing Persistent Homology revisited. arxiv:2211.09075
  • Barbara Giunti, Guillaume Houry, Michael Kerber: Average complexity of matrix reduction for clique filtrations. Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation (ISSAC 2022), pp. 187-196 (link).
  • Aruni Choudhary, Michael Kerber, Sharath Raghvendra: Improved Approximate Rips Filtrations with Shifted Integer Lattices. Journal of Applied and Computational Topology 5, pp. 425-458, 2021 (link). The conference version appeared at the European Symposium on Algorithms (ESA 2017), pp. 28:1-28:13.
  • Michael Kerber, Robert Tichy, Mario Weitzer: Constrained Triangulations, Volumes of Polytopes, and Unit Equations. Publicationes Mathematicae Debrecen 99, pp.69-99, 2021. The conference version appeared at the 33rd International Symposium on Computational Geometry (SoCG 2017), 46:1-46:15. Available at arXiv:1609.05017
  • Rene Corbet, Michael Kerber, Michael Lesnick, Georg Osang: Computing the multicover bifiltration. 37th International Symposium on Computational Geometry (SoCG 2021), pp.27:1-27:17. Available at arXiv:2103.07823.
  • Mickael Buchet, Bianca Dornelas, Michael Kerber: Collapses of Higher-Order Delaunay complexes. 37th European Workshop on Computational Geometry (EuroCG 2021) (link).
  • Michael Kerber, Alexander Rolle: Fast Minimal Presentations of Bi-Graded Persistence Modules. SIAM Symposium on Algorithm Engineering and Experiments (ALENEX 2021). Available at arXiv:2010.15623.
  • Michael Kerber: Multi-Parameter Persistent Homology is Practical. Extended abstract for the workshop Topological Data Analysis and Beyond within the 34th Conference on Neural Information Processing Systems. (NeurIPS 2020) (poster).
  • Michael Kerber, Arnur Nigmetov: Metric Spaces with Expensive Distances. International Journal of Computational Geometry & Applications 30, pp.141-165, 2020. Available at arXiv:1901.08805.
  • Ulderico Fugacci, Michael Kerber, Hugo Manet: Topology-Preserving Terrain Simplification. Proceedings of the 28th International Conference on Advances in Geographic Information Systems (SIGSPATIAL 2020), pp.36-47. Available at arXiv:1912.03032.
  • Michael Kerber, Hannah Schreiber: On the expected complexity of matrix reduction for random complexes. Extended abstract presented at Computer Algebra in Scientific Computing (CASC 2020).
  • Michael Kerber, Arnur Nigmetov: Efficient Approximation of the Matching Distance for 2-parameter persistence. Proceedings of the 36th International Symposium on Computational Geometry (SoCG 2020), pp. 53:1-53:16. Available at arXiv:1912.05826.
  • Havard Bjerkevik, Magnus Botnan, Michael Kerber: Computing the interleaving distance is NP-hard. Foundations of Computational Mathematics 20, pp.1237-1271, 2020. (link).
  • Rene Corbet, Ulderico Fugacci, Michael Kerber, Claudia Landi, Bei Wang: A Kernel for Multi-Parameter Persistent Homology. Computer and Graphics X (2), 2019. Special Section on SMI 2019 (link) (Best paper award).
  • Michael Kerber, Michael Lesnick, Steve Oudot: Exact computation of the matching distance on 2-parameter persistence modules. Proceedings of the 35th International Symposium on Computational Geometry (SoCG 2019), pp. 46:1-46:15. Available at arXiv:1812.09085.
  • Ulderico Fugacci, Michael Kerber: Chunk Reduction for Multi-Parameter Persistent Homology. Proceedings of the 35th International Symposium on Computational Geometry (SoCG 2019), pp.37:1-37:14. Available at arXiv:1812.08580.
  • Pratyush Pranav, Rien van de Weygaert, Gert Vegter, Bernard J.T. Jones, Robert J. Adler, Job Feldbrugge, Changbom Park, Thomas Buchert, Michael Kerber: Topology and Geometry of Gaussian random fields I: on Betti Numbers, Euler characteristic and Minkowski functionals. Monthly Notices of the Royal Astronomical Society 485 (3), pp. 4167-4208, 2019 (link). Also available at arXiv:1812.07310.
  • Aruni Choudhary, Michael Kerber, Sharath Raghvendra: Improved Topological Approximations by Digitization. ACM-SIAM Symposium on Discrete Algorithms (SODA 2019), pp.2675-2688. Available at arXiv:1812.04966
  • Michael Kerber, Hannah Schreiber: Barcodes of Towers and a Streaming Algorithm for Persistent Homology. Discrete and Computational Geometry 61, pp. 852-879, 2019. (link). The conference version appeared at the 33rd International Symposium on Computational Geometry (SoCG 2017).
