ANR project ADDS

Algorithms for Multi-Dimensional Data via Sketches.



Massive geometric data is increasingly common thanks to the proliferation of ubiquitous data-collecting devices, presenting vexing challenges for algorithmic processing. Our approach to deal with this amount of data is to, given an approximation parameter eps, construct a small-sized sketch S of the input data, then solve the problem on S, and finally extend this solution to a (1+eps)-approximation to the original problem. Our research is divided into three parts, requiring expertise in statistics, computational geometry, learning, combinatorics, and algorithms. First, we consider the combinatorial properties of geometric data that are relevant to build compact sketches. Second, we consider the time and space complexities of constructing accurate sketches of data in high dimensions, based on the combinatorial and geometric understanding. Finally, we show how to use the small sketches in order to improve the accuracy and running time of optimization algorithms.



Team





Doctorants

Funded:

Associated:



Internships:



Scientific Visits and Collaborations.



Meetings, Workshops



Invited Talks



Software

  1. Shadoks: Shadoks approach to low-makespan coordinated motion planning.

  2. LowCrossingMatchings: Matchings with low crossing numbers.

  3. poLYG: Polygon area minimization and maximization as in CG:SHOP challenge 2019.



Publications (HAL pour les publications sous ADDS)


    All related publications need to mention the support from the project as follows:
    Supported by the French ANR PRC grant ADDS (ANR-19-CE48-0005).

    To appear

  1. Maximizing Covered Area in a Euclidean Plane with Connectivity Constraint. (Chien-Chung Huang, Mathieu Mari, Claire Mathieu, Joseph Mitchell, Nabil H. Mustafa).
    Theory of Computing (TOC), to appear.

  2. A Tight Analysis of Geometric Local Search. (Bruno Jartoux, Nabil H. Mustafa).
    Discrete & Computational Geometry (DCG), to appear.

    2021

  3. Shadoks Approach to Low-Makespan Coordinated Motion Planning. (Loďc Crombez, Guilherme D. da Fonseca, Yan Gerard, Aldo Gonzalez-Lorenzo, Pascal Lafourcade, Luc Libralesso).
    Proc. of the 37th ACM Symposium on Computational Geometry (SoCG '21), 2021.
  4. Escaping the Curse of Spatial Partitioning: Matchings With Low Crossing Numbers and Their Applications. (Monika Csikos, Nabil H. Mustafa).
    Proc. of the 37th ACM Symposium on Computational Geometry (SoCG '21), 2021.
  5. Tverberg Theorems over Discrete Sets of Points. (Jesús A. De Loera, Thomas Hogan, Frédéric Meunier, Nabil H. Mustafa).
    Book chapter in Contemporary Mathematics: Polytopes and Discrete Geometry, AMS, 2021.

    2020

  6. Optimal Bound on the Combinatorial Complexity of Approximating Polytopes. (Rahul Arya, Sunil Arya, Guilherme D. da Fonseca, David Mount).
    ACM-SIAM Symposium on Discrete Algorithms (SODA), 2020.

  7. Efficient Algorithms for Battleship. (Loic Crombez, Guilherme D. da Fonseca, Yan Gerard).
    International Conference on Fun with Algorithms (FUN), 2020.

  8. An Application of the Universality Theorem for Tverberg Partitions to Data Depth and Hitting Convex Sets. (Imre Barany, Nabil H. Mustafa).
    Computational Geometry: Theory and Applications, 2020.