# create convex hull polygons / cluster for sets of N points in a point dataset

I have 50k points in a feature class which I need to build convex hull or polygon for each set of 50 points that are nearby each other. I guess the question is very similar to create census areas for each 200 households. I've tried all tools in ArcGIS Desktop 10.1 but none of them does what I'm after. I also tried some other third-party tools which allows me to create convex hull based on K-means algorithm - means I can specify the number of convex hulls to be generated but still can't see how to create convex hulls for a specified number of points. I'm open to any solutions not just limited to ArcGIS, but the final result need to be imported back to ArcGIS. Any advise would be appreciated! Thanks.

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Perhaps a nearest neighbor clustering algorithm in which you specify the minimum number of points will be sufficient? See the description on the CrimeStat manual for NN hierarchical clustering. Part of the problem with saying I want 50 points is that you could have 51 points at the exact same location (or that all meet the same criteria), and so no unique solution exists. Any solution in that situation wouldn't make sense anyway. – Andy W Aug 20 '12 at 12:16
Andy is correct: this problem is incompletely specified. Could you step back a little and explain why you want to build these polygons? What scientific question are you addressing and, in that context, how would these polygons be interpreted if they could be found? What is the basis for the 50 point restriction? What would it mean to have to relax that a little? – whuber Aug 20 '12 at 15:53
A very closely related (but as yet unanswered) question is gis.stackexchange.com/questions/31236/…. A solution to one is likely to lead to a solution to the other. – whuber Aug 20 '12 at 20:23
Re Andy/Whuber: Thanks guys. The issue I'm trying to address is we have 50,000 existing hydrants in the city for inspection, and we want assign the work to our field crews in groups of 50 hydrants nearby each other, so that the work load is in a manageable size for individuals and we can also track the inspection progress. In fact it doesn’t have to be exactly 50 hydrants for each group, +/- 10 is fine. – Jack Z Aug 21 '12 at 0:54