Bibliography

Major publications by the team in recent years

• 1N. Bonichon, P. Bose, J.-L. De Carufel, V. Despré, D. Hill, M. Smid.
  
  Improved Routing on the Delaunay Triangulation, in: ESA 2018 - 26th Annual European Symposium on Algorithms, Helsinki, Finland, 2018. [ DOI : 10.4230/LIPIcs.ESA.2018.22 ]
  
  https://hal.archives-ouvertes.fr/hal-01881280
• 2L. Castelli Aleardi, O. Devillers.
  
  Array-based Compact Data Structures for Triangulations: Practical Solutions with Theoretical Guarantees, in: Journal of Computational Geometry, 2018, vol. 9, n^o 1, pp. 247-289. [ DOI : 10.20382/jocg.v9i1a8 ]
  
  https://hal.inria.fr/hal-01846652
• 3N. Chenavier, O. Devillers.
  
  Stretch Factor in a Planar Poisson-Delaunay Triangulation with a Large Intensity, in: Advances in Applied Probability, 2018, vol. 50, n^o 1, pp. 35-56. [ DOI : 10.1017/apr.2018.3 ]
  
  https://hal.inria.fr/hal-01700778
• 4O. Devillers, M. Karavelas, M. Teillaud.
  
  Qualitative Symbolic Perturbation: Two Applications of a New Geometry-based Perturbation Framework, in: Journal of Computational Geometry, 2017, vol. 8, n^o 1, pp. 282–315. [ DOI : 10.20382/jocg.v8i1a11 ]
  
  https://hal.inria.fr/hal-01586511
• 5O. Devillers, S. Lazard, W. Lenhart.
  
  3D Snap Rounding, in: Proceedings of the 34th International Symposium on Computational Geometry, Budapest, Hungary, June 2018, pp. 30:1–30:14. [ DOI : 10.4230/LIPIcs.SoCG.2018.30 ]
  
  https://hal.inria.fr/hal-01727375
• 6R. Imbach, G. Moroz, M. Pouget.
  
  Reliable Location with Respect to the Projection of a Smooth Space Curve, in: Reliable Computing, 2018, vol. 26, pp. 13-55.
  
  https://hal.archives-ouvertes.fr/hal-01920444
• 7I. Iordanov, M. Teillaud.
  
  Implementing Delaunay Triangulations of the Bolza Surface, in: 33rd International Symposium on Computational Geometry (SoCG 2017), Brisbane, Australia, July 2017, pp. 44:1–44:15. [ DOI : 10.4230/LIPIcs.SoCG.2017.44 ]
  
  https://hal.inria.fr/hal-01568002
• 8R. Jha, D. Chablat, L. Baron, F. Rouillier, G. Moroz.
  
  Workspace, Joint space and Singularities of a family of Delta-Like Robot, in: Mechanism and Machine Theory, September 2018, vol. 127, pp. 73-95. [ DOI : 10.1016/j.mechmachtheory.2018.05.004 ]
  
  https://hal.archives-ouvertes.fr/hal-01796066
• 9S. Lazard, M. Pouget, F. Rouillier.
  
  Bivariate triangular decompositions in the presence of asymptotes, in: Journal of Symbolic Computation, 2017, vol. 82, pp. 123–133. [ DOI : 10.1016/j.jsc.2017.01.004 ]
  
  https://hal.inria.fr/hal-01468796
• 10P. Machado Manhães De Castro, O. Devillers.
  
  Expected Length of the Voronoi Path in a High Dimensional Poisson-Delaunay Triangulation, in: Discrete and Computational Geometry, 2018, vol. 60, n^o 1, pp. 200–219. [ DOI : 10.1007/s00454-017-9866-y ]
  
  https://hal.inria.fr/hal-01477030

Publications of the year

Doctoral Dissertations and Habilitation Theses

• 11I. Iordanov.
  
  Delaunay triangulations of a family of symmetric hyperbolic surfaces in practice, Université de Lorraine, March 2019.
  
  https://hal.inria.fr/tel-02072155

Articles in International Peer-Reviewed Journals

• 12B. Bukh, X. Goaoc.
  
  Shatter functions with polynomial growth rates, in: SIAM Journal on Discrete Mathematics, 2019, vol. 33, n^o 2, pp. 784–794, https://arxiv.org/abs/1701.06632, forthcoming. [ DOI : 10.1137/17M1113680 ]
  
  https://hal.inria.fr/hal-02050524
• 13J. A. De Loera, X. Goaoc, F. Meunier, N. Mustafa.
  
