We present efficient algorithms for partitioning 2dimensional space into faces arising from the boundaries of overlapping polygons. In particular, we examine the case where the partitioning arises from overlaying m k-sided simple polygons. A dynamic data structure is presented for storing the partitioning that arises from m polygons with at most k sides each in space O(km) if the polygons are a...

We consider the geometric optimization problem of nding the maximum area axis-parallel rectangle (MAAPR) in an n-vertex general polygon. We characterize the MAAPR for general polygons by considering di erent cases based on the types of contacts between the rectangle and the polygon. We present a general framework for solving a key subcase of the MAAPR problem which dominates the running time fo...

Punctured polygons are polygons with internal holes which are also polygons. The external and internal polygons are of the same type, and they are mutually as well as self-avoiding. Based on an assumption about the limiting area distribution for unpunctured polygons, we rigorously analyse the effect of a finite number of punctures on the limiting area distribution in a uniform ensemble, where p...

This paper considers the geometric optimization problem of nding the Largest area axis-parallel Rectangle (LR) in an n-vertex general polygon. We characterize the LR for general polygons by considering diierent cases based on the types of contacts between the rectangle and the polygon. A general framework is presented for solving a key subproblem of the LR problem which dominates the running ti...

In this paper, we analyze the time complexity of finding regular polygons in a set of n points. We use two different approaches to find regular polygons, depending on their number of edges. Those with o(n) edges are found by sweeping a line through the set of points, while the larger polygons are found by random sampling. We can find all the polygons with high probability in O(n ) expected time...