Department of Computer Science

Theory of Combinatorial Algorithms
Prof. Emo Welzl
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    2013
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CGAL Geometric Algorithms Library
  Activity Report 2013

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


Personnel



Guests


  • Christof Lutteroth, University of Auckland, New Zealand (Jan 7)
    Constraint-based User Interfaces - Specification and Solving (Mittagsseminar, Jan 7, 2013)
  • Jan Foniok, Queen's University, Kingston, Ontario, Canada (Jan 7-10)
    Adjoint functors in graph theory (Mittagsseminar, Jan 10, 2013)
  • Sonoko Moriyama, Tohoku University, Sendai, Japan (Mar 4-12)
  • Jan Vondrák, IBM Almaden Research Center, San Jose, USA (Mar 22)
    Online Algorithms for Welfare Maximization in Allocation Problems (Mittagsseminar, Mar 22, 2013)
  • Dominik Scheder, Aarhus University, Danmark (Mar 22-28)
    After Traxler and Amano: The relationship between average sensitivity, clause size, and solution density (Mittagsseminar, Mar 27, 2013)
  • Heuna Kim, Korea Advanced Institute of Science and Technology, Korea (Mar 28)
    On the Numbers of Edges of a Fan-Crossing Free Graph (Mittagsseminar, Mar 28, 2013)
  • Antonis Thomas, University of Edinburgh, UK (Apr 4-5)
    A Pure Nash Equilibria and Treewidth (Mittagsseminar, Apr 4, 2013)
  • Matias Korman, Universitat Politècnica de Catalunya, Barcelona, Spain (Apr 14-19)
    On the Complexity of Barrier Resilience for Fat Regions (Mittagsseminar, Apr 16, 2013)
  • József Solymosi, University of British Columbia, Vancouver, Canada (Apr 29 - May 4)
    On Erdos' unit distances problem (Mittagsseminar, Apr 30, 2013)
  • Uli Wagner, Institute of Science and Technology Austria, Klosterneuburg, Austria (Apr 29 - May 4)
    Helly vs. Betti (Mittagsseminar, May 2, 2013)
  • Nati Linial, Hebrew University of Jerusalem, Israel (Apr 29 - May 4)
    Simplicial complexes - A combinatorial perspective (Mittagsseminar, May 3, 2013)
  • Tillmann Miltzow, FU Berlin, Germany (Mai 1 - Jun 30)

Grants


  • Minors and Embeddability of Simplicial Complexes

    (Financed by the Swiss National Science Foundation). The goal of this project is to study higher dimensional analogues of graph planarity (embeddings of simplicial complexes into Euclidean spaces) both from an algorithmic and from a combinatorial point of view.
    Embeddings of simplicical complexes into Euclidean spaces are a classical topic in geometric topology (closely related to the classification of embeddings up to ambient isotopy, the most famous special case of which is classical know theory). The most basic case of the embeddability problem, graph planarity, is also a fundamental topic in graph theory, discrete geometry, and theoretical computer science and has been studied intensively both from a structural and from an algorithmic point of view (including close connections to the theory of graph minors and (linear time) algorithms for planarity testing, to mention just two aspects most relevant to this project). Equally important in discrete geometry is the study of the quantitative failure of planarity, i.e., crossing numbers, and relations to graph parameters such as edge expansion and bisection width.
    In this project, we investigate higher-dimensional analogues of these notions and problems. Typical questions include: For which dimensions k and d is there an algorithm that decides if a given k-dimensional complex embeds into d-dimensional Euclidean space? When is the problem computationally intractable or even undecidable? What is the maximum complexity (number of simplices, in terms of the number of vertices, say) of a simplicial complex that embeds into d-space? What are the connections between the eigenvalues of the Laplacian of a simplicial complex and its embeddability properties?

