4 papers
cs.CG2026
A greedy maximal sweepline algorithm for a Jordan curve
Apurva Mudgal
We give a greedy sweepline algorithm for a Jordan curve and prove that it is maximal in the sense of [1]. Our proof uses Kőnig's lemma.
cs.CG2026
A proof of Jordan curve theorem based on the sweepline algorithm for trapezoidal decomposition of a polygon
Apurva Mudgal
We prove the Jordan curve theorem by generalizing the sweepline algorithm for trapezoidal decomposition of a polygon. Our proof uses Zorn's lemma (or, equivalently the axiom of cho…
cs.CG2025
Hardness and Approximation Schemes for Discrete Packing and Domination
Raghunath Reddy Madireddy, Apurva Mudgal, Supantha Pandit
We present polynomial-time approximation schemes based on local search} technique for both geometric (discrete) independent set (\mdis) and geometric (discrete) dominating set (\md…
cs.CG2024
Convexity of near-optimal orthogonal-pair-free sets on the unit sphere
Apurva Mudgal
A subset of the unit sphere is called orthogonal-pair-free if and only if there do not exist two distinct points at distance from each o…