Department of Computer Science

Theory of Combinatorial Algorithms
Prof. Emo Welzl
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  Activity Report 2014

Theory of Combinatorial Algorithms
Teaching and Research Group Emo Welzl

Institut für Theoretische Informatik
Departement Informatik
ETH Zürichphone +41-44-632 73 92
CH-8092 Zürichfax+41-44-632 10 63



  • Bartosz Walczak, EPFL/Jagiellonian University, Kraków, Poland (Jan 21)
    On-line coloring games and the chromatic number of geometric intersection graphs (Mittagsseminar, Jan 21, 2014)
  • Robin Moser, (Feb 10-14)
  • Sonoko Moriyama, Tohoku University, Sendai, Japan (Feb 24-27)
    Minimal non-orientable matroids of rank three (Mittagsseminar, Feb 27, 2014)
  • Martin Jaggi (Mar 3-31)
  • Jerri Nummenpalo, Aalto University, Finland (Apr 3)
    Polytopal Big Data Statistics (Apr 3, 2014)
  • Micha Sharir, Tel Aviv University, Israel (Apr 12-20)
    Algebraic techniques for incidence problems (Mittagsseminar, Apr 15, 2014)
  • Malte Milatz, RWTH Aachen, Germany (May 15)
    Methods for Khovanov homology (Mittagsseminar, May 15, 2014)
  • Lothar Narins, FU Berlin, Germany (May 15 - Jul 9)
    The Connectedness of the Independence Complex of Line Graphs (Mittagsseminar, May 22, 2014)
  • Zuzana Safernová, Charles University, Prague, Czech Republic (Jun 9 - Jul 4)
    Bounds for Pach's selection theorem (Mittagsseminar, Jun 10, 2014)
  • Imre Bárány, Alfréd Rényi Mathematical Institute, Budapest, Hungary (Jun 12-16)
  • Jean Cardinal, Université Libre de Bruxelles, Brussels, Belgium (Jun 30 - Jul 4)
  • Radoslav Fulek, Columbia University, New York, USA (Jun 30 - Jul 4)
    Towards the Hanani-Tutte Theorem for Clustered Graphs (Combinatorial Algorithms Day, Jun 30, 2014)
  • Anna Gundert, Universität zu Köln, Germany (Jun 30 - Jul 4)
    Generalizing Bipartiteness to Higher Dimensions (Combinatorial Algorithms Day, Jun 30, 2014)
  • Tillmann Miltzow, FU Berlin, Germany (Jun 30 - Jul 4)
  • Yoshio Okamoto, UEC Tokyo, Japan (Jun 30 - Jul 4)
    Extended Formulations for Sparsity Matroids (Combinatorial Algorithms Day, Jun 30, 2014)
  • Andres Ruiz Vargas, EPF Lausanne, Switzerland (Jun 30 - Jul 4)
    Disjoint Edges in Topological Graphs and the Tangled-Thrackle Conjecture (Combinatorial Algorithms Day, Jun 30, 2014)
  • Shakhar Smorodinsky, Ben-Gurion University, Be'er Sheva, Israel (Jun 30 - Jul 4)
    On Distinct Distances Between Points and Lines (Combinatorial Algorithms Day, Jun 30, 2014)
  • József Solymosi, University of British Columbia, Vancouver, Canada (Jun 30 - Jul 4)
    On extensions of the Elekes-Szabó Theorem (Combinatorial Algorithms Day, Jun 30, 2014)
  • Bettina Speckmann, TU Eindhoven, The Netherlands (Jun 30 - Jul 4)
  • Miloš Stojaković, University of Novi Sad, Serbia (Jun 30 - Jul 4)
    Saturation Games on Graphs (Combinatorial Algorithms Day, Jun 30, 2014)
  • Tibor Szabó, FU Berlin, Germany (Jun 30 - Jul 4)
    On the Cycles of Degree-3 Critical Graphs (Combinatorial Algorithms Day, Jun 30, 2014)
  • Csaba Dávid Tóth, California State University Northridge, California, USA (Jun 30 - Jul 4)
    Approximate Interior Barriers (Combinatorial Algorithms Day, Jun 30, 2014)
  • Takeaki Uno, National Institute of Informatics (NII), Tokyo, Japan (Jun 30 - Jul 4)
    Clustering by Iterative Graph Modification (Combinatorial Algorithms Day, Jun 30, 2014)
  • Uli Wagner, Institute of Science and Technology Austria, Klosterneuburg, Austria (Jun 30 - Jul 4)
    Eliminating Tverberg Points (Combinatorial Algorithms Day, Jun 30, 2014)
  • Mary Inaba, University of Tokyo, Japan (Jul 10 - Jul 13)
  • Christian Müller New York University, USA (Jul 10-11)
    Sparse model estimation and selection with the LASSO and the TREX in systems biology applications (Mittagsseminar, Jul 11, 2014)
  • Yurii Nesterov, Université Catholique de Louvain, Brussels, Belgium (Jul 11)
  • Alexander Pilz, TU Graz, Austria (Aug 18-22)
  • Micha Sharir, Tel Aviv University, Israel (Aug 19-22)
  • Luis Barba, Carleton University / Université Libre de Bruxelles, Canada / Belgium (Sep 15-18)
    Detecting intersections between convex polyhedra (Mittagsseminar, Sep 16, 2014)
  • Jean Cardinal, Université Libre de Bruxelles, Brussels, Belgium (Sep 30 - Oct 3)
    General Position Subsets in d-space (Mittagsseminar, Oct 2, 2014)
  • Michael Kaufmann, Universität Tübingen, Germany (Oct 6 - 8)
  • Matias Korman, National Institute of Informatics, Tokyo, Japan (Oct 12 - 29)
    Computing extremal distances in polygonal domains (Mittagsseminar, Oct 14, 2014)


