Merge branch 'develop'HEADmain

22 files changed, 1450 insertions, 114 deletions

diff --git a/.gitignore b/.gitignore
index 01b4c2f..35861e5 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,6 +1,6 @@
 
-# Created by https://www.toptal.com/developers/gitignore/api/csharp,dotnetcore,visualstudiocode
-# Edit at https://www.toptal.com/developers/gitignore?templates=csharp,dotnetcore,visualstudiocode
+# Created by https://www.toptal.com/developers/gitignore/api/csharp,dotnetcore,visualstudiocode,tex,latex
+# Edit at https://www.toptal.com/developers/gitignore?templates=csharp,dotnetcore,visualstudiocode,tex,latex
 
 ### Csharp ###
 ## Ignore Visual Studio temporary files, build results, and
@@ -401,6 +401,441 @@ obj/
 /node_modules
 /wwwroot/node_modules
 
+### LaTeX ###
+## Core latex/pdflatex auxiliary files:
+*.aux
+*.lof
+*.lot
+*.fls
+*.out
+*.toc
+*.fmt
+*.fot
+*.cb
+*.cb2
+.*.lb
+
+## Intermediate documents:
+*.dvi
+*.xdv
+*-converted-to.*
+# these rules might exclude image files for figures etc.
+# *.ps
+# *.eps
+# *.pdf
+
+## Generated if empty string is given at "Please type another file name for output:"
+.pdf
+
+## Bibliography auxiliary files (bibtex/biblatex/biber):
+*.bbl
+*.bcf
+*.blg
+*-blx.aux
+*-blx.bib
+*.run.xml
+
+## Build tool auxiliary files:
+*.fdb_latexmk
+*.synctex
+*.synctex(busy)
+*.synctex.gz
+*.synctex.gz(busy)
+*.pdfsync
+
+## Build tool directories for auxiliary files
+# latexrun
+latex.out/
+
+## Auxiliary and intermediate files from other packages:
+# algorithms
+*.alg
+*.loa
+
+# achemso
+acs-*.bib
+
+# amsthm
+*.thm
+
+# beamer
+*.nav
+*.pre
+*.snm
+*.vrb
+
+# changes
+*.soc
+
+# comment
+*.cut
+
+# cprotect
+*.cpt
+
+# elsarticle (documentclass of Elsevier journals)
+*.spl
+
+# endnotes
+*.ent
+
+# fixme
+*.lox
+
+# feynmf/feynmp
+*.mf
+*.mp
+*.t[1-9]
+*.t[1-9][0-9]
+*.tfm
+
+#(r)(e)ledmac/(r)(e)ledpar
+*.end
+*.?end
+*.[1-9]
+*.[1-9][0-9]
+*.[1-9][0-9][0-9]
+*.[1-9]R
+*.[1-9][0-9]R
+*.[1-9][0-9][0-9]R
+*.eledsec[1-9]
+*.eledsec[1-9]R
+*.eledsec[1-9][0-9]
+*.eledsec[1-9][0-9]R
+*.eledsec[1-9][0-9][0-9]
+*.eledsec[1-9][0-9][0-9]R
+
+# glossaries
+*.acn
+*.acr
+*.glg
+*.glo
+*.gls
+*.glsdefs
+*.lzo
+*.lzs
+
+# uncomment this for glossaries-extra (will ignore makeindex's style files!)
+# *.ist
+
+# gnuplottex
+*-gnuplottex-*
+
+# gregoriotex
+*.gaux
+*.glog
+*.gtex
+
+# htlatex
+*.4ct
+*.4tc
+*.idv
+*.lg
+*.trc
+*.xref
+
+# hyperref
+*.brf
+
+# knitr
+*-concordance.tex
+# TODO Uncomment the next line if you use knitr and want to ignore its generated tikz files
+# *.tikz
+*-tikzDictionary
+
+# listings
+*.lol
+
+# luatexja-ruby
+*.ltjruby
+
+# makeidx
+*.idx
+*.ilg
+*.ind
+
+# minitoc
+*.maf
+*.mlf
+*.mlt
+*.mtc[0-9]*
+*.slf[0-9]*
+*.slt[0-9]*
+*.stc[0-9]*
+
+# minted
+_minted*
+*.pyg
+
+# morewrites
+*.mw
+
+# newpax
+*.newpax
+
+# nomencl
+*.nlg
+*.nlo
+*.nls
+
+# pax
+*.pax
+
+# pdfpcnotes
+*.pdfpc
+
+# sagetex
+*.sagetex.sage
+*.sagetex.py
+*.sagetex.scmd
+
+# scrwfile
+*.wrt
+
+# sympy
+*.sout
+*.sympy
+sympy-plots-for-*.tex/
+
+# pdfcomment
+*.upa
+*.upb
+
+# pythontex
+*.pytxcode
+pythontex-files-*/
+
+# tcolorbox
+*.listing
+
+# thmtools
+*.loe
+
+# TikZ & PGF
+*.dpth
+*.md5
+*.auxlock
+
+# todonotes
+*.tdo
+
+# vhistory
+*.hst
+*.ver
+
+# easy-todo
+*.lod
+
+# xcolor
+*.xcp
+
+# xmpincl
+*.xmpi
+
+# xindy
+*.xdy
+
+# xypic precompiled matrices and outlines
+*.xyc
+*.xyd
+
+# endfloat
+*.ttt
+*.fff
+
+# Latexian
+TSWLatexianTemp*
+
+## Editors:
+# WinEdt
+*.bak
+*.sav
+
+# Texpad
+.texpadtmp
+
+# LyX
+*.lyx~
+
+# Kile
+*.backup
+
+# gummi
+.*.swp
+
+# KBibTeX
+*~[0-9]*
+
+# TeXnicCenter
+*.tps
+
+# auto folder when using emacs and auctex
+./auto/*
+*.el
+
+# expex forward references with \gathertags
+*-tags.tex
+
+# standalone packages
+*.sta
+
+# Makeindex log files
+*.lpz
+
+# xwatermark package
+*.xwm
+
+# REVTeX puts footnotes in the bibliography by default, unless the nofootinbib
+# option is specified. Footnotes are the stored in a file with suffix Notes.bib.
+# Uncomment the next line to have this generated file ignored.
+#*Notes.bib
+
+### LaTeX Patch ###
+# LIPIcs / OASIcs
+*.vtc
+
+# glossaries
+*.glstex
+
+### TeX ###
+
+# these rules might exclude image files for figures etc.
+# *.ps
+# *.eps
+# *.pdf
+
+
+
+
+# latexrun
+
+# algorithms
+
+# achemso
+
+# amsthm
+
+# beamer
+
+# changes
+
+# comment
+
+# cprotect
+
+# elsarticle (documentclass of Elsevier journals)
+
+# endnotes
+
+# fixme
+
+# feynmf/feynmp
+
+
+# glossaries
+
+# uncomment this for glossaries-extra (will ignore makeindex's style files!)
+# *.ist
+
+# gnuplottex
+
+# gregoriotex
+
+# htlatex
+
+# hyperref
+
+# knitr
+# TODO Uncomment the next line if you use knitr and want to ignore its generated tikz files
+# *.tikz
+
+# listings
+
+# luatexja-ruby
+
+# makeidx
+
+# minitoc
+
+# minted
+
+# morewrites
+
+# newpax
+
+# nomencl
+
+# pax
+
+# pdfpcnotes
+
+# sagetex
+
+# scrwfile
+
+# sympy
+
+# pdfcomment
+
+# pythontex
+
+# tcolorbox
+
+# thmtools
+
+# TikZ & PGF
+
+# todonotes
+
+# vhistory
+
+# easy-todo
+
+# xcolor
+
+# xmpincl
+
+# xindy
+
+# xypic precompiled matrices and outlines
+
+# endfloat
+
+# Latexian
+
+# WinEdt
+
+# Texpad
+
+# LyX
+
+# Kile
+
+# gummi
+
+# KBibTeX
+
+# TeXnicCenter
+
+# auto folder when using emacs and auctex
+
+# expex forward references with \gathertags
+
+# standalone packages
+
+# Makeindex log files
+
+# xwatermark package
+
+# REVTeX puts footnotes in the bibliography by default, unless the nofootinbib
+# option is specified. Footnotes are the stored in a file with suffix Notes.bib.
+# Uncomment the next line to have this generated file ignored.
+
+### TeX Patch ###
+# LIPIcs / OASIcs
+
+# glossaries
+
 ### VisualStudioCode ###
 
