Pankaj K. Agarwal

activity

20232026

collaborators

5 papers

cs.CG2026

Point and Line Nearest-Neighbor Searching in 3-Space

Pankaj K. Agarwal, Esther Ezra, Micha Sharir

This paper presents data structures for nearest-neighbor (NN) searching problems involving points, lines, segments, and triangles in 3-space, achieving significantly better perform…

cs.CG2026

Nearly-Tight Bounds for Vertical Decomposition in Three and Four Dimensions

Pankaj K. Agarwal, Esther Ezra, Micha Sharir

Vertical decomposition is a widely used general technique for decomposing the cells of arrangements of semi-algebraic sets in $R^{d}$ into constant-complexity subcells. In…

cs.CG2024

Semi-Algebraic Off-line Range Searching and Biclique Partitions in the Plane

Pankaj K. Agarwal, Esther Ezra, Micha Sharir

Let $P$ be a set of $m$ points in $R^{2}$ , let $Σ$ be a set of $n$ semi-algebraic sets of constant complexity in $R^{2}$ , let $(S, +)$ be a semigroup, and let $w: P…

cs.CG2023

Vertical Decomposition in 3D and 4D with Applications to Line Nearest-Neighbor Searching in 3D

Pankaj K. Agarwal, Esther Ezra, Micha Sharir

Vertical decomposition is a widely used general technique for decomposing the cells of arrangements of semi-algebraic sets in $d$ -space into constant-complexity subcells. In this p…

cs.RO2023

Near-Optimal Min-Sum Motion Planning for Two Square Robots in a Polygonal Environment

Pankaj K. Agarwal, Dan Halperin, Micha Sharir +1

Let $W \subset R^{2}$ be a planar polygonal environment (i.e., a polygon potentially with holes) with a total of $n$ vertices, and let $A, B$ be two robots, each mo…