  • Crossing-Free Configurations in the Plane - Counting, Enumeration, and Sampling

    (Financed by the Swiss National Science Foundation - EuroGIGA/ComPoSe). The goal of this project is the understanding of crossing-free geometric graphs-these are graphs with an embedding on a given planar point set where the edges are drawn as straight line segments without crossings. Often we are restricted to certain types of graphs, most prominently triangulations, but also spanning cycles, spanning trees or (perfect) matchings (and crossing-free partitions), among others. A primary goal is to enumerate, count, or sample graphs of a certain type for a given point set-so these are algorithmic questions-, or to give estimates for the maximum and minimum number of such graphs on any set of n points-these are problems in extremal combinatorial geometry.

    Contact: E. Welzl, M. Wettstein

  • Redundancy in Linear and Neuromuscular Systems

    (Financed by the Swiss National Science Foundation). Understanding and removing redundancy in a given data to improve computational efficiency or discover its fundamental structure is a universal problem in science and engineering, as the data or the mathematical model to be analyzed in any realistic situation often contains redundant information that is implied by the rest. This research project has two intertwined goals, one of them theoretical, the other one driven by a concrete application. On the theoretical level, we want to understand the structure of redundancy and the complexity of redundancy removal in explicitly or implicitly given linear and more abstract systems. Here we strongly build on our expertise in computational geometry as well as combinatorial optimization. On the application side, we want to compute redundancy and assess the role of redundancy in neuromuscular control, a field that is trying to understand how the nervous system is selecting and implementing specific muscle commands that meet the constraints of specific tasks. This part of the project will be performed in close collaboration with Francisco Valero-Cuevas. He pioneered in modeling the interplay of various muscles in terms of zonotopes whose internal structure determines the possible tasks that the muscles under consideration can achieve together.

