A proof of Jordan curve theorem based on the sweepline algorithm for trapezoidal decomposition of a polygon
For mathematicians and educators, this work offers a novel algorithmic proof of a fundamental theorem that was previously considered inaccessible at the undergraduate level.
The authors provide the first algorithmic proof of the Jordan curve theorem by generalizing the sweepline algorithm for trapezoidal decomposition of a polygon, making the proof accessible for undergraduate discrete mathematics courses.
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 choice). Though several proofs have been given for the Jordan curve theorem by various authors, ours is the {\bf first algorithmic proof} of Jordan curve theorem using computational geometry. Further, with some preparation, the proof can be taught as part of an undergraduate discrete mathematics course, where till now the proof of this theorem was considered inaccessible.