 # Local History for Visual Studio Code
@@ -413,4 +848,4 @@ obj/
 # Support for Project snippet scope
 !.vscode/*.code-snippets
 
-# End of https://www.toptal.com/developers/gitignore/api/csharp,dotnetcore,visualstudiocode
+# End of https://www.toptal.com/developers/gitignore/api/csharp,dotnetcore,visualstudiocode,tex,latex
diff --git a/.vscode/launch.json b/.vscode/launch.json
index 7f48531..0f7ced4 100644
--- a/.vscode/launch.json
+++ b/.vscode/launch.json
@@ -5,39 +5,17 @@
     "version": "0.2.0",
     "configurations": [
         {
-            "name": ".NET Core Launch (console)",
+            "name": "lots-o-graphs",
             "type": "coreclr",
             "request": "launch",
             "preLaunchTask": "build",
             "program": "${workspaceFolder}/src/Program/bin/Debug/net5.0/Program.dll",
             "args": [
-                "../../graphs/Project4Graph2.txt",
-                "0",
-                "6"
+                "../../graphs"
             ],
             "cwd": "${workspaceFolder}/src/Program",
             "console": "integratedTerminal",
             "stopAtEntry": false
         },
-        {
-            "name": "smol graff",
-            "type": "coreclr",
-            "request": "launch",
-            "preLaunchTask": "build",
-            "program": "${workspaceFolder}/src/Program/bin/Debug/net5.0/Program.dll",
-            "args": [
-                "../../graphs/Project4Graph1.txt",
-                "0",
-                "5"
-            ],
-            "cwd": "${workspaceFolder}/src/Program",
-            "console": "integratedTerminal",
-            "stopAtEntry": false
-        },
-        {
-            "name": ".NET Core Attach",
-            "type": "coreclr",
-            "request": "attach"
-        }
     ]
 }
\ No newline at end of file
diff --git a/README.md b/README.md
index a0abc2b..048ea7a 100644
--- a/README.md
+++ b/README.md
@@ -1,5 +1,5 @@
 # NetworkFlow
-CS 456: Project4 - Network Flow
+CS 456: Project5 - Global Min Cut
 