    Contact: B. Gärtner, K. Fukuda

  • Simultaneous Embeddings

    (Financed by the Swiss National Science Foundation). We use the term simultaneous (geometric) embedding to refer to any kind of problem in which two or more graphs are to be embedded simultaneously, usually subject to certain constraints. One reason for the strong interest in simultaneous embeddings lies in a wealth of applications in areas such as bio-informatics, network analysis, and software engineering. For instance, in order to compare two phylogenetic trees one would like to have a "nice" simultaneous drawing of two trees sharing the same set of leaves, so-called tanglegrams. More generally, simultaneous embeddings come into play whenever large or dynamically changing graphs are to be visualized. Given a large graph, only part of it can be shown at a time with a sufficient level of detail. When browsing from one such part to a neighboring one, it is desirable to have a certain overlap that is common to both parts and drawn the same way for both parts. In this way, the user can maintain her mental map and more easily keep track of her current location in the graph. In the context of dynamic graphs, a simultaneous drawing for several instances of the graph at different timesteps allows to visually examine the differences in order to, for instance, draw conclusions regarding the capacity utilization of a network. Beyond these motivating applications the study of simultaneous embeddings revealed a rich collection of interesting and challenging combinatorial and algorithmic problems, many of which are still far from being solved. The goal of this project is, on one hand, to gain more insights into some of these problems and, on the other hand, to develop new models in order to address some shortcomings of the existing settings studied so far. The project will be carried out as an international collaboration within the collaborative research project "GraDr: Graph Drawings and Representations", which comprises altogether 12 partners from seven European countries.

    Contact: M. Hoffmann, V. Kusters


  • Books

  • Journals (with refereeing)

    O. Aichholzer, G. Aloupis, E. Demaine, M. Demaine, M. Hoffmann, S. Fekete, A. Lubiw, J. Snoeyink, A. Winslow. Covering Folded Shapes, Journal of Computational Geometry , 5:1 (2014), 150-168.

    O. Aichholzer, T. Hackl, M. Hoffmann, A. Pilz, G. Rote, B. Speckmann, B. Vogtenhuber, Plane Graphs with Parity Constraints, Graphs and Combinatorics, 30:1 (2014), 47-69.

    A. Baertschi, S. Suri, Conflict-free chromatic art gallery coverage, Algorithmica 68:1 (2014), 265-283.

    B. Bukh, J. Matoušek, Erdős-Szekeres-type statements: Ramsey function and decidability in dimension 1, Duke Mathematical Journal (2013), to appear.

    M. Čadek, M. Krčál, J. Matoušek, L. Vokřínek, U. Wagner, Extendability of continuous maps is undecidable, Discrete & Computational Geometry 51:1 (2014), 24-66.

    M. Čadek, M. Krčál, J. Matoušek, F. Sergeraert, L. Vokřínek, U. Wagner, Computing all maps into a sphere, Journal of the ACM (2013), to appear.

    J. Foniok, B. Gärtner, L. Klaus, M. Sprecher, Counting Unique-Sink Orientations, Discrete Applied Mathematics 163:2 (2014), 155-164.

    F. Frati, J. Gudmundsson, E. Welzl, On the Number of Upward Planar Orientations of Maximal Planar Graphs, Theoretical Computer Science 544 (2014), 32-59.

    T. Hertli, 3-SAT Faster and Simpler - Unique-SAT Bounds for PPSZ Hold in General, SIAM Journal of Computing 43:2 (2014), 718-729.

    M. Hoffmann and Cs.D. Tóth, Vertex-Colored Encompassing Graphs, Graphs and Combinatorics 30:4 (2014), 933-947.

    J. Matoušek, Near-optimal separators in string graphs, Combinatorics, Probability and Computing 23:1 (2014), 135-139.

    J. Matoušek, U. Wagner, On Gromov's method of selecting heavily covered points, Discrete and Computational Geometry (2012), to appear.

    H. Tyagi, V. Cevher, Learning non-parametric basis independent models from point queries via low-rank methods, Applied and Computational Harmonic Analysis 37:3 (2014), 389-412.