    Contact: U. Wagner

  • 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

  • Computational Geometric Learning

    (Financed by European Commission). High dimensional geometric data are ubiquitous in science and engineering, and thus processing and analyzing them is a core task in these disciplines. The Computational Geometric Learning project (CG Learning) aims at extending the success story of geometric algorithms with guarantees, as achieved in the CGAL library and the related EU funded research projects, to spaces of high dimensions. This is not a straightforward task. For many problems, no efficient algorithms exist that compute the exact solution in high dimensions. This behavior is commonly called the curse of dimensionality. We plan to address the curse of dimensionality by focusing on inherent structure in the data like sparsity or low intrinsic dimension, and by resorting to fast approximation algorithms. The following two kinds of approximation guarantee are particularly desirable: first, the solution approximates an objective better if more time and memory resources are employed (algorithmic guarantee), and second, the approximation gets better when the data become more dense and/or more accurate (learning theoretic guarantee). To lay the foundation of a new field---computational geometric learning---we will follow an approach integrating both theoretical and practical developments, the latter in the form of the construction of a high quality software library and application software.

    Contact: B. Gärtner, C. Müller


Publications


  • Books

  • Journals (with refereeing)

    O. Aichholzer, T. Hackl, M. Hoffmann, C. Huemer, A. Pór, F. Santos, B. Speckmann, B. Vogtenhuber, Maximizing maximal angles for plane straight-line graphs, Computational Geometry: Theory and Applications 46:1 (2013), 17-28.

    O. Aichholzer, T. Hackl, M. Hoffmann, A. Pilz, G. Rote, B. Speckmann, B. Vogtenhuber, Plane Graphs with Parity Constraints, Graphs and Combinatorics, to appear.

    A. Baertschi, S. Suri, Conflict-free chromatic art gallery coverage, Algorithmica (2012), to appear.

    K. Fukuda, H. Miyata, and S. Moriyama, Complete enumeration of small realizable oriented matroids, Discrete and Computational Geometry (2012), to appear.

    H. Gebauer, On the Construction of 3-Chromatic Hypergraphs with Few Edges, Journal of Combinatorial Theory Series A (2012), to appear.

    J. Giesen, M. Jaggi, S. Laue, Approximating Parameterized Convex Optimization Problems, ACM Transactions on Algorithms (2012), to appear.

    M. Hoffmann and Cs.D. Tóth, Vertex-Colored Encompassing Graphs Graphs and Combinatorics, to appear.

    Y.-L. Hwong, J. Keiren, V. Kusters, S. Leemans, T. Willemse, Analysing the Control Software of the Compact Muon Solenoid Experiment at the Large Hadron Collider, Science of Computer Programming, to appear.

    J. Matoušek, The determinant bound for discrepancy is almost tight, Proceedings of the American Mathematical Society (2012), to appear.

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

    A. Razen, E. Welzl, On the Number of Crossing-Free Partitions, Computational Geometry - Theory and Applications (2012), to appear.

    H. Tyagi, E. Vural, P. Frossard, Tangent space estimation bounds for smooth manifolds, IMA Journal of Mathematical Control and Information (2013), to appear.

    M. Sharir, A. Sheffer, E. Welzl, Counting Plane Graphs: Perfect Matchings, Spanning Cycles, and Kasteleyn's Technique, Journal of Combinatorial Theory, Series A 120:4 (2013), 777-794.

    U. Wagner, Minors, Embeddability, and Extremal Problems for Hypergraphs, Thirty Essays on Geometric Graph Theory, ed. J. Pach, (2012), 569-607.

  • Conference Proceedings (with selection process)

    A. Asinowski, J. Cardinal, N. Cohen, S. Collette, T. Hackl, M. Hoffmann, K. Knauer, S. Langerman, M. Lason, P. Micek, G. Rote and T. Ueckerdt, Coloring Hypergraphs Induced by Dynamic Point Sets and Bottomless Rectangles, Proc. 13th Algorithms and Data Structures Symposium (WADS) (2013), to appear.

    M. Čadek, M. Krčál, J. Matoušek, L. Vokřínek, U. Wagner, Extending continuous maps: polynomiality and undecidability (extended abstract), Proc. 45rd annual ACM symposium on Theory of computing (STOC) (2013), to appear.

