Equitable subdivisions within polygonal regions
Computational Geometry, 2006•Elsevier
We prove a generalization of the Ham-Sandwich Theorem. Specifically, let P be a simple
polygonal region containing| R|= kn red points and| B|= km blue points in its interior with k⩾
2. We show that P can be partitioned into k relatively-convex regions each of which contains
exactly n red and m blue points. A region of P is relatively-convex if it is closed under
geodesic (shortest) paths in P. We outline an O (kN2log2N) time algorithm for computing
such a k-partition, where N=| R|+| B|+| P|.
polygonal region containing| R|= kn red points and| B|= km blue points in its interior with k⩾
2. We show that P can be partitioned into k relatively-convex regions each of which contains
exactly n red and m blue points. A region of P is relatively-convex if it is closed under
geodesic (shortest) paths in P. We outline an O (kN2log2N) time algorithm for computing
such a k-partition, where N=| R|+| B|+| P|.
We prove a generalization of the Ham-Sandwich Theorem. Specifically, let P be a simple polygonal region containing |R|=kn red points and |B|=km blue points in its interior with k⩾2. We show that P can be partitioned into k relatively-convex regions each of which contains exactly n red and m blue points. A region of P is relatively-convex if it is closed under geodesic (shortest) paths in P. We outline an O(kN2log2N) time algorithm for computing such a k-partition, where N=|R|+|B|+|P|.
Elsevier
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