    H. Tyagi, S. Stich, B. Gärtner, On two continuum armed bandit problems in high dimensions, Theory of Computing Systems (2014), to appear.

  • Conference Proceedings (with selection process)

    O. Aichholzer, J. Cardinal, V. Kusters, S. Langerman, P. Valtr, Reconstructing Point Set Order Types from Radial Orderings, Proc. 25th International Symposium on Algorithms and Computation (ISAAC) (2014), to appear.

    I. Bárány, J. Matoušek, A. Por, Curves in Rd intersecting every hyperplane at most d+1 times, Proc. 30th Annual ACM Symposium on Computational Geometry (SoCG) (2014), 565-571.

    K. Buchin, A. van Goethem, M. Hoffmann, M. van Kreveld, B. Speckmann. Travel-time Maps: Linear Cartograms with Fixed Vertex Locations, Proc. 8th International Conference on Geographic Information Science (GIScience) (2014) LNCS 8728, 18-33.

    M. Elias, J. Matoušek, E. Roldán-Pensado, Z. Safernová, Lower bounds on geometric Ramsey functions, Proc. 30th Annual ACM Symposium on Computational Geometry (SoCG) (2014), 558-564.

    W. Evans, V.Kusters, M. Saumell, B. Speckmann, Column Planarity and Partial Simultaneous Geometric Embedding, 22nd International Symposium on Graph Drawing (2014), to appear.

    A. Francke, Cs.D. Tóth, A Census of Plane Graphs with Polyline Edges, Proc. 30th Annual ACM Symposium on Computational Geometry (SoCG) (2014), 242-250.

    B. Gärtner, Sampling with Removal in LP-type Problems, Proc. 30th Annual ACM Symposium on Computational Geometry (SoCG) (2014), 511-518.

    B. Gärtner, A. Krause, H. Tyagi, Efficient Sampling for Learning Sparse Additive Models in High Dimensions, Advances in Neural Information Processing Systems (NIPS) (2014), to appear.

    B. Gärtner, H. Tyagi, Continuum armed bandit problem of few variables in high dimensions, Proc. 11th Workshop on Approximation and Online Algorithms (WAOA) (2014) LNCS 8447, 108-119.

    X. Goaoc, J. Matoušek, P. Paták, Z. Safernová, Simplifying inclusion-exclusion formulas, European Conference on Combinatorics, Graph Theory and Applications (Eurocomb) (2013), to appear.

    A. Gundert, M. Szedlák, Higher Dimensional Discrete Cheeger Inequalities, Proc. 30th Annual ACM Symposium on Computational Geometry (SoCG) (2014), 181-188.

    T.Hertli, Breaking the PPSZ Barrier for Unique 3-SAT, 41st International Colloquium on Automata, Languages and Programming (ICALP) (2014), to appear.

    M. Hoffmann, V. Kusters, T. Miltzow, Halving Balls in Deterministic Linear Time, Proc. 22nd Annual European Symposium on Algorithms (ESA) (2014) LNCS 8737, 566-578.

    J. Matoušek, E. Sedgwick, M. Tancer, U. Wagner, Embeddability in the 3-sphere is decidable, Proc. 30th Annual ACM Symposium on Computational Geometry (SoCG) (2014), 78-84.

    S. Stich, On low complexity Acceleration Techniques for Randomized Optimization, 13th International Conference on Parallel Problem Solving From Nature (PPSN) (2014) LNCS 8672, 130-140.

    M. Wettstein, Counting and Enumerating Crossing-free Geometric Graphs, Proc. 30th Annual ACM Symposium on Computational Geometry (SoCG) (2014), 1-10.