  • Aruni Choudhary, Michael Kerber, Sharath Raghvendra: Polynomial-Sized Topological Approximations Using The Permutahedron. Discrete and Computational Geometry (link). The conference version appeared at the 32nd International Symposium on Computational Geometry (SoCG 2016), pp.31:1-31:16, 2016 (link). Also available at arXiv:1601.02732.
  • Rene Corbet, Michael Kerber: The Representation Theorem of Persistent Homology Revisited and Generalized. Journal of Applied and Computational Topology 2, pp. 1-31, 2018. (link) Available at arXiv:1707.08864.
  • Oswin Aichholzer, Michael Kerber, Istvan Talata, Birgit Vogtenhuber: A Note on Planar Monohedral tilings. 34th European Workshop on Computational Geometry (EuroCG 2018), pp. 31:1-31:6 (pdf).
  • Michael Kerber, Dmitriy Morozov, Arnur Nigmetov: Geometry helps to Compare Persistence Diagrams. Journal of Experimental Algorithms 22, 2017 (link). A conference version appeared at ALENEX 2016, pp.103-112 (pdf) © SIAM 2016.
  • Ulrich Bauer, Michael Kerber, Jan Reininghaus, Hubert Wagner: PHAT - Persistent Homology Algorithms Toolbox. Journal of Symbolic Computation 78, pp.76-90, 2017 - Special Issue on Algorithms and Software for Computational Topology. (pdf)
    © Elsevier 2017. The website of the article is http://dx.doi.org/10.1016/j.jsc.2016.03.008. A short version appeared at the 4th International Congress of Mathematical Software (ICMS 2014).
  • Pratyush Pranav, Herbert Edelsbrunner, Rien van de Weygaert, Gert Vegter, Michael Kerber, Bernard Jones, Mathijs Wintraecken: The Topology of the Cosmic Web in Terms of Persistent Betti Numbers. Monthly Notices of the Royal Astronomical Society Main Journal 465 (4): 4281-4310, 2016 (link). Available at arXiv:1608.04519
  • Michael Kerber: Persistent Homology: State of the art and challenges. Internationale Mathematische Nachrichten 231, pp.15-33, 2016. (pdf)
  • Michael Kerber, Don Sheehy, Primoz Skraba: Persistent Homology and Nested Dissection. ACM-SIAM Symposium on Discrete Algorithms (SODA 2016), pp.1234-1245. (pdf) © SIAM 2016.
  • Dan Halperin, Michael Kerber, Doron Shaharabani: The Offset Filtration of Convex Objects. European Symposium on Algorithms (ESA 2015), pp.705-716 (link). Available at arXiv:1407.6132
  • Michael Kerber, Sharath Raghvendra: Approximation and Streaming Algorithms for Projective Clustering via Random Projections. Proceedings of 2015 Canadian Conference on Computational Geometry (CCCG 2015), pp.179-185. Available at arXiv:1407.2063
  • Aruni Choudhary, Michael Kerber: Local Doubling Dimension of Point Sets. Proceedings of the 2015 Canadian Conference on Computational Geometry (CCCG 2015), pp.156-164. Available at arXiv:1406.4822
  • Sergio Cabello, Michael Kerber: Semi-dynamic connectivity in the plane. Proceedings of the 2015 Algorithms and Data Structure Symposium (WADS 2015), pp.115-126. Available at arXiv:1502.03690
  • Michael Kerber, Michael Sagraloff: Root Refinement for Real Polynomials using Quadratic Interval Refinement. Journal of Computational and Applied Mathematics 280 pp.377-395, 2015 (link)
  • Chen Gu, Leonidas Guibas, Michael Kerber: Topology-driven Trajectory Synthesis with an Example on Retinal Cell Motions. 14th International Workshop on Algorithms in Bioinformatics (WABI 2014), pp.326-340. (pdf)
    © Springer, 2014. The final publication is available via Springer
  • Mabel Iglesias-Ham, Michael Kerber, Caroline Uhler: Sphere Packing with Limited Overlap. Canadian Conference on Computational Geometry (CCCG 2014), pp.155-161. Available at arXiv:1401.0468
  • Ulrich Bauer, Michael Kerber, Jan Reininghaus: Distributed Computation of Persistent Homology. SIAM Algorithm Engineering and Experiments (ALENEX 2014), pp.31-38. Available at arxiv:1310.0710
  • Michael Kerber, R.Sharathkumar: Approximate Cech Complex in Low and High Dimensions. 24th International Symposium on Algorithms and Computation (ISAAC 2013), LNCS 8283, pp.666-676. Available at arXiv:1307.3272
  • Haochen Tang, Michael Kerber, Qixing Huang, Leo Guibas: Locating Lucrative Passengers for Taxicab Drivers. 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems (ACM SIGSPATIAL GIS 2013), pp.504-507 (pdf)
  • Yang Li, Qixing Huang, Michael Kerber, Lin Zhang, Leo Guibas: Large-Scale Joint Map Matching of GPS Traces. 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems (ACM SIGSPATIAL GIS 2013), pp.214-223 (pdf)
  • Michael Kerber: Embedding the Dual Complex of Hyper-Rectangular Partitions. Journal of Computational Geometry 4 (1) pp. 13-37, 2013 (link).
