Geometric Streaming Algorithms with a Sorting Primitive

We solve several fundamental geometric problems under a new streaming model recently proposed by Ruhl et al. [2, 12]. In this model, in one pass the input stream can be scanned to generate an output stream or be sorted based on a user-defined comparator; all intermediate streams must be of size O(n). We obtain the following geometric results for any fixed constant > 0: – We can construct 2D convex hulls in O(1) passes with O(n ) extra space. – We can construct 3D convex hulls in O(1) expected number of passes with O(n ) extra space. – We can construct a triangulation of a simple polygon in O(1) expected number of passes with O(n ) extra space, where n is the number of vertices on the polygon. – We can report all k intersections of a set of 2D line segments in O(1) passes with O(n ) extra space, if an intermediate stream of size O(n + k) is allowed. We also consider a weaker model, where we do not have the sorting primitive but are allowed to choose a scan direction for eve...

• Type: Conference
• Year: 2007
• Where: ISAAC
• Authors: Eric Y. Chen
• Keywords: 2d Convex Hull, Convex Hull, Extra Space, ISAAC 2007