    M. Geyer, M. Hoffmann, M. Kaufmann, V. Kusters, Planar Packing of Binary Trees, Proc. 13th Algorithms and Data Structures Symposium (WADS) (2013), to appear.

    H. Tyagi, E. Vural, P. Frossard, Tangent space estimation bounds for smooth manifolds, 10th International Conference on Sampling Theory and Applications (SAMPTA) (2013), to appear.

  • Other (including submitted work)

    C. Ambühl, B. Gärtner, B. von Stengel, Optimal Lower Bounds for Projective List Update Algorithms, (2012), submitted.

    B. Bukh, J. Matoušek, Erdős-Szekeres-type statements: Ramsey function and decidability in dimension 1, (2012), submitted.

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

    M. Čadek, M. Krčál, J. Matoušek, L. Vokřínek, U. Wagner, Extendability of continuous maps is undecidable, (2012).

    J. Cardinal, M. Hoffmann, V. Kusters, On Universal Point Sets for Planar Graphs, Proc. Thailand-Japan Joint Conference on Computational Geometry and Graphs (TJJCCGG), (2012), to appear.

    P. Cheilaris, S. Smorodinsky, M. Sulovský, The potential to improve the choice: list conflict-free coloring for geometric hypergraphs, (2011), submitted.

    J. Foniok, B. Gärtner, L. Klaus, M. Sprecher, Counting Unique-Sink Orientations, (2011), submitted.

    P. Frossard, H. Tyagi, E. Vural, Tangent space estimation for smooth embeddings of Riemannian manifolds, (2012), submitted.

    B. Gärtner, C. Müller, S. Stich, Optimization of Convex Functions with Random Pursuit, (2011), submitted.

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

    B. Gärtner, H. Tyagi, Continuum armed bandit problem of few variables in high dimensions, (2013).

    M. Geyer, M. Kaufmann, V. Kusters, M. Hoffmann, C. D. Tóth, Planar Packing of Binary Trees, (2012), submitted.

    X. Goaoc, J. Matoušek, P. Paták, Z. Safernová, Simplifying inclusion-exclusion formulas, (2012), submitted.

    Y.-L. Hwong, V. Kusters, T. Willemse, Analysing the control software of the compact muon solenoid experiment at the large hadron collider, (2011), submitted.

    J. Matoušek, U. Wagner, On Gromov's method of selecting heavily covered points, (2011), submitted.


Lectures


B. GÄRTNER
"Computational Geometry: Linear Programming", Mini-Course, IMPA Summer Program, Rio de Janeiro, Brazil (Jan 21-25, 2013).
"The Linear Complementarity Problem: An Advertisement", Graduiertenkolleg "Methods for Discrete Structures", FU Berlin, Germany (May 6, 2013).

V. KUSTERS
"On Universal Point Sets for Planar Graphs", Noon seminar at Technische Universiteit Eindhoven, Netherlands (Jan 8, 2013).

E. WELZL
"The Counting of Crossing-Free Configurations in the Plane", CS-Colloquium, Fakultät für Informatik, Universität Wien, Austria (Mar 20, 2013).

Courses and Seminars


Spring 13

See also the Course Catalogue

Fall 12

See also the Course Catalogue

Spring 12

See also the Course Catalogue


Organization of Workshops etc.


  • 11th Gremo Workshop on Open Problems 2013, Sellamatt (SG), Switzerland, Jun 24 - 28, 2013, (Michael Hoffmann).
  • Workshop on Combinatorics and Probability, Mathematisches Forschungsinstitut Oberwolfach, Germany, Apr 14 - 20, 2013, (Bela Bollobas, Michael Krivelevich, Emo Welzl)