  • Ulrich Bauer, Michael Kerber, Jan Reininghaus: Clear and Compress: Computing Persistent Homology in Chunks. TopoInVis 2013 (Best Paper Award). Available at arxiv:1303.0477
  • Chao Chen, Michael Kerber: An Output Sensitive Algorithm for Persistent Homology. Computational Geometry: Theory and Applications 46 (4) pp. 435-447, 2013 - Special Issue on the 27th Annual Symposium on Computational Geometry (link). The conference version appeared in the Proceedings of the 27th Annual Symposium on Computational Geometry, pp. 207-215 (SoCG 2011) (pdf, ps) © ACM, 2011.
  • Michael Kerber, Herbert Edelsbrunner: 3D Kinetic Alpha Complexes and Their Implementation. SIAM Algorithm Engineering and Experiments (ALENEX) 2013. The extended version The Medusa of Spatial Sorting: 3D Kinetic Alpha Complexes and Implementation is available at arXiv:1209.5434
  • Herbert Edelsbrunner, Carl-Philipp Heisenberg, Michael Kerber, Gabriel Krens: The Medusa of Spatial Sorting: Topological Construction. arXiv:1207.6474
  • Eric Berberich, Dan Halperin, Michael Kerber, Roza Pogalnikova: Deconstructing Approximate Offsets. Discrete and Computational Geometry 48 (2012), pp.964-989 (link). The conference version appeared in the Proceedings of the 27th Annual Symposium on Computational Geometry (SoCG 2011), pp. 187-196 (pdf, ps), © ACM, 2011
    An extended abstract was presented at the 26th European Workshop on Computational Geometry (EuroCG 2010) (pdf)
  • Herbert Edelsbrunner, Michael Kerber: Alexander Duality for Functions: the Persistent Behavior of Land and Water and Shore. Proceedings of the 28th Annual Symposium on Computational Geometry, pp. 249-258 (SoCG 2012) (pdf)
    © ACM, 2012. This is the authors' version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in the Proceedings of the 2012 Annual Symposium on Computational Geometry (SoCG 2012)
  • Herbert Edelsbrunner, Michael Kerber: Dual Complexes of Cubical Subdivisions of R^n. Discrete and Computational Geometry 47 (2012), pp.393-414 (pdf) © Springer, 2012.
  • Gavin Brown, Michael Kerber, Miles Reid: Fano 3-folds in codimension 4, Tom and Jerry, Part I. Compositio Mathematica 148 (4) pp.1171-1194, 2012 (link). Available at arXiv:1009.4313
  • Michael Kerber, Michael Sagraloff: A Worst-case Bound for Topology Computation of Algebraic Curves. Journal of Symbolic Computation 47 (2012), pp.239-258. Available at arXiv:1104.1510
  • Michael Kerber, Michael Sagraloff: Efficient Real Root Approximation. Proceedings of the 36th International Symposium on Symbolic and Algebraic Computation (ISSAC 2011), pp. 209-216 (pdf, ps) Supplementary material: pdf, ps
    © ACM, 2011. This is the authors' version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in ISSAC'11: International Symposium on Symbolic and Algebraic Computation Proceedings
    An improved version of the result is available as Root Refinement for Real Polynomials arXiv:1104.1362
  • Eric Berberich, Michael Hemmer, Michael Kerber: A Generic Algebraic Kernel for Non-linear Geometric Applications. Proceedings of the 27th Annual Symposium on Computational Geometry, pp. 179-186 (SoCG 2011) (pdf, ps)
    © ACM, 2011. This is the authors' version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in the Proceedings of the 2011 Annual Symposium on Computational Geometry (SoCG 2011)
  • Chao Chen, Michael Kerber: Persistent Homology Computation With a Twist. 27th European Workshop on Computational Geometry (EuroCG 2011). (pdf)
  • Herbert Edelsbrunner, Michael Kerber: Covering and packing with spheres by diagonal distortion in R^n. Rainbow of Computer Science - Essays Dedicated to Hermann Maurer on the Occasion of His 70th Birthday, eds. C. Calude, G. Rozenberg and A. Salomaa, LNCS 6570, pp. 20-35. (pdf)
  • Michael Kerber, Michael Sagraloff: A Note on the Complexity of Real Algebraic Hypersurfaces. Journal on Graphs and Combinatorics 27 (3) pp. 419-430 (pdf)
    © Springer, 2011. The original publication is available at www.springerlink.com
