4 papers · 1 filter
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.
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…
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…
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…