Dissertations



Master Theses


  • Akaki Mamageishvili, 3-Dimensional thickenings and embeddings of 2-dimensional complexes,
    Advisor: Uli Wagner / 9.4.2013
  • Marco Nembrini, Lossless Data Compression (LDC),
    Advisors: Marcus Hutter (Australian National University, Canberra), Emo Welzl / 1.3.2013
  • Manuel Wettstein, Algorithms for Counting Crossing-free Configurations,
    Advisor: Emo Welzl / 5.4.2013
  • May Szedlak, An Alternative Model for Random Hypergraphs,
    Advisor: Anna Gundert / to be completed
  • Hörður Yngvason, A study of zonotopes with applications in biomechanics,
    Advisors: Bernd Gärtner, Komei Fukuda / to be completed

Bachelor and Semester Theses / Internship Projects


  • Vitor Bosshard, Regular Unique Sink Orientations,
    Advisor: Bernd Gärtner / to be completed
  • Isabelle Hurbain, Understanding the PPSZ Algorithm for Clause Satisfaction Problems,
    Advisor: Timon Hertli / to be completed
  • Steve Muller, Optimal Randomized Algorithms,
    Advisor: Emo Welzl / to be completed
  • Nico Neureiter, Verifying Unsatisfiability Using a Certificate,
    Advisor: Timon Hertli / to be completed
  • Patrick Schnider, Shortest Paths in Disk Coverings,
    Advisors: Michael Hoffmann, Torsten Mütze / to be completed.

Miscellaneous


A. FRANCKE
Teach. Assistance Informatics (for Biology and Pharmacy) (D-BIOL, D-PHARM) (Spring 13).

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

Program committee member of

B. GÄRTNER
Member of the CGAL Editorial Board.
Program committee member of

Mitglied im Ausbildungs- und Beratungszentrum für Informatikunterricht ABZ und im Kinderlabor.
Mobilitätsberater des Departements Informatik Kursleiter "Programmieren für Kinder mit Scratch", Primarschule Oetwil am See, Switzerland (Jan 7 - Apr 16, 2013).

T. HERTLI
Teach. Assistance Coordinator.
Teach. Assistance Satisfiability of Boolean Formulas - Combinatorics and Algorithms (D-INFK) (Spring 13).

M. HOFFMANN
Informatik Koordinator.
Member of the CGAL Editorial Board.

V. KUSTERS
Coordinator Mittagsseminar.
Research visit with Bettina Speckmann at Technische Universiteit Eindhoven, Netherlands (Jan 7-11, 2013).
Teach. Assistance Geometric Graphs: Combinatorics and Algorithms (D-INFK) (Spring 13).
Contact Assistant Algorithms, Probability, and Computing (D-INFK) (Fall 13).

J. MATOUŠEK
Elected member of the

Editorial Board member of

Program committee member of

S. STICH
Webmaster www-gremo.
Contact Assistant Informatics (D-MATH, D-PHYS) (Fall 13).
Teach. Assistance Algorithms Lab (D-INFK) (Fall 13).

H. TYAGI
Teach. Assistance Informatics II (D-BAUG) (Spring 13).

E. WELZL
Head of Institute of Theoretical Computer Science, ETH Zurich, and member of the board of the Department of Computer Science, ETH Zurich.

Coreferee for dissertations of

  • Daniel Werner, Computational Aspects of some Problems from Discrete Geometry in Higher Dimensions, (Fachbereich Mathematik und Informatik, Berlin Free University; defense: January 13, 2013; referee: Günter Rote)

Editorial/Advisory Board member of

Member (chair, contact person) of selection committees for

  • 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.

Member of the

Program committee member of

  • 25th Canadian Conference on Computational Geometry (CCCG `13), Waterloo, Canada (August 7-11, 2013).
  • 8th International Conference on Algorithms and Complexity (CIAC `13), Barcelona, Spain (May 22-24, 2013).

Member of ETH Quality Audit Preparation Chapter Review Group "Personal".

Delegierter für Professorenwahlen an der ETH Zürich.
Mitglied der Unterrichtskommission des Departements Informatik der ETH Zürich.


Software


21-Dec-2012 / stich@inf.ethz.ch