Geodesic ham-sandwich cuts

Let P be a simple polygon with m vertices, k of which are reflex, and which contains r red points and b blue points in its interior. Let n = m + r + b. A ham-sandwich geodesic is a shortest path in P between two points on the boundary of P that simultaneously bisects the red points and the blue points. We present an O(n log k)-time algorithm for finding a ham-sandwich geodesic. We also show that this algorithm is optimal in the algebraic computation tree model when parameterizing the running time with respect to n and k.

• Type: Conference
• Year: 2004
• Where: COMPGEOM
• Authors: Prosenjit Bose, Erik D. Demaine, Ferran Hurtado, John Iacono, Stefan Langerman, Pat Morin
• Keywords: Blue Points, COMPGEOM 2004, Ham-sandwich Geodesic, Red Points