  • Other (including submitted work)

    O. Aichholzer, Th. Hackl, M. Korman, M. van Kreveld, M. Löffler, A. Pilz, B. Speckmann, E. Welzl, Packing Plane Spanning Trees and Paths in Complete Geometric Graphs, Proc. 26th Canadian Conference on Computational Geometry (CCCG) (2014), 6 pages.

    O. Aichholzer, M. Hoffmann, M. van Kreveld, G. Rote, Graph Drawings with Relative Edge Length Specifications Proc. 26th Canadian Conference on Computational Geometry (CCCG) (2014), 7 pages.

    M. Čadek, M. Krčál, J. Matoušek, L. Vokřínek, U. Wagner, Polynomial-time computation of homotopy groups and Postnikov systems in fixed dimension, (2012), submitted.

    D. Clemens, H. Gebauer, A. Liebenau, The random graph intuition for the tournament game, (2013), submitted.

    K. Fukuda, L. Klaus, H. Miyata, Enumeration of PLCP-orientations of the 4-cube, (2013), submitted.

    B. Gärtner, C. Müller, S. Stich, Variable Metric Random Pursuit, (2012), submitted.

    M. Hoffmann, M. van Kreveld, V. Kusters, G. Rote, Quality Ratios of Measures for Graph Drawing Styles, Proc. 26th Canadian Conference on Computational Geometry (CCCG) (2014), 7 pages.

    M. Hoffmann, V. Kusters, T. Miltzow, Separating Balls with a Hyperplane, Abstracts of the 30th European Workshop on Computational Geometry (EuroCG), Ein-Gedi, Israel (2014).

    V. Kusters, B. Speckmann, Characterizing Graphs With A Sliceable Rectangular Dual, (2013), submitted.

    A. Thomas, J. van Leeuwen, Pure Nash Equilibria in Graphical Games and Treewidth, (2013), submitted.


"Breaking the PPSZ Barrier for Unique 3-SAT", CSE Theory Seminar, UC San Diego, USA (Jan 27, 2014).

"Planar Packing of Binary Trees", EuroGIGA Final Conference, Freie Universität Berlin, Germany (Feb 18, 2014).

"Probabilistic Estimate Sequences", TAO reserach seminar, INRIA Saclay, Île-de-France, France (Mar 25, 2014).
"Probabilistic Estimate Sequences", 8th workshop on Theory of Randomized Search Heuristics (ThRaSH 2014) Jena, Germany (Apr 4, 2014).
"Randomized Methods in Optimization", 8th Zurich Machine Learning and Data Science Meetup, Zurich, Switzerland (Sep 30, 2014).

"When Conflicting Constraints can be Resolved - the Local Lemma and Satisfiability ", The Institute Colloquium, Institute of Science and Technology (IST Austria), Klosterneuburg, Maria Gugging, Austria (Jan 13, 2014).
"The Counting of Crossing-Free Geometric Graphs - Algorithms and Combinatorics", Pre-Workshop (WALCOM) School on Algorithms and Combinatorics, IIT Chennai, India (Feb 10, 2014).
"The Counting of Crossing-Free Geometric Graphs - Algorithms and Combinatorics”, Summit 240 Conference, Alfréd Rényi Institute of Mathematics, Budapest, Hungary (Jul 10, 2014; invited plenary talk).

"Counting and Enumerating Crossing-free Perfect Matchings", EuroGIGA Final Conference, Freie Universität Berlin, Germany (Feb 21, 2014).
"Counting and Enumerating Crossing-free Geometric Graphs", Japanese-Swiss Workshop on Combinatorics and Computational Geometry, University of Tokyo, Japan (Jun 4, 2014).
"Counting and Enumerating Crossing-free Geometric Graphs", 30th Annual Symposium on Computational Geometry (SoCG), University of Kyoto, Japan (Jun 8, 2014).

Courses and Seminars

Fall 14

See also the Course Catalogue

Spring 14

See also the Course Catalogue

Organization of Workshops etc.