 Professor: Dr. John Matta
 
diff --git a/docs/report/report.pdf b/docs/report/report.pdf
new file mode 100644
index 0000000..5092c22
--- /dev/null
+++ b/docs/report/report.pdf
diff --git a/docs/report/report.tex b/docs/report/report.tex
new file mode 100644
index 0000000..02472ac
--- /dev/null
+++ b/docs/report/report.tex
@@ -0,0 +1,65 @@
+\documentclass[11pt]{scrartcl}
+
+% Metadata
+\title{Global Min Cut}
+\subtitle{CS 456: Project 5}
+\author{Neil Kollack and Toby Vincent}
+
+% Packages
+\usepackage{styles/packages}
+\usepackage{styles/header}
+\usepackage{styles/title}
+\usepackage{styles/section}
+\usepackage{csvsimple}
+\usepackage{graphicx}
+\usepackage{amsmath}
+
+\begin{document}
+\maketitle
+
+\section{Introduction}
+
+The goal of this project was to analyze and compare the Edmonds-Karp algorithm with Karger's approximation algorithm for finding the global minimum cut of a graph. The global minimum cut problem consists of finding the lowest capacity cut through a graph. Being a NP Hard problem, the runtime of finding the exact solution using the Edmonds–Karp algorithm is $O(\vert V \vert ^ 2 \vert E \vert ^ 2)$, and as such, we aim to experiment with Karger's approximation algorithm to discover its viability, and what trade-offs are made compared to the Edmonds–Karp algorithm.
+
+\section{Results}
+
+\begin{table}[h]
+    \centering
+    \resizebox{\textwidth}{!}{%
+    \csvautotabular{../../output/constant_cuts.csv}}
+    \resizebox{\textwidth}{!}{%
+    \csvautotabular{../../output/constant_times.csv}}
+    \caption{\label{tab:constant} Minimum cut and associated runtimes for $10$ iterations}
+\end{table}
+
+\begin{table}[h]
+    \centering
+    \resizebox{\textwidth}{!}{%
+    \csvautotabular{../../output/linear_cuts.csv}}
+    \resizebox{\textwidth}{!}{%
+    \csvautotabular{../../output/linear_times.csv}}
+    \caption{\label{tab:linier} Minimum cut and associated runtimes for $n$ iterations}
+\end{table}
+
+\begin{table}[h]
+    \centering
+    \resizebox{\textwidth}{!}{%
+    \csvautotabular{../../output/polynomial_cuts.csv}}
+    \resizebox{\textwidth}{!}{%
+    \csvautotabular{../../output/polynomial_times.csv}}
+    \caption{\label{tab:polynomial} Minimum cut and associated runtimes for $n^2\ln n$ iterations}
+\end{table}
+
+\section{Analysis}
+
+When looking at the probability of not finding the minimum cut we know that when repeating the contraction algorithm $n^2 ln(n)$ times that the probability of not finding the minimum cut is $1/n^2$. However, when running the algorithm only n times there is a rather noticeable change in the probability. Simplifying the probability equation down from $P_n = 1-[ 1- \binom{n}{2}^{-1}]^n$ to $P_n = 1-[ 1-\frac{2}{n^2-n} ]^n$ it becomes apparent that while running the algorithm n times is moving toward a low probability of not finding the minimum cut, it is nowhere near as effective as $n^2 ln(n)$ times.  Where running n times the failure rate never really reaches a sufficiently small probability, whereas $n^2 ln(n)$ would reach a point of failure that is sufficient on graphs with very small n values.
+
+When also taking into account that we performed 5 repetitions, the probability of failure for $n^2 ln(n)$ drops immediately to almost zero, even at n = 2. Where n still has at least a 1\% overall failure rate.  This is reflected in our data, where $n^2 ln(n)$ did not fail on any repetitions and n failed a majority of the time but at least one of the five repetitions came up with the correct answer.
+
+As for the runtimes, as expected with the Contraction Algorithm being $O(\vert V \vert ^2* \vert E \vert *log(V))$, which is at least a factor less than the Edmonds-Karp method, the approximation method is much faster even when ran $n^2 ln(n)$ times.  Therefore, with the accuracy of the $n^2 ln(n)$ iteration Contraction Algorithm matching that of the exact method, and its runtime proving to be better, this experiment would seem to conclude that the $n^2 ln(n)$ iteration approximation is the preferable choice of all options examined
+
+\section{Conclusion}
+
+Due to the insurmountable runtimes of the algorithm on a larger graph for $n^2\ln n$ iterations, it is unfeasible to run the number of repetitions needed for a dataset large enough to conclusively show the probability of not finding the minimum cut converges to zero. Even with parallelization of the main iteration loop the runtime of larger graphs was still excessive. That being said, even five repetitions of the algorithm illustrates the disparity between the different iteration counts that where chosen for this experiment. The level of experimentation was a successfully demonstrated the viability of using Karger's algorithm as a solution to an otherwise difficult problem.
+
+\end{document}
\ No newline at end of file
diff --git a/docs/report/styles/header.sty b/docs/report/styles/header.sty
new file mode 100644
index 0000000..b86e98e
--- /dev/null
+++ b/docs/report/styles/header.sty
@@ -0,0 +1,35 @@
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{styles/header}[2021/09/29 Header style]
+
+% ┌───────────────────────────────────┐   
+% │                   Title: Subtitle │ ──┬─ [Header]
+% │                            Author │ ──┘
+% │ Title                             │ ──┬─ Title
+% │ Subtitle                          │ ──┘
+% │                                   │ 
+% │ A Section                         │ ──┬─ Sections
+% │ ...                               │   │
+% │ 1.1 A Subsection                  │ ──┤
+% │ ...                               │   │
+% │ Another Section                   │ ──┤
+% │ ...                               │   │
+% │ 2.1 A Subsection                  │ ──┤
+% │ ...                               │   │
+% │ 2.2 Another Subsection            │ ──┘
+% │ ...                               │ 
+% │                                   │
+% │                                   │
+% └───────────────────────────────────┘
+
+\pagestyle{myheadings}
+
+\newsavebox{\headingbox}
+\sbox{\headingbox}{%
+    \begin{minipage}[b]{0.5\textwidth}
+        \begin{flushright}
+            \@title \\
+            \@subtitle \\
+            \@author \\
+        \end{flushright}
+    \end{minipage}}
+\markright{\hfill\usebox{\headingbox}}
diff --git a/docs/report/styles/packages.sty b/docs/report/styles/packages.sty
new file mode 100644
index 0000000..262b9d1
--- /dev/null
+++ b/docs/report/styles/packages.sty
@@ -0,0 +1,12 @@
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{styles/packages}[2021/09/29 Package imports]
+
+\RequirePackage[english]{babel}
+\RequirePackage[letterpaper,top=2.54cm,bottom=2.54cm,left=2.54cm,right=2.54cm,marginparwidth=1.75cm]{geometry}
+\RequirePackage{lipsum}
+\RequirePackage{array}
+\RequirePackage[colorlinks=true, allcolors=blue]{hyperref}
+\RequirePackage[autostyle, english = american]{csquotes}
+
+% Styles
+\MakeOuterQuote{"}
\ No newline at end of file
diff --git a/docs/report/styles/section.sty b/docs/report/styles/section.sty
new file mode 100644
index 0000000..ed4d606
--- /dev/null
+++ b/docs/report/styles/section.sty
@@ -0,0 +1,35 @@
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{styles/section}[2021/09/29 Section style]
+
+% ┌───────────────────────────────────┐   
+% │                   Title: Subtitle │ ──┬─ Header
+% │                            Author │ ──┘
+% │ Title                             │ ──┬─ Title
+% │ Subtitle                          │ ──┘
+% │                                   │ 
+% │ A Section                         │ ──┬─ [Sections]
+% │ ...                               │   │
+% │ 1.1 A Subsection                  │ ──┤
+% │ ...                               │   │
+% │ Another Section                   │ ──┤
+% │ ...                               │   │
+% │ 2.1 A Subsection                  │ ──┤
+% │ ...                               │   │
+% │ 2.2 Another Subsection            │ ──┘
+% │ ...                               │ 
+% │                                   │
+% │                                   │
+% └───────────────────────────────────┘
+
+\RequirePackage{indentfirst}
+% \RequirePackage{titlesec}
+% \titlespacing*{\section}{0pt}{1.1\baselineskip}{\baselineskip}
+
+% Paragraph spacing
+\setlength{\parskip}{1em}
+
+\RedeclareSectionCommand[
+    afterindent=false,
+    beforeskip=.5\baselineskip,
+    afterskip=.5\baselineskip
+]{section}
\ No newline at end of file
diff --git a/docs/report/styles/title.sty b/docs/report/styles/title.sty
new file mode 100644
index 0000000..fdeabbe
--- /dev/null
+++ b/docs/report/styles/title.sty
@@ -0,0 +1,29 @@
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{styles/title}[2021/09/29 Title style]
+
+% ┌───────────────────────────────────┐   
+% │                   Title: Subtitle │ ──┬─ Header
+% │                            Author │ ──┘
+% │ Title                             │ ──┬─ [Title]
+% │ Subtitle                          │ ──┘
+% │                                   │ 
+% │ A Section                         │ ──┬─ Sections
+% │ ...                               │   │
+% │ 1.1 A Subsection                  │ ──┤
+% │ ...                               │   │
+% │ Another Section                   │ ──┤
+% │ ...                               │   │
+% │ 2.1 A Subsection                  │ ──┤
+% │ ...                               │   │
+% │ 2.2 Another Subsection            │ ──┘
+% │ ...                               │ 
+% │                                   │
+% │                                   │
+% └───────────────────────────────────┘
+
+\renewcommand{\maketitle}{
+	\begin{flushleft}
+		{\Huge \bfseries \sffamily \@title }\\[2ex]
+		{\Large \sffamily \@subtitle }\\[4ex]
+	\end{flushleft}
+}
diff --git a/graphs/celegansneural.graph b/graphs/celegansneural.graph
new file mode 100644
index 0000000..961595d
--- /dev/null
+++ b/graphs/celegansneural.graph
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diff --git a/graphs/florida-bay.graph b/graphs/florida-bay.graph
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+127

