Chan’s Algorithm It is Jarvis’s march applied to big blobs of points.

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Presentation transcript:

Chan’s Algorithm It is Jarvis’s march applied to big blobs of points

Chan’s algorithm Each blob is the convex hull of m points What is m ? m = min(exp(2, exp(2,t)), n)

Chan’s algorithm Partition P into r disjoint sets of size m Compute convex hull of each set Set p 0 = (-∞, 0) and let p 1 be the bottommost point Do an m – step Jarvis march (note this) Stop if the march returns to p 1, else increase m and repeat

Chan’s algorithm Analysis –Time-complexity in O(n log h) »The time-complexity of each iteration is in O(n log m) where m = exp(2, exp(2,t)), for t =1, 2, … » Number of iterations is bounded above by log log h »Thus the complexity is O(n exp(2, log log h + 1)). This simplifies to O(n log h)