  • Sebastian Stich, Convex Optimization with Random Pursuit
    Advisor: Bernd Gärtner (referee) / Co-referees: Yurii Nesterov, Université catholique de Louvain, Christian L. Müller, New York University, Emo Welzl, ETH Zürich / Defense: Jul 11, 2014.

Master Theses

  • Luca Eggemann, Survey on Random SAT,
    Advisors: Timon Hertli, Emo Welzl / to be completed
  • Nathanael Gutmann, Intersection Restricted Families of Sets,
    Advisor: Emo Welzl / to be completed
  • Isabelle Hurbain, Towards a Derandomization of the PPSZ Algorithm for Multiple Satisfying Assignments,
    Advisor: Timon Hertli / 31.3.2014

Bachelor and Semester Theses / Internship Projects

  • Stephan Ammann, Draw an outerplanar graph and a matching at the same time,
    Advisors: Michael Hoffmann, Vincent Kusters / to be completed
  • Luca Eggemann, A View of Triangulations as Maximal Cliques,
    Advisor: Emo Welzl / 8.5.2014
  • Qinheping Hu, Survey on Partial Satisfaction,
    Advisors: Timon Hertli, Emo Welzl / 22.8.2014
  • Patrick Schnider, Shortest Paths in Disk Coverings,
    Advisors: Michael Hoffmann, Torsten Mütze / 1.1.2014


Editorial Board Member of European J. Combinatorics, Computational Geometry: Theory and Applications, Applied Mathematics Research eXpress.

Mitglied im Ausbildungs- und Beratungszentrum für Informatikunterricht ABZ und im Kinderlabor.
Mobilitätsberater des Departements Informatik

Teach. Assistance Coordinator.
Teach. Assistance Satisfiability of Boolean Formulas - Combinatorics and Algorithms (D-INFK) (Spring 14).

Informatik Koordinator.
Teach. Assistance Algorithms Lab (D-INFK) (Fall 14).
Member of the CGAL Editorial Board.

Program committee member of

Coordinator Mittagsseminar.
Teach. Assistance Polynomials (D-INFK) (Spring 14).
Teach. Assistance Algorithms, Probability, and Computing (D-INFK) (Fall 14).

Elected member of the

Editorial Board member of

Program committee member of

Webmaster www-gremo.

Program committee member of

Teach. Assistance Polyhedral Computation (D-MATH) (Spring 14).
Teach. Assistance Algorithms, Probability, and Computing (D-INFK) (Fall 14).

Teach. Assistance Algorithms Lab (D-INFK) (Fall 14).

Teach. Assistance Data Mining: Learning from Large Data Sets (D-INFK) (Spring 14).
Contact Assistant Geometry: Combinatorics and Algorithms (D-INFK) (Fall 14).

Member of the board (deputy head) of the Department of Computer Science, ETH Zurich.

Editorial/Advisory Board member of

Member (chair, contact person) of selection committees for

  • Assistant Professor of Plant Cell and Developmental Biology/Plant-Microbial Interactions, Department of Biology, ETH Zurich, (chair).
  • Professor of Applied Mathematics, Department of Mathematics, ETH Zurich, (chair).
  • Professor of Biological Systems Theory, Department of Biosystems Science and Engineering, ETH Zurich, (chair).
  • Professor of Computer Science, Computer Science Department, Ecole normale superieure (ENS), Paris, France.
  • Professor of Mathematics, Department of Mathematics, ETH Zurich.
  • Professor / Assistant Professor (Tenure Track) of Networked Systems, Department of Information Technology and Electrical Engineering, ETH Zurich.

Member of the

Program committee member of

  • 14th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT `14), Copenhagen, Denmark (July 2-4, 2014).

Member of ETH Quality Audit Preparation Chapter Review Group "Personal".
Delegierter für Professorenwahlen an der ETH Zürich.

Contact Assistant Algorithms, Probability, and Computing (D-INFK) (Fall 14).


01-Oct-2014 /