4 papers · 1 filter
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,…
Intersection patterns of set systems on manifolds with slowly growing homological shatter functions
Sergey Avvakumov, Marguerite Bin, Xavier Goaoc
A theorem of MatouÅ¡ek asserts that for any , any set system whose shatter function is enjoys a fractional Helly theorem of order : in the -wise intersectio…
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…