  The discrete yet ubiquitous theorems of Caratheodory, Helly, Sperner, Tucker, and Tverberg, in: Bulletin of the American Mathematical Society, 2019, vol. 56, pp. 415-511, https://arxiv.org/abs/1706.05975. [ DOI : 10.1090/bull/1653 ]
  
  https://hal.inria.fr/hal-02050466
• 14V. Despré, F. Lazarus.
  
  Computing the Geometric Intersection Number of Curves, in: Journal of the ACM (JACM), November 2019, vol. 66, n^o 6, pp. 1-49, https://arxiv.org/abs/1511.09327 - 59 pages, 33 figures, revised version accepted to Journal of the ACM. The time complexity for testing if a curve is homotopic to a simple one has been reduced to $O(n+\ell log\ell )$. [ DOI : 10.1145/3363367 ]
  
  https://hal.archives-ouvertes.fr/hal-02385419
• 15X. Goaoc, P. Paták, Z. Patáková, M. Tancer, U. Wagner.
  
  Shellability is NP-complete, in: Journal of the ACM (JACM), 2019, vol. 66, n^o 3, https://arxiv.org/abs/1711.08436, forthcoming. [ DOI : 10.1145/3314024 ]
  
  https://hal.inria.fr/hal-02050505

International Conferences with Proceedings

• 16J.-D. Boissonnat, O. Devillers, K. Dutta, M. Glisse.
  
  Randomized incremental construction of Delaunay triangulations of nice point sets, in: ESA 2019 - 27th Annual European Symposium on Algorithms, Munich, Germany, September 2019. [ DOI : 10.4230/LIPIcs.ESA.2019.22 ]
  
  https://hal.inria.fr/hal-02185566
• 17K. Buchin, P. M. M. de Castro, O. Devillers, M. Karavelas.
  
  Hardness results on Voronoi, Laguerre and Apollonius diagrams, in: CCCG 2019 - Canadian Conference on Computational Geometry, Edmonton, Canada, 2019.
  
  https://hal.inria.fr/hal-02186693
• 18D. Chablat, G. Moroz, F. Rouillier, P. Wenger.
  
  Using Maple to analyse parallel robots, in: Maple Conference 2019, Waterloo, Canada, October 2019.
  
  https://hal.inria.fr/hal-02406703
• 19S. Diatta, G. Moroz, M. Pouget.
  
  Reliable Computation of the Singularities of the Projection in R3 of a Generic Surface of R4, in: MACIS 2019, Gebze-Istanbul, Turkey, 2019.
  
  https://hal.inria.fr/hal-02406758
• 20X. Goaoc, A. Holmsen, C. Nicaud.
  
  An experimental study of forbidden patterns in geometric permutations by combinatorial lifting, in: 35th International Symposium on Computational Geometry, Portland, United States, 2019, https://arxiv.org/abs/1903.03014. [ DOI : 10.4230/LIPIcs.SoCG.2019.40 ]
  
  https://hal.inria.fr/hal-02050539
• 21V. Ledoux, G. Moroz.
  
  Evaluation of Chebyshev polynomials on intervals and application to root finding, in: Mathematical Aspects of Computer and Information Sciences 2019, Gebze, Turkey, November 2019, https://arxiv.org/abs/1912.05843.
  
  https://hal.inria.fr/hal-02405752

Conferences without Proceedings

• 22O. Devillers, C. Duménil.
  
  A Poisson sample of a smooth surface is a good sample, in: EuroCG 2019, Utrecht, Netherlands, February 2019.
  
  https://hal.archives-ouvertes.fr/hal-02394144
• 23R. Imbach, M. Pouget, C. Yap.
  
  Clustering Complex Zeros of Triangular System of Polynomials, in: CASC 2019, Moscow, Russia, 2019, https://arxiv.org/abs/1806.10164.
  
  https://hal.archives-ouvertes.fr/hal-01825708
• 24G. Krait, S. Lazard, G. Moroz, M. Pouget.
  
  Numerical Algorithm for the Topology of Singular Plane Curves, in: EuroCG 2019, Utrecht, Netherlands, 2019.
  
  https://hal.archives-ouvertes.fr/hal-02294028

Internal Reports

• 25I. Barany, M. Fradelizi, X. Goaoc, A. Hubard, G. Rote.
  
