Finding equitable convex partitions of points in a polygon efficiently

Finding Skew Partitions Efficiently

A skew partition as defined by Chvátal is a partition of the vertex set of a graph into four nonempty parts A B C D such that there are all possible edges between A and B and no edges between C and D. We present a polynomial-time algorithm for testing whether a graph admits a skew partition. Our algorithm solves the more general list skew partition problem, where the input contains, for each ve...

Finding H-partitions efficiently

We study the concept of an H-partition of the vertex set of a graph G, which includes all vertex partitioning problems into four parts which we require to be nonempty with only external constraints according to the structure of a model graph H , with the exception of two cases, one that has already been classified as polynomial, and the other one remains unclassified. In the context of more gen...

Finding the Maximum Area Centrosymmetric Polygon in a Convex Polygon

Finding the Maximum Area Parallelogram in a Convex Polygon

We consider the problem of finding the maximum area parallelogram (MAP) inside a given convex polygon. Our main result is an algorithm for computing the MAP in an n-sided polygon in O(n2) time. Achieving this running time requires proving several new structural properties of the MAP, and combining them with a rotating technique of Toussaint [10]. We also discuss applications of our result to th...

Finding all Maximal Area Parallelograms in a Convex Polygon

We consider the problem of finding the maximum area parallelogram (MAP) inside a given convex polygon. Our main result is an algorithm for computing the MAP in an n-sided polygon in O(n) time. Achieving this running time requires proving several new structural properties of the MAP. Our algorithm actually computes all the locally maximal area parallelograms (LMAPs). In addition to the algorithm...