Reilly Browne

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20232026

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cs.CG2026

Strong Lower Bounds for Weak Epsilon-Nets

Sujoy Bhore, Reilly Browne, Da Wei Zheng

Let $P$ be a finite point set in $R^{d}$ . A weak $ε$ -net for $P$ with respect to convex sets is a finite set $X \subset R^{d}$ intersecting every convex set c…

cs.CG2026

Decomposing a Simple Polygon with Geodesic Unit-Balls

Reilly Browne, Prahlad Narasimhan Kasthurirangan

We consider covering and partitioning a simple polygon into pieces which either have unit geodesic radius or unit geodesic diameter, using the $ℓ_{2}$ -metric for distances. There…

cs.DS2026

Single-Criteria Metric $r$ -Dominating Set Problem via Minor-Preserving Support

Reilly Browne, Hsien-Chih Chang

Given an unweighted graph $G$ , the *minimum $r$ -dominating set problem* asks for the smallest-cardinality subset $S$ such that every vertex in $G$ is within radius $r$ of some vert…

cs.CG2026

Covering and Partitioning Complex Objects with Small Pieces

Anders Aamand, Mikkel Abrahamsen, Reilly Browne +6

We study the problems of covering or partitioning a polygon $P$ (possibly with holes) using a minimum number of small pieces, where a small piece is a connected sub-polygon contain…

Strong Lower Bounds for Weak Epsilon-Nets

Decomposing a Simple Polygon with Geodesic Unit-Balls

Single-Criteria Metric r-Dominating Set Problem via Minor-Preserving Support

Covering and Partitioning Complex Objects with Small Pieces

Single-Criteria Metric $r$ -Dominating Set Problem via Minor-Preserving Support