3 papers
cs.CG2022
On Semialgebraic Range Reporting
Peyman Afshani, Pingan Cheng
In the problem of semialgebraic range searching, we are to preprocess a set of points in such that the subset of points inside a semialgebraic region described by $O…
cs.CG2020
Lower Bounds for Semialgebraic Range Searching and Stabbing Problems
Peyman Afshani, Pingan Cheng
In the semialgebraic range searching problem, we are to preprocess points in s.t. for any query range from a family of constant complexity semialgebraic sets, al…
cs.CG2020
2D Fractional Cascading on Axis-aligned Planar Subdivisions
Peyman Afshani, Pingan Cheng
Fractional cascading is one of the influential techniques in data structures, as it provides a general framework for solving the important iterative search problem. In the problem,…