(Most fair region) Let $P$ be a set of $n$ points in the two-dimensional plane. Each point in $P$ is either colored red or blue. Given an axis-aligned rectangle $R_{ab}$ of size $a\times b$ , design a fast algorithm to decide where to place $R_{ab}$ in the plane so that the absolute difference between the number of red points and the number of blue points lying inside $R_{ab}$ is minimized. As a motivating example, think of each point in $P$ as the geographical location of each person. The color of each person could be assigned based on either gender, or political affiliation, or native/non-native speaker, favourite hero etc. We look at the simple setting where there are only two groups/colors. The goal is to detect region(s) which has a fair representation of both groups. Fairness in general is a very popular topic in computer science these days.
(Most unfair region) Let $P$ be a set of $n$ points in the two-dimensional plane. Each point in $P$ is either colored red or blue. Given an axis-aligned rectangleRabof size $a \times b$, design a fast algorithm to decide where to place $R_{ab}$ in the plane so that the absolute difference between the number of red points and the number of blue points lying inside $R_{ab}$ is maximized. Following the previous motivating example, this could help detect a region where there is huge gender disparity or detect a region where a particular political party has a strong majority.
These are two related open problems which our course instructor on computational geometry has asked us to work on. Could anyone suggest some literature/resources related to these so that I am able to navigate and appreciate the problem better ? (I haven't been able to find anything related to this on google)
P.S.: I am a 2nd year undergrad student, and this is my first computational geometry course. This "research project problem" is to give us a better flavour of what it takes to be a CS researcher.