  Random polytopes and the wet part for arbitrary probability distributions, Rényi Institute of Mathematics ; University College London ; Université Paris-Est ; Université de Lorraine ; Freie Universität Berlin, 2019, https://arxiv.org/abs/1902.06519.
  
  https://hal.inria.fr/hal-02050632
• 26J.-D. Boissonnat, O. Devillers, K. Dutta, M. Glisse.
  
  Randomized incremental construction of Delaunay triangulations of nice point sets, Inria, 2019.
  
  https://hal.inria.fr/hal-01950119
• 27P. Bose, J.-L. De Carufel, O. Devillers.
  
  Expected Complexity of Routing in Θ 6 and Half-Θ 6 Graphs, Inria, 2019, 18 p, https://arxiv.org/abs/1910.14289.
  
  https://hal.inria.fr/hal-02338733
• 28V. Despré, J.-M. Schlenker, M. Teillaud.
  
  Flipping Geometric Triangulations on Hyperbolic Surfaces, Inria, December 2019, https://arxiv.org/abs/1912.04640.
  
  https://hal.inria.fr/hal-02400219
• 29O. Devillers, P. Duchon, M. Glisse, X. Goaoc.
  
  On Order Types of Random Point Sets, Inria, 2019, https://arxiv.org/abs/1812.08525.
  
  https://hal.inria.fr/hal-01962093

Other Publications

• 30L. Valque.
  
  3D Snap Rounding, Université de Lyon, June 2019.
  
  https://hal.inria.fr/hal-02393625

References in notes

• 31D. Attali, J.-D. Boissonnat, A. Lieutier.
  
  Complexity of the Delaunay triangulation of points on surfaces: the smooth case, in: Proceedings of the 19th Annual Symposium on Computational Geometry, 2003, pp. 201–210. [ DOI : 10.1145/777792.777823 ]
  
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• 32F. Aurenhammer, R. Klein, D. Lee.
  
  Voronoi diagrams and Delaunay triangulations, World Scientific, 2013.
  
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• 33M. Bogdanov, O. Devillers, M. Teillaud.
  
  Hyperbolic Delaunay complexes and Voronoi diagrams made practical, in: Journal of Computational Geometry, 2014, vol. 5, pp. 56–85.
• 34M. Bogdanov, M. Teillaud, G. Vegter.
  
  Delaunay triangulations on orientable surfaces of low genus, in: Proceedings of the 32nd International Symposium on Computational Geometry, 2016, pp. 20:1–20:15. [ DOI : 10.4230/LIPIcs.SoCG.2016.20 ]
  
  https://hal.inria.fr/hal-01276386
• 35J.-D. Boissonnat, O. Devillers, S. Hornus.
  
  Incremental construction of the Delaunay graph in medium dimension, in: Proceedings of the 25th Annual Symposium on Computational Geometry, 2009, pp. 208–216.
  
  http://hal.inria.fr/inria-00412437/
• 36J.-D. Boissonnat, O. Devillers, R. Schott, M. Teillaud, M. Yvinec.
  
  Applications of random sampling to on-line algorithms in computational geometry, in: Discrete and Computational Geometry, 1992, vol. 8, pp. 51–71.
  
  http://hal.inria.fr/inria-00090675
• 37Y. Bouzidi, S. Lazard, G. Moroz, M. Pouget, F. Rouillier, M. Sagraloff.
  
  Improved algorithms for solving bivariate systems via Rational Univariate Representations, Inria, February 2015.
  
  https://hal.inria.fr/hal-01114767
• 38Y. Bouzidi, S. Lazard, M. Pouget, F. Rouillier.
  
  Separating linear forms and Rational Univariate Representations of bivariate systems, in: Journal of Symbolic Computation, May 2015, vol. 68, pp. 84-119. [ DOI : 10.1016/j.jsc.2014.08.009 ]
  
  https://hal.inria.fr/hal-00977671
• 39P. Calka.
  
  Tessellations, convex hulls and Boolean model: some properties and connections, Université René Descartes - Paris V, 2009, Habilitation à diriger des recherches.
  
  https://tel.archives-ouvertes.fr/tel-00448249
• 40M. Caroli, P. M. M. de Castro, S. Loriot, O. Rouiller, M. Teillaud, C. Wormser.
  