diff --git a/graphs/karateWeighted.graph b/graphs/karateWeighted.graph
new file mode 100644
index 0000000..72a6161
--- /dev/null
+++ b/graphs/karateWeighted.graph
@@ -0,0 +1,34 @@
+0 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 10 1 11 1 12 1 13 1 17 1 19 1 21 1 31 1

+1 0 1 2 1 3 1 7 1 13 1 17 1 19 1 21 1 30 1

+2 0 1 1 1 3 1 7 1 8 1 9 1 13 1 27 1 28 1 32 1

+3 0 1 1 1 2 1 7 1 12 1 13 1

+4 0 1 6 1 10 1

+5 0 1 6 1 10 1 16 1

+6 0 1 4 1 5 1 16 1

+7 0 1 1 1 2 1 3 1

+8 0 1 2 1 30 1 32 1 33 1

+9 2 1 33 1

+10 0 1 4 1 5 1

+11 0 1

+12 0 1 3 1

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+14 32 1 33 1

+15 32 1 33 1

+16 5 1 6 1

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+20 32 1 33 1

+21 0 1 1 1

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+23 25 1 27 1 29 1 32 1 33 1

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+25 23 1 24 1 31 1

+26 29 1 33 1

+27 2 1 23 1 24 1 33 1

+28 2 1 31 1 33 1

+29 23 1 26 1 32 1 33 1

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+32 2 1 8 1 14 1 15 1 18 1 20 1 22 1 23 1 29 1 30 1 31 1 33 1

+33 8 1 9 1 13 1 14 1 15 1 18 1 19 1 20 1 22 1 23 1 26 1 27 1 28 1 29 1 30 1 31 1 32 1

diff --git a/graphs/polbooksWeighted.graph b/graphs/polbooksWeighted.graph
new file mode 100644
index 0000000..d3a32ed
--- /dev/null
+++ b/graphs/polbooksWeighted.graph
@@ -0,0 +1,105 @@
+0 1 1 2 1 3 1 4 1 5 1 6 1

+1 0 1 3 1 5 1 6 1

+2 0 1 4 1 5 1 7 1

+3 0 1 1 1 5 1 8 1 9 1 10 1 11 1 12 1 13 1 14 1 15 1 16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 1 26 1 27 1

+4 0 1 2 1 5 1 6 1 28 1 29 1 30 1 31 1

+5 0 1 1 1 2 1 3 1 4 1 6 1 7 1

+6 0 1 1 1 4 1 5 1 7 1 10 1 12 1 18 1 22 1 25 1 29 1

+7 2 1 5 1 6 1 14 1 30 1 58 1 71 1 85 1

+8 3 1 9 1 10 1 11 1 12 1 13 1 14 1 20 1 21 1 22 1 23 1 24 1 26 1 27 1 32 1 33 1 35 1 37 1 40 1 41 1 42 1 43 1 44 1 45 1 46 1

+9 3 1 8 1 11 1 12 1 14 1 20 1 24 1 27 1 41 1 45 1 47 1 48 1 49 1 50 1 51 1 52 1

+10 3 1 6 1 8 1 11 1 12 1 15 1 16 1 19 1 21 1 33 1 35 1 37 1 38 1 39 1 55 1

+11 3 1 8 1 9 1 10 1 12 1 13 1 14 1 17 1 20 1 21 1 22 1 26 1 27 1 29 1 45 1 47 1 50 1 56 1

+12 3 1 6 1 8 1 9 1 10 1 11 1 13 1 14 1 15 1 17 1 18 1 23 1 24 1 32 1 33 1 36 1 38 1 39 1 40 1 41 1 44 1 46 1 47 1 54 1 55 1

