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 …
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
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 …
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 …
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 …
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 …
classes of objects are represented by colors. We study the algorithmic problem of creating …
The balanced connected subgraph problem
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 …
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 …
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 …
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 …
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 …
states that any $ d $ mass distributions in $\mathbb {R}^ d $ can be simultaneously bisected …