  Robust and Efficient Delaunay Triangulations of Points on or Close to a Sphere, in: Proceedings of the 9th International Symposium on Experimental Algorithms, Lecture Notes in Computer Science, 2010, vol. 6049, pp. 462–473.
  
  http://hal.inria.fr/inria-00405478/
• 41M. Caroli, M. Teillaud.
  
  3D Periodic Triangulations, in: CGAL User and Reference Manual, CGAL Editorial Board, 2009. [ DOI : 10.1007/978-3-642-04128-0_6 ]
  
  http://doc.cgal.org/latest/Manual/packages.html#PkgPeriodic3Triangulation3Summary
• 42M. Caroli, M. Teillaud.
  
  Computing 3D Periodic Triangulations, in: Proceedings of the 17th European Symposium on Algorithms, Lecture Notes in Computer Science, 2009, vol. 5757, pp. 59–70.
• 43M. Caroli, M. Teillaud.
  
  Delaunay Triangulations of Point Sets in Closed Euclidean $d$-Manifolds, in: Proceedings of the 27th Annual Symposium on Computational Geometry, 2011, pp. 274–282. [ DOI : 10.1145/1998196.1998236 ]
  
  https://hal.inria.fr/hal-01101094
• 44B. Chazelle and others.
  
  Application challenges to computational geometry: CG impact task force report, in: Advances in Discrete and Computational Geometry, Providence, B. Chazelle, J. E. Goodman, R. Pollack (editors), Contemporary Mathematics, American Mathematical Society, 1999, vol. 223, pp. 407–463.
• 45P. Chossat, G. Faye, O. Faugeras.
  
  Bifurcation of hyperbolic planforms, in: Journal of Nonlinear Science, 2011, vol. 21, pp. 465–498.
  
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• 46V. Damerow, C. Sohler.
  
  Extreme points under random noise, in: Proceedings of the 12th European Symposium on Algorithms, 2004, pp. 264–274.
  
  http://dx.doi.org/10.1007/978-3-540-30140-0_25
• 47O. Devillers.
  
  The Delaunay hierarchy, in: International Journal of Foundations of Computer Science, 2002, vol. 13, pp. 163-180.
  
  https://hal.inria.fr/inria-00166711
• 48O. Devillers, M. Glisse, X. Goaoc.
  
  Complexity analysis of random geometric structures made simpler, in: Proceedings of the 29th Annual Symposium on Computational Geometry, June 2013, pp. 167-175. [ DOI : 10.1145/2462356.2462362 ]
  
  https://hal.inria.fr/hal-00833774
• 49O. Devillers, M. Glisse, X. Goaoc, R. Thomasse.
  
  On the smoothed complexity of convex hulls, in: Proceedings of the 31st International Symposium on Computational Geometry, Lipics, 2015. [ DOI : 10.4230/LIPIcs.SOCG.2015.224 ]
  
  https://hal.inria.fr/hal-01144473
• 50L. Dupont, D. Lazard, S. Lazard, S. Petitjean.
  
  Near-optimal parameterization of the intersection of quadrics: I. The generic algorithm, in: Journal of Symbolic Computation, 2008, vol. 43, n^o 3, pp. 168–191. [ DOI : 10.1016/j.jsc.2007.10.006 ]
  
  http://hal.inria.fr/inria-00186089/en
• 51L. Dupont, D. Lazard, S. Lazard, S. Petitjean.
  
  Near-optimal parameterization of the intersection of quadrics: II. A classification of pencils, in: Journal of Symbolic Computation, 2008, vol. 43, n^o 3, pp. 192–215. [ DOI : 10.1016/j.jsc.2007.10.012 ]
  
  http://hal.inria.fr/inria-00186090/en
• 52L. Dupont, D. Lazard, S. Lazard, S. Petitjean.
  
  Near-Optimal Parameterization of the Intersection of Quadrics: III. Parameterizing Singular Intersections, in: Journal of Symbolic Computation, 2008, vol. 43, n^o 3, pp. 216–232. [ DOI : 10.1016/j.jsc.2007.10.007 ]
  
  http://hal.inria.fr/inria-00186091/en
• 53M. Glisse, S. Lazard, J. Michel, M. Pouget.
  
  Silhouette of a random polytope, in: Journal of Computational Geometry, 2016, vol. 7, n^o 1, 14 p.
  
  https://hal.inria.fr/hal-01289699
• 54M. Hemmer, L. Dupont, S. Petitjean, E. Schömer.
  