+13 3 1 8 1 11 1 12 1 17 1 29 1 32 1 40 1 42 1 43 1 44 1 47 1 57 1

+14 3 1 8 1 9 1 11 1 12 1 7 1 25 1 26 1 58 1

+15 3 1 10 1 12 1 16 1 55 1

+16 3 1 10 1 15 1

+17 3 1 11 1 12 1 13 1 47 1

+18 3 1 6 1 12 1

+19 3 1 10 1 55 1 56 1 77 1

+20 3 1 8 1 9 1 11 1 24 1 40 1 48 1 49 1 53 1 57 1

+21 3 1 8 1 10 1 11 1 23 1

+22 3 1 6 1 8 1 11 1 25 1 40 1 52 1

+23 3 1 8 1 12 1 21 1 27 1 32 1 33 1 47 1 54 1

+24 3 1 8 1 9 1 12 1 20 1 26 1 40 1 47 1 53 1

+25 3 1 6 1 14 1 22 1 40 1

+26 3 1 8 1 11 1 14 1 24 1 40 1 45 1 47 1 53 1

+27 3 1 8 1 9 1 11 1 23 1 40 1 41 1 47 1 54 1

+28 4 1 66 1 72 1

+29 4 1 6 1 11 1 13 1

+30 4 1 7 1 31 1 58 1 66 1 67 1 70 1 73 1 74 1 75 1 76 1 77 1 79 1 80 1 82 1 83 1 84 1 86 1 93 1 99 1

+31 4 1 30 1 49 1 73 1 74 1 75 1 76 1 77 1 78 1 82 1 91 1

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+34 35 1 36 1 37 1 38 1 39 1

+35 34 1 8 1 10 1 36 1 37 1 38 1 39 1 40 1 43 1 44 1

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+37 34 1 8 1 10 1 35 1 33 1 38 1 47 1

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+39 34 1 10 1 35 1 12 1 38 1 33 1 40 1 42 1

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+43 8 1 35 1 13 1 42 1 56 1

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+47 9 1 40 1 41 1 11 1 12 1 13 1 42 1 36 1 37 1 17 1 33 1 45 1 46 1 23 1 24 1 26 1 27 1 54 1

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+49 9 1 20 1 31 1 48 1 57 1 58 1 72 1 76 1

+50 9 1 11 1 58 1

+51 9 1 52 1 58 1 64 1 65 1 69 1

+52 9 1 22 1 51 1 58 1 64 1

+53 40 1 20 1 24 1 26 1 76 1

+54 40 1 41 1 12 1 47 1 23 1 27 1

+55 10 1 12 1 15 1 19 1

+56 11 1 19 1 43 1 57 1

+57 13 1 56 1 20 1 48 1 49 1

+58 14 1 7 1 30 1 49 1 50 1 51 1 52 1 64 1 65 1 68 1 69 1 77 1 85 1

+59 60 1 61 1 62 1 63 1 99 1

+60 59 1 62 1 63 1 84 1 86 1 99 1

+61 59 1 86 1 95 1 101 1

+62 59 1 60 1 63 1 84 1 99 1 100 1

+63 59 1 60 1 62 1 99 1

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+65 64 1 58 1 51 1 67 1 68 1 69 1 85 1

+66 64 1 28 1 30 1 67 1 70 1 72 1 73 1 74 1 76 1 80 1 84 1 85 1 86 1 88 1 89 1 90 1 93 1 96 1 97 1 99 1 100 1

+67 64 1 65 1 66 1 30 1 103 1 104 1

+68 64 1 58 1 65 1 71 1

+69 64 1 58 1 65 1 51 1 104 1

+70 64 1 66 1 30 1 71 1 72 1 75 1 90 1

+71 7 1 68 1 70 1 72 1 73 1 74 1 75 1 76 1 77 1 78 1 79 1 80 1 81 1 82 1 83 1

+72 71 1 28 1 66 1 49 1 70 1 73 1 74 1 75 1 76 1 78 1 79 1 80 1 82 1 84 1 85 1 86 1 87 1 88 1 89 1 90 1 91 1 92 1

+73 71 1 72 1 66 1 30 1 31 1 74 1 75 1 82 1 83 1 84 1 86 1 89 1 92 1 93 1 94 1 95 1 96 1 97 1 98 1 99 1 100 1

+74 71 1 72 1 73 1 66 1 30 1 31 1 75 1 78 1 79 1 82 1 84 1 87 1 88 1 91 1 98 1 99 1

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+76 71 1 72 1 75 1 66 1 30 1 31 1 49 1 53 1 77 1 82 1 83 1 84 1 86 1

+77 71 1 75 1 58 1 30 1 19 1 31 1 76 1

+78 71 1 72 1 74 1 75 1 31 1

+79 71 1 72 1 74 1 75 1 30 1 84 1 91 1 100 1

+80 71 1 72 1 66 1 30 1

+81 71 1 84 1 86 1 97 1

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+83 71 1 73 1 75 1 30 1 76 1 84 1 87 1 100 1

+84 72 1 74 1 75 1 66 1 73 1 60 1 30 1 62 1 76 1 79 1 81 1 82 1 83 1 86 1 87 1 88 1 89 1 94 1 96 1 97 1 99 1 100 1 101 1