    An extended abstract of this work was presented at 7th Japan Conference on Computational Geometry and Graphs (JCCGG'09) (pdf, ps)
  • Paul Bendich, Herbert Edelsbrunner, Michael Kerber: Computing Robustness and Persistence for Images. IEEE Transactions on Visualization and Computer Graphics 16 (2010), pp. 1251-1260 (pdf) © IEEE 2010
  • Paul Bendich, Herbert Edelsbrunner, Michael Kerber, Amit Patel: Persistent Homology under Non-uniform Error. Invited paper for the 35th International Symposium on Mathematical Foundations of Computer Science (MFCS 2010), LNCS 6281, pp. 12-23 (pdf)
    © Springer, 2010. The original publication is available at www.springerlink.com
  • Eric Berberich, Efi Fogel, Dan Halperin, Michael Kerber, Ophir Setter: Arrangements on Parametric Surfaces II: Concretizations and Applications. Mathematics in Computer Science 4 (1), pp.67-91 (pdf) © Birkhäuser 2010
  • Michael Kerber: Geometric Algorithms for Algebraic Curves and Surfaces. PhD Thesis, Saarland University, 2009 (pdf, ps)
  • Michael Sagraloff, Michael Kerber, Michael Hemmer: Certified Complex Root Isolation via Adaptive Root Separation Bounds. 9th Asian Symposium on Computer Mathematics (ASCM'09) (pdf)
  • Eric Berberich, Michael Kerber, Michael Sagraloff: An Efficient Algorithm for the Stratification and Triangulation of Algebraic Surfaces. Computational Geometry: Theory and Applications 43 (3) pp. 257-278 - Special Issue on 24th Annual Symposium on Computational Geometry
  • Michael Kerber: On the Complexity of Reliable Root Approximation. 11th International Workshop on Computer Algebra in Scientific Computing (CASC'09). LNCS 5743, pp. 155-167 (pdf, ps)
    © Springer, 2009. The original publication is available at www.springerlink.com
  • Michael Kerber: Division-Free Computation of Subresultants Using Bezout Matrices. International Journal of Computer Mathematics 86 (12) pp. 2186-2200, 2009
  • Eric Berberich, Michael Kerber, Michael Sagraloff: Exact Geometric-Topological Analysis of Algebraic Surfaces. Proceedings of the twenty-fourth Annual Symposium on Computational Geometry (SoCG 2008), pp. 164-173 (pdf, ps)
    © ACM, 2008. This is the authors' version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in the Proceedings of the twenty-fourth Annual Symposium on Computational Geometry (SoCG 2008) http://doi.acm.org/10.1145/1377676.1377703
    An extended abstract of this work was presented at the 24th European Workshop on Computational Geometry (pdf, ps).
  • Pavel Emeliyanenko, Michael Kerber: Visualizing and Exploring Planar Algebraic Arrangements - a Web Application. Video presented at the 24th Annual Symposium on Computational Geometry (SoCG 2008)
  • Eric Berberich, Michael Kerber: Exact arrangements on Tori and Dupin cyclides. Proceedings of the 2008 ACM Symposium on Solid and Physical Modeling (SPM 2008), pp. 59-66 (pdf, ps)
    © ACM, 2008. This is the authors' version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in the Proceedings of the ACM Solid and Physical Modelling Symposium (SPM 2008) http://doi.acm.org/10.1145/1364901.1364912
    An extended abstract of this work was presented at the 24th European Workshop on Computational Geometry (pdf, ps).
  • Arno Eigenwillig, Michael Kerber: Exact and Efficient 2D-Arrangements of Arbitrary Algebraic Curves. Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2008), pp. 122-131 (pdf, ps).
    © SIAM 2008. The provided download is an author-prepared version of the article.
  • Arno Eigenwillig, Michael Kerber, Nicola Wolpert: Fast and Exact Geometric Analysis of Real Algebraic Plane Curves. Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC 2007), pp. 151-158 (pdf, ps).
    © ACM, 2007. This is the authors' version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in the Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation (ISSAC 2007). http://doi.acm.org/10.1145/1277548.1277570
  • Michael Kerber: Analysis of Real Algebraic Plane Curves. Diploma Thesis, Saarbrücken 2006 (pdf, ps).