19 citations · 59 across the 23 of their papers we have counts for
14 papers · 1 filter
Intersection patterns of set systems on manifolds with slowly growing homological shatter functions
Sergey Avvakumov, Marguerite Bin, Xavier Goaoc
A theorem of Matoušek asserts that for any , any set system whose shatter function is enjoys a fractional Helly theorem of order : in the -wise intersection…
Hitting and Covering Affine Families of Convex Polyhedra, with Applications to Robust Optimization
Jean Cardinal, Xavier Goaoc, Sarah Wajsbrot
Geometric hitting set problems, in which we seek a smallest set of points that collectively hit a given set of ranges, are ubiquitous in computational geometry. Most often, the set…
A canonical tree decomposition for order types, and some applications
Mathilde Bouvel, Valentin Féray, Xavier Goaoc +1
We introduce and study a notion of decomposition of planar point sets (or rather of their chirotopes) as trees decorated by smaller chirotopes. This decomposition is based on the c…
Intersection patterns in spaces with a forbidden homological minor
Xavier Goaoc, Andreas F. Holmsen, Zuzana Patáková
In this paper we study generalizations of classical results on intersection patterns of set systems in , such as the fractional Helly theorem or the -theorem,…
Convex Hulls of Random Order Types
Xavier Goaoc, Emo Welzl
We establish the following two main results on order types of points in general position in the plane (realizable simple planar order types, realizable uniform acyclic oriented mat…
An Experimental Study of Forbidden Patterns in Geometric Permutations by Combinatorial Lifting
Xavier Goaoc, Andreas Holmsen, Cyril Nicaud
We study the problem of deciding if a given triple of permutations can be realized as geometric permutations of disjoint convex sets in . We show that this question,…