+85 72 1 7 1 58 1 65 1 66 1

+86 72 1 73 1 66 1 84 1 60 1 30 1 61 1 76 1 81 1 89 1 93 1 97 1 100 1 101 1

+87 72 1 74 1 84 1 83 1 98 1

+88 72 1 74 1 66 1 84 1 89 1

+89 72 1 73 1 66 1 84 1 86 1 88 1

+90 72 1 66 1 70 1 91 1 99 1

+91 72 1 74 1 75 1 31 1 90 1 79 1 98 1 100 1

+92 72 1 73 1 75 1

+93 73 1 66 1 86 1 30 1 94 1 99 1 102 1

+94 73 1 84 1 93 1 95 1 96 1 101 1 102 1

+95 73 1 94 1 61 1 102 1

+96 73 1 66 1 84 1 94 1 97 1 100 1

+97 73 1 66 1 84 1 86 1 96 1 81 1

+98 73 1 74 1 87 1 91 1 100 1

+99 73 1 74 1 66 1 84 1 93 1 60 1 59 1 30 1 62 1 63 1 90 1 100 1

+100 73 1 66 1 84 1 86 1 96 1 98 1 99 1 62 1 79 1 91 1 83 1 101 1

+101 84 1 86 1 94 1 100 1 61 1

+102 93 1 94 1 95 1 46 1

+103 67 1 104 1

+104 67 1 69 1 103 1

diff --git a/output/constant_cuts.csv b/output/constant_cuts.csv
new file mode 100644
index 0000000..9fbdcbd
--- /dev/null
+++ b/output/constant_cuts.csv
@@ -0,0 +1,7 @@
+Graph,Exact Cuts,Contract1 Cuts,Contract2 Cuts,Contract3 Cuts,Contract4 Cuts,Contract5 Cuts
+celegansneural.graph,1,1,9,4,1,12
+Project4Graph2.txt,10,10,10,10,11,11
+Project4Graph1.txt,5,5,5,5,5,11
+polbooksWeighted.graph,2,5,3,4,7,4
+karateWeighted.graph,1,1,2,2,2,2
+florida-bay.graph,2,16,204,13,288,12
diff --git a/output/constant_times.csv b/output/constant_times.csv
new file mode 100644
index 0000000..53ff7d6
--- /dev/null
+++ b/output/constant_times.csv
@@ -0,0 +1,7 @@
+Graph,Exact (ms),Contract1 (ms),Contract2 (ms),Contract3 (ms),Contract4 (ms),Contract5 (ms)
+celegansneural.graph,1750.2084,81.0912,18.408,18.5579,17.5412,17.3655
+Project4Graph2.txt,0.0775,0.5155,0.4025,0.4386,0.1804,0.4783
+Project4Graph1.txt,0.0502,0.4511,0.4779,0.3802,0.4031,0.4454
+polbooksWeighted.graph,102.1129,44.3344,21.2961,21.3725,22.2797,21.3039
+karateWeighted.graph,3.1357,20.9576,1.2417,0.6967,0.7071,20.8144
+florida-bay.graph,513.2117,25.1122,49.1835,24.0553,24.487,24.4457
diff --git a/output/linear_cuts.csv b/output/linear_cuts.csv
new file mode 100644
index 0000000..50780b3
--- /dev/null
+++ b/output/linear_cuts.csv
@@ -0,0 +1,7 @@
+Graph,Exact Cuts,Contract1 Cuts,Contract2 Cuts,Contract3 Cuts,Contract4 Cuts,Contract5 Cuts
+celegansneural.graph,1,1,1,1,1,1
+Project4Graph2.txt,10,11,11,10,11,17
+Project4Graph1.txt,5,13,11,5,5,5
+polbooksWeighted.graph,2,4,2,3,3,2
+karateWeighted.graph,1,1,1,1,1,1
+florida-bay.graph,2,2,13,2,2,13
diff --git a/output/linear_times.csv b/output/linear_times.csv
new file mode 100644
index 0000000..2416aa9
--- /dev/null
+++ b/output/linear_times.csv
@@ -0,0 +1,7 @@
+Graph,Exact (ms),Contract1 (ms),Contract2 (ms),Contract3 (ms),Contract4 (ms),Contract5 (ms)
+celegansneural.graph,1750.2084,557.0621,503.0906,399.7002,413.8505,406.6934
+Project4Graph2.txt,0.0775,0.3823,0.4282,0.4109,0.1151,0.4346
+Project4Graph1.txt,0.0502,0.3987,0.369,0.341,0.3666,0.3754
+polbooksWeighted.graph,102.1129,73.3894,54.0188,34.3985,53.5005,32.6633
+karateWeighted.graph,3.1357,21.8032,21.3198,43.1202,21.163,0.8361
+florida-bay.graph,513.2117,87.747,88.7737,84.243,127.649,88.0672
diff --git a/output/polynomial_cuts.csv b/output/polynomial_cuts.csv
new file mode 100644
index 0000000..b7f40fa
--- /dev/null
+++ b/output/polynomial_cuts.csv
@@ -0,0 +1,7 @@
+Graph,Exact Cuts,Contract1 Cuts,Contract2 Cuts,Contract3 Cuts,Contract4 Cuts,Contract5 Cuts
+celegansneural.graph,1,1,1,1,1,1
+Project4Graph2.txt,10,10,10,10,10,10
+Project4Graph1.txt,5,5,5,5,5,5
+polbooksWeighted.graph,2,2,2,2,2,2
+karateWeighted.graph,1,1,1,1,1,1
+florida-bay.graph,2,2,2,2,2,2
diff --git a/output/polynomial_times.csv b/output/polynomial_times.csv
new file mode 100644
index 0000000..3d70aa4
--- /dev/null
+++ b/output/polynomial_times.csv
@@ -0,0 +1,7 @@
+Graph,Exact (ms),Contract1 (ms),Contract2 (ms),Contract3 (ms),Contract4 (ms),Contract5 (ms)
+celegansneural.graph,1750.2084,774759.5932,703439.1859,687873.8018,716489.0127,689531.893
+Project4Graph2.txt,0.0775,0.9838,1.9534,0.7784,0.7699,0.3623
+Project4Graph1.txt,0.0502,0.6279,0.2741,0.6162,0.3017,0.5493
+polbooksWeighted.graph,102.1129,6181.3018,6342.346,6557.8713,6485.526,6532.7274
+karateWeighted.graph,3.1357,134.6114,110.5004,129.3092,110.1674,130.8909
+florida-bay.graph,513.2117,41388.8641,42039.0769,43972.4187,43956.6237,43784.628
diff --git a/src/NetworkFlow/Graph.cs b/src/NetworkFlow/Graph.cs
index a66732d..54c2b29 100644
--- a/src/NetworkFlow/Graph.cs
+++ b/src/NetworkFlow/Graph.cs
@@ -1,22 +1,36 @@
 using System;
 using System.Collections.Generic;
+using System.Linq;
 
 namespace NetworkFlow
 {
     using Nodes = Dictionary<int, Node>;
     using Path = List<int>;
-    public class Graph
+    public class Graph : ICloneable
     {
 
         Dictionary<int, Node> _nodes;
+        public bool Undirected;
 
         public Nodes Nodes { get => _nodes; set => _nodes = value; }
 
-        public Graph()
+        public Graph(bool undirected = false)
         {
+            Undirected = undirected;
             Nodes = new Nodes();
         }
 
