Enclosing Circle Algorithm

McNair Project

Enclosing Circle Algorithm
Project Information
Project Title	Enclosing Circle Algorithm
Owner	Christy Warden
Start Date	201701
Deadline	201704
Primary Billing
Notes
Has project status	Active
Copyright © 2016 edegan.com. All Rights Reserved.

Overview

This program takes in a set of points and the minimum number that should be included inside a unit, and returns circles of the smallest total area which encompass all of the data points. Function make_circle and all of its helper functions were taken from https://www.nayuki.io/res/smallest-enclosing-circle/smallestenclosingcircle.py.

Input: A sequence of pairs of floats or ints, e.g. [(0,5), (3.1,-2.7)]. Output: A triple of floats representing a circle. Returns the smallest circle that encloses all the given points. Runs in expected O(n) time, randomized.

Algorithm Description

Location

The original script is located in:

E:\McNair\Software\CodeBase\EnclosingCircle.py

Applications

VC Data

The Enclosing Circle Algorithm will be applied to VC data acquired through the SDC Platinum database. The script makes use of the Python GeoPy GeoCoder to get latitude and longitude coordinates to be used by the Enclosing Circle Algorithm.

Geopy Geocoder User Agreements can be found here.

The relevant files are located in:

E:\McNair\Projects\Accelerators\Enclosing_Circle

The results may eventually be plotted to a graph using python as well. Here is documentation for a python library called basemap.

CURRENT STATUS: Bug fixes needed in EnclosingCircle.py. The program errors with a key error on line 187 in cases where n is not a multiple of the length of the dataset. I made some temporary fixes to the enclosing circle file located in the above directory, but I am not certain if it is a permanent fix.

Speeding up with C

With the large amount of VC data we have, the enclosing circle algorithm would take an extremely long amount of time to run (on the order of weeks/months). If we can compile the code into C, we can speed up runtime dramatically. I've listed some possible sources for running python code as C.

PyPy. Documentation here.

Cython

Cython. Documentation here. Basic tutorial for Cython is given here.

Currently, the RDP is missing a compiler to run Cython successfully. The error that appears is "unable to find vcvarsall.bat".

Getting a C++ Compiler

These are proposed fixes to solve the Cython error shown above. A possible C++ Compiler for Python can be downloaded directly from Windows here.

The C++ Compiler for Python has been downloaded and installed. Instructions for installation and uninstallation can be found here.

The Installation file is located in :

E:\McNair\Software\Utilities\VCForPython27.msi

Running Python vs. Cython

A trial test run on 82 coordinates resulted int the following time stamps:

EnclosingCircle in python: 16.069 seconds
Enclosing Circle in cython:  9.633 seconds

The test files can be found in the following:

EnclosingCircle in python: E:\McNair\Projects\Accelerators\EnclosingCircle\EnclosingCircle.py
EnclosingCircle in cython: E:\McNair\Projects\Accelerators\EnclosingCircle\EnclosingCircleC_Test.py

Usage

The basic tutorial for cython can be found phttp://docs.cython.org/en/latest/src/tutorial/cython_tutorial.html here].

Essentially, a setup.py file needs to be created with the following format:

try:
    from setuptools import setup
    from setuptools import Extension
except ImportError:
    from distutils.core import setup
    from distutils.extension import Extension

from Cython.Build import cythonize
setup(
    ext_modules = cythonize("filename.pyx")
)

Then, after changing to the proper directory, execute the following from the command line

python setup.py build_ext --inplace

This will wrap your python program in C, and produce a filename.pyd file.

To use this new python code wrapped in C, simply import the pyd file as if it were a python file:

import filename

Treat this file as any other module. It will work just as if it were in Python, except it exhibits a faster run time.

NOTE: We fixed Enclosing Circle and drastically improved its runtime, so we decided to go with its Python implementation.

Results

A data set with cities, companies, start year, end year, and geocoded coordinates (Cleaned) can be found at:

E:\McNair\Projects\Accelerators\EnclosingCircle\vc_clean.txt

Statistics about the data set can be found in:

E:\McNair\Projects\Accelerators\EnclosingCircle\vc_stats.txt

There is also an excel file with a histogram of the data under the same name.

NEXT STEP: We need to determine how many companies we want in each circle, and then we can begin running the enclosing circle algorithm on the city data.

The final data of cities at a given year and their minimized circles can be found at:

 E:\McNair\Projects\Accelerators\EnclosingCircle\vc_circles.txt