Parallel Enclosing Circle Algorithm

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McNair Project
Parallel Enclosing Circle Algorithm
Project logo 02.png
Project Information
Project Title Parallel Enclosing Circle Algorithm
Owner Oliver Chang
Start Date July 31, 2017
Deadline October 4, 2017
Primary Billing
Notes
Has project status Complete
Is dependent on Enclosing Circle Algorithm
Copyright © 2016 edegan.com. All Rights Reserved.


A thin-wrapper around the enclosing circle algorithm which allows for instance-level parallelization. This project consists of the python files in E:\McNair\Projects\OliverLovesCircles\src\python.

Parallelization is implemented via Python2's subprocess.open() which is non-blocking and available in the standard library.

The Problem

Note that this is not the classical enclosing circle algorithm. Rather, we seek to minimize the sum of enclosing circles containing at least n points. Thus, multiple circles are allowed and inclusion in multiple circles is possible.

This algorithm has terrible time-performance characteristics, so we make the assumption that we can divide a large number of points with k-means and then solve those subproblems. In other words, we make the simplifying assumption that the Enclosing Circle Algorithm has Optimal Substructure.

Parameters

  • in circles.py:
    • ITERATIONS: the number of iterations to attempt for each k to find minimum for that k
    • MIN_POINTS_PER_CIRCLE (AKA n): the minimum number of data points that must be included in a circle
  • in vc_circles.py
    • NUMBER_INSTANCES: number of parallel instances to run; assume no data-races between instances
    • SWEEP_CYCLE_SECONDS: amount of time before removing completed jobs from the current job and adding new jobs if any files are left to process
    • TIMEOUT_MINUTES: maximum running time of a parallel instance of the algorithm
    • SPLIT_THRESHOLD: if a dataset has more than this threshold of data points, it will be split via k-means

Example Usage

$ python vc_circles.py --infile E:/McNair/Projects/OliverLovesCircles/CoLevelForCirclesNotRunGTE200.txt
$ python outjoiner.py

where CoLevelForCirclesNotRunGTE200.txt is a tab-separated values file with the columns placestate, place, statecode, year, latitude, longitude, coname, datefirstinv, placens, geoid, city

This command will populate (and overwrite) any files in data/. The format of the filenames in this directory are {city}{sep}{state}{sep}{year}{sep}{num}.tsv where num is a 0-indexed integer of a split city/state/year infile that has greater than SPLIT_THRESHOLD

Bugs/Issues

  1. "St. Paul" and "St. Louis" have un-enclosed points--speculate because of weird file path issues
  2. Some place/state/year combinations do not run to completion regardless of how tractable the number of points
  3. How to merge small enclosing circles? This is a better measure of agglomeration regardless
  4. How to separate outliers?

Related Pages

External Links

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