+        public Graph(Graph o)
+        {
+            Undirected = o.Undirected;
+            Nodes = o.Nodes.ToDictionary(entry => entry.Key,
+                                       entry => (Node)entry.Value.Clone());
+        }
+
+        public Graph ShallowCopy() => (Graph)this.MemberwiseClone();
+        public object Clone() => new Graph(this);
+        // public object Clone() => new Graph(this._nodes, Undirected);
+
         /// <summary>
         /// Indexer; Retrieves the node with node.Id of <c>id</c> 
         /// </summary>
@@ -31,8 +45,14 @@ namespace NetworkFlow
         /// </summary>
         public void AddNode(int id)
         {
-            if (!this.Nodes.ContainsKey(id))
-                this.Nodes.Add(id, new(id));
+            this.Nodes.TryAdd(id, new(id));
+        }
+
+        public void RemoveNode(int id)
+        {
+            if (this[id].Edges.Count > 1)
+                throw new Exception("Removing this node would leave orphaned batma... edges, I mean edges.");
+            this.Nodes.Remove(id);
         }
 
         /// <summary>
@@ -41,7 +61,20 @@ namespace NetworkFlow
         public void AddEdge(int u, int v, double capacity)
         {
             AddNode(u);
-            this[u].Edges.Add(v, capacity);
+            AddNode(v);
+
+            if (!Nodes[u].Edges.TryAdd(v, capacity))
+                Nodes[u].Edges[v] += capacity;
+
+            if (Undirected && !Nodes[v].Edges.TryAdd(u, capacity))
+                Nodes[v].Edges[u] += capacity;
+        }
+
+        public void RemoveEdge(int u, int v)
+        {
+            Nodes[u].Edges.Remove(v);
+            if (Undirected && Nodes[v].Edges.ContainsKey(u))
+                Nodes[v].Edges.Remove(u);
         }
 
         /// <summary>
@@ -81,7 +114,7 @@ namespace NetworkFlow
                 maxFlow += capacity;
 
                 // output the current progress
-                Console.WriteLine($"The augmenting path is {String.Join(",", path)} capacity = {capacity}");
+                // Console.WriteLine($"The augmenting path is {String.Join(",", path)} capacity = {capacity}");
             }
 
             // output when completed
@@ -129,9 +162,46 @@ namespace NetworkFlow
             // return an empty path if a path to terminal node was not found
             return new();
         }
+
+
+        public double Contraction()
+        {
+
+            Random random = new Random();
+
+            // while nodes > 2
+            while (Nodes.Count > 2)
+            {
+                // pick a random edge
+                Node node = Nodes.Values.ElementAt(random.Next(0, Nodes.Count));
+
+                int u = node.Id;
+                int v = node.Edges.Keys.ElementAt(random.Next(0, node.Edges.Count));
+
+                // redirect edges of one node (v) to other node (u)
+                // this includes changing the edges that point to v for each node that v has in its edges
+                foreach (var edge in Nodes[v].Edges)
+                    if (edge.Key != u)
+                    {
+                        AddEdge(u, edge.Key, edge.Value);
+                        RemoveEdge(v, edge.Key);
+                    }
+
+                // remove the edge from both sides (u and v)
+                RemoveEdge(u, v);
+
+                // delete node whose edges were redirected (v)
+                RemoveNode(v);
+            }
+
+            // return the sum of the remaining edges' weights
+            return Nodes.ElementAt(0).Value.Edges.ElementAt(0).Value;
+        }
+
+
     }
 
-    public struct Node
+    public struct Node : ICloneable
     {
         public int Id { get; set; }
         public Dictionary<int, double> Edges { get; set; }
@@ -141,5 +211,14 @@ namespace NetworkFlow
             Id = id;
             Edges = new();
         }
+
+        public Node(Node o)
+        {
+            Id = o.Id;
+            Edges = o.Edges.ToDictionary(entry => entry.Key,
+                                       entry => entry.Value);
+        }
+
+        public object Clone() => new Node(this);
     }
 }
\ No newline at end of file
diff --git a/src/Program/Analysis.cs b/src/Program/Analysis.cs
new file mode 100644
index 0000000..f817200
--- /dev/null
+++ b/src/Program/Analysis.cs
@@ -0,0 +1,89 @@
+
+using System;
+using System.Collections.Generic;
+using System.Diagnostics;
+using System.Linq;
+using System.Threading.Tasks;
+using NetworkFlow;
+
+namespace Program
+{
+    public struct Result
+    {
+        public double MinCut;
+        public TimeSpan Runtime;
+
+        public Result(double minCut, TimeSpan runtime)
+        {
+            MinCut = minCut;
+            Runtime = runtime;
+        }
+
+        public override string ToString() => $"{MinCut} @ {Runtime.TotalMilliseconds}";
+    }
+
+    class Analysis
+    {
+        Graph _graph;
+        Result _exact = new();
+        Result Exact { get => _exact.Equals(default(Result)) ? (_exact = CalculateExact()) : _exact; }
+        int Repetitions;
+
+        public Analysis(Graph graph, int repetitions)
+        {
+            _graph = graph;
+            Repetitions = repetitions;
+        }
+
+        public List<Result> Analize(int iterations)
+        {
+            List<Result> results = new();
+            results.Add(Exact);
+            Console.WriteLine($"Exact {Exact}");
+            for (int i = 0; i < Repetitions; i++)
+            {
+                results.Add(CalculateApprox(iterations));
+                Console.WriteLine($"Contract_{i + 1} {results.Last()}");
+            }
+
+            return results;
+        }
+
+        Result CalculateExact()
+        {
+            Stopwatch stopwatch = Stopwatch.StartNew();
+            double result = double.MaxValue;
+
+            // loop t for all nodes
+            foreach (var node in _graph.Nodes.Keys.ToList().Skip(1))
+            {
+                var graphClone = (Graph)_graph.Clone();
+
+                // take min of current result and new result
+                double currentResult = graphClone.MaxFlow(0, node);
+                if (currentResult != 0)
+                    result = Math.Min(result, currentResult);
+            }
+
+            return new(result, stopwatch.Elapsed);
+        }
+
+        Result CalculateApprox(int iterations)
+        {
+            Stopwatch stopwatch = Stopwatch.StartNew();
+            double result = double.MaxValue;
+
+            #region Parallel_Loop
+            Parallel.For(0, iterations, j =>
+            {
+                var graphClone = (Graph)_graph.Clone();
+                double currentResult = graphClone.Contraction();
+                if (currentResult != 0)
+                    result = Math.Min(result, currentResult);
+            });
+            #endregion
+
+            return new(result, stopwatch.Elapsed);
+        }
+    }
+}
\ No newline at end of file
diff --git a/src/Program/Program.cs b/src/Program/Program.cs
index 90e80bd..05a91dc 100644
--- a/src/Program/Program.cs
+++ b/src/Program/Program.cs
@@ -6,102 +6,73 @@ using Graph = NetworkFlow.Graph;
 
 namespace Program
 {
+
     class Program
     {
         static void Main(string[] args)
         {
-            // attempt to read file from command line args, otherwise asks for a file
-            FileInfo inputFile = (args.Length > 0) ? new FileInfo(args[0]) : ReadFileName();
-
-            // attempt to get source and terminal nodes from command line args
-            string source = (args.Length >= 2) ? args[1] : default(string);
-            string terminal = (args.Length >= 3) ? args[2] : default(string);
-
+            List<Analysis> Analysii = new();
+            DirectoryInfo graphDir = new DirectoryInfo((args.Length > 0) ? args[0] : "graphs");
+            DirectoryInfo outDir = new("../../output");
+            outDir.Create();
 