  A complete, exact and efficient implementation for computing the edge-adjacency graph of an arrangement of quadrics, in: Journal of Symbolic Computation, 2011, vol. 46, n^o 4, pp. 467-494. [ DOI : 10.1016/j.jsc.2010.11.002 ]
  
  https://hal.inria.fr/inria-00537592
• 55J. Hidding, R. van de Weygaert, G. Vegter, B. J. Jones, M. Teillaud.
  
  Video: the sticky geometry of the cosmic web, in: Proceedings of the 28th Annual Symposium on Computational Geometry, 2012, pp. 421–422.
• 56J. B. Hough, M. Krishnapur, Y. Peres, B. Virág.
  
  Determinantal processes and independence, in: Probab. Surv., 2006, vol. 3, pp. 206-229.
• 57I. Iordanov, M. Teillaud.
  
  Implementing Delaunay triangulations of the Bolza surface, in: Proceedings of the Thirty-third International Symposium on Computational Geometry, 2017, pp. 44:1–44:15. [ DOI : 10.4230/LIPIcs.SoCG.2017.44 ]
  
  https://hal.inria.fr/hal-01568002
• 58S. Lazard, L. M. Peñaranda, S. Petitjean.
  
  Intersecting quadrics: an efficient and exact implementation, in: Computational Geometry: Theory and Applications, 2006, vol. 35, n^o 1-2, pp. 74–99.
• 59S. Lazard, M. Pouget, F. Rouillier.
  
  Bivariate triangular decompositions in the presence of ssymptotes, Inria, September 2015.
  
  https://hal.inria.fr/hal-01200802
• 60M. Mazón, T. Recio.
  
  Voronoi diagrams on orbifolds, in: Computational Geometry: Therory and Applications, 1997, vol. 8, pp. 219–230.
• 61A. Pellé, M. Teillaud.
  
  Periodic meshes for the CGAL library, 2014, International Meshing Roundtable, Research Note.
  
  https://hal.inria.fr/hal-01089967
• 62G. Rong, M. Jin, X. Guo.
  
  Hyperbolic centroidal Voronoi tessellation, in: Proceedings of the ACM Symposium on Solid and Physical Modeling, 2010, pp. 117–126.
  
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• 63A. Rényi, R. Sulanke.
  
  Über die konvexe Hülle von $n$ zufällig gerwähten Punkten I, in: Z. Wahrsch. Verw. Gebiete, 1963, vol. 2, pp. 75–84.
  
  http://dx.doi.org/10.1007/BF00535300
• 64A. Rényi, R. Sulanke.
  
  Über die konvexe Hülle von $n$ zufällig gerwähten Punkten II, in: Z. Wahrsch. Verw. Gebiete, 1964, vol. 3, pp. 138–147.
  
  http://dx.doi.org/10.1007/BF00535973
• 65F. Sausset, G. Tarjus, P. Viot.
  
  Tuning the fragility of a glassforming liquid by curving space, in: Physical Review Letters, 2008, vol. 101, pp. 155701(1)–155701(4).
  
  http://dx.doi.org/10.1103/PhysRevLett.101.155701
• 66M. Schindler, A. C. Maggs.
  
  Cavity averages for hard spheres in the presence of polydispersity and incomplete data, in: The European Physical Journal E, 2015, pp. 38–97.
  
  http://dx.doi.org/10.1103/PhysRevE.88.022315
• 67D. A. Spielman, S.-H. Teng.
  
  Smoothed analysis: why the simplex algorithm usually takes polynomial time, in: Journal of the ACM, 2004, vol. 51, pp. 385–463.
  
  http://dx.doi.org/10.1145/990308.990310
• 68M. Teillaud.
  
  Towards dynamic randomized algorithms in computational geometry, Lecture Notes Comput. Sci., Springer-Verlag, 1993, vol. 758. [ DOI : 10.1007/3-540-57503-0 ]
  
  http://www.springer.com/gp/book/9783540575030
• 69R. van de Weygaert, G. Vegter, H. Edelsbrunner, B. J. Jones, P. Pranav, C. Park, W. A. Hellwing, B. Eldering, N. Kruithof, E. Bos, J. Hidding, J. Feldbrugge, E. ten Have, M. van Engelen, M. Caroli, M. Teillaud.
  
  Alpha, Betti and the megaparsec universe: on the homology and topology of the cosmic web, in: Transactions on Computational Science XIV, Lecture Notes in Computer Science, Springer-Verlag, 2011, vol. 6970, pp. 60–101.
  
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