A survey of mass partitions

E Roldán-Pensado, P Soberón - Bulletin of the American Mathematical …, 2022 - ams.org
Mass partition problems describe the partitions we can induce on a family of measures or
finite sets of points in Euclidean spaces by dividing the ambient space into pieces. In this …

Discrete geometry on colored point sets in the plane—a survey

M Kano, J Urrutia - Graphs and Combinatorics, 2021 - Springer
Discrete geometry on colored point sets in the plane has a long history, but this research
area has been extensively developed in the last 2 decades. In 2003, a short survey entitled …

Sharing a pizza: bisecting masses with two cuts

L Barba, A Pilz, P Schnider - arXiv preprint arXiv:1904.02502, 2019 - arxiv.org
Assume you have a pizza consisting of four ingredients (eg, bread, tomatoes, cheese and
olives) that you want to share with your friend. You want to do this fairly, meaning that you …

The complexity of sharing a pizza

P Schnider - arXiv preprint arXiv:2109.06752, 2021 - arxiv.org
Assume you have a 2-dimensional pizza with $2 n $ ingredients that you want to share with
your friend. For this you are allowed to cut the pizza using several straight cuts, and then …

Diverse partitions of colored points

M van Kreveld, B Speckmann, J Urhausen - Algorithms and Data …, 2021 - Springer
Imagine that a set of objects is represented by points in space and that different types or
classes of objects are represented by colors. We study the algorithmic problem of creating …

The balanced connected subgraph problem

S Bhore, S Chakraborty, S Jana, JSB Mitchell… - Discrete Applied …, 2022 - Elsevier
The problem of computing induced subgraphs that satisfy some specified restrictions arises
in various applications of graph algorithms and has been well studied. In this paper, we …

Combinatorial depth measures for hyperplane arrangements

P Schnider, P Soberón - arXiv preprint arXiv:2302.07768, 2023 - arxiv.org
Regression depth, introduced by Rousseeuw and Hubert in 1999, is a notion that measures
how good of a regression hyperplane a given query hyperplane is with respect to a set of …

Ham-sandwich cuts and center transversals in subspaces

P Schnider - arXiv preprint arXiv:1903.12516, 2019 - arxiv.org
The Ham-Sandwich theorem is a well-known result in geometry. It states that any $ d $ mass
distributions in $\mathbb {R}^ d $ can be simultaneously bisected by a hyperplane. The …

Ham-sandwich cuts and center transversals in subspaces

P Schnider - Discrete & Computational Geometry, 2020 - Springer
Abstract The Ham-Sandwich theorem is a well-known result in geometry. It states that any d
mass distributions in R^ d R d can be simultaneously bisected by a hyperplane. The result is …

Equipartitions with wedges and cones

P Schnider - arXiv preprint arXiv:1910.13352, 2019 - arxiv.org
A famous result about mass partitions is the so called\emph {Ham-Sandwich theorem}. It
states that any $ d $ mass distributions in $\mathbb {R}^ d $ can be simultaneously bisected …