Finding equitable convex partitions of points in a polygon efficiently

Authors:
John Gunnar Carlsson;Benjamin Armbruster;Yinyu Ye
Affiliations:
Stanford University, Stanford, CA;Stanford University, Stanford, CA;Stanford University, Stanford, CA
Venue:
ACM Transactions on Algorithms (TALG)
Year:
2010

Citing 3
Cited 4

2-Dimension Ham Sandwich Theorem for Partitioning into Three Convex Pieces

JCDCG '98 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Generalized Balanced Partitions of Two Sets of Points in the Plane

JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Equitable subdivisions within polygonal regions

Computational Geometry: Theory and Applications - Special issue on the Japan conference on discrete and computational geometry 2004

Convex Partitions with 2-Edge Connected Dual Graphs

COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Convex partitions with 2-edge connected dual graphs

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Abstract

Previous work has developed algorithms for finding an equitable convex partition that partitions the plane into n convex pieces each containing an equal number of red and blue points. Motivated by a vehicle routing heuristic, we look at a related problem where each piece must contain one point and an equal fraction of the area of some convex polygon. We first show how algorithms for solving the older problem lead to approximate solutions for this new equitable convex partition problem. Then we demonstrate a new algorithm that finds an exact solution to our problem in O(N nlog N) time or operations, where n is the number of points, m the number of vertices or edges of the polygon, and N:=n+m the sum.