-            if (!inputFile.Exists)
+            if (!graphDir.Exists)
             {
-                Console.WriteLine($"Failed to open {inputFile}: File does not exist.");
-                return;
+                Console.WriteLine($"Failed to open {graphDir}: Graph does not exist.");
+                System.Environment.Exit(1);
             }
 
-            // read file into graph
-            Graph graph = ReadFile(inputFile.FullName);
-
-            // verify command line source and terminal values or gets new values from the user
-            (int s, int t) = ReadSourceAndTerminal(graph, source, terminal);
-
-            // call maxFlow
-            double maxFlow = graph.MaxFlow(s, t);
-            Console.WriteLine($"The max flow is {maxFlow}");
-        }
+            string cuts_header = $"Graph,Exact Cuts,Contract1 Cuts,Contract2 Cuts,Contract3 Cuts,Contract4 Cuts,Contract5 Cuts";
+            string times_header = $"Graph,Exact (ms),Contract1 (ms),Contract2 (ms),Contract3 (ms),Contract4 (ms),Contract5 (ms)";
+            List<string> constant_cuts = new() { cuts_header };
+            List<string> constant_times = new() { times_header };
+            List<string> linear_cuts = new() { cuts_header };
+            List<string> linear_times = new() { times_header };
+            List<string> polynomial_cuts = new() { cuts_header };
+            List<string> polynomial_times = new() { times_header };
 
-        public static (int s, int t) ReadSourceAndTerminal(Graph graph, string source, string terminal)
-        {
-            int s, t;
-            // retries until it succeeds
-            while (true)
+            foreach (var file in graphDir.EnumerateFiles())
             {
-                // try to parse supplied values
-                bool isSetSource = int.TryParse(source, out s);
-                bool isSetTerminal = int.TryParse(terminal, out t);
-
-                // validates the values are ints and the graph contains the corresponding node
-                if (!(isSetSource && graph.Nodes.ContainsKey(s)))
-                {
-                    if (source != default(string))
-                        Console.WriteLine($"Invalid Source Node: {source}");
-                    Console.Write($"Enter the Source Node: ");
-                    // asks for a new value
-                    source = Console.ReadLine();
-                }
-                // validates the values are ints and the graph contains the corresponding node
-                if (!(isSetTerminal && graph.Nodes.ContainsKey(t)))
-                {
-                    if (terminal != default(string))
-                        Console.WriteLine($"Invalid Terminal Node: {terminal}");
-                    Console.Write($"Enter the Terminal Node: ");
-                    // asks for a new value
-                    terminal = Console.ReadLine();
-                }
-                // if everything is correct then we can return
-                if (isSetSource && isSetTerminal && graph.Nodes.ContainsKey(s) && graph.Nodes.ContainsKey(t))
-                    break;
+                Graph graph = ReadFile(file);
+                Analysis analysis = new(graph, 5);
+                List<Result> results;
+                int iter;
+                Console.WriteLine(file.Name);
+
+                iter = 10;
+                Console.WriteLine($"\nconstant ({iter}):");
+                results = analysis.Analize(iter);
+                constant_cuts.Add($"{file.Name},{String.Join(",", results.Select(r => r.MinCut))}");
+                constant_times.Add($"{file.Name},{String.Join(",", results.Select(r => r.Runtime.TotalMilliseconds))}");
+
+                iter = graph.Nodes.Count;
+                Console.WriteLine($"\nlinier ({iter}):");
+                results = analysis.Analize(iter);
+                linear_cuts.Add($"{file.Name},{String.Join(",", results.Select(r => r.MinCut))}");
+                linear_times.Add($"{file.Name},{String.Join(",", results.Select(r => r.Runtime.TotalMilliseconds))}");
+
+                iter = (int)(Math.Pow(graph.Nodes.Count, 2) * Math.Log(graph.Nodes.Count, Math.E));
+                Console.WriteLine($"\npolynomial ({iter}):");
+                results = analysis.Analize(iter);
+                polynomial_cuts.Add($"{file.Name},{String.Join(",", results.Select(r => r.MinCut))}");
+                polynomial_times.Add($"{file.Name},{String.Join(",", results.Select(r => r.Runtime.TotalMilliseconds))}");
             }
 
-
-            return (s, t);
+            File.WriteAllLines($"{outDir.FullName}/constant_cuts.csv", constant_cuts);
+            File.WriteAllLines($"{outDir.FullName}/constant_times.csv", constant_times);
+            File.WriteAllLines($"{outDir.FullName}/linear_cuts.csv", linear_cuts);
+            File.WriteAllLines($"{outDir.FullName}/linear_times.csv", linear_times);
+            File.WriteAllLines($"{outDir.FullName}/polynomial_cuts.csv", polynomial_cuts);
+            File.WriteAllLines($"{outDir.FullName}/polynomial_times.csv", polynomial_times);
         }
 
-        public static FileInfo ReadFileName()
-        {
-            string filePath;
-
-            // continues to ask for a valid filepath until obtained
-            while (true)
-            {
-                Console.Write("Enter a path to a points file: ");
-                filePath = Console.ReadLine();
-
-                if (String.IsNullOrEmpty(filePath))
-                    Console.WriteLine("File path cannot be empty!");
-                else if (!System.IO.File.Exists(filePath))
-                    Console.WriteLine($"{filePath} does not exist.");
-                else
-                    break;
-            }
-
-            FileInfo file = new FileInfo(filePath);
-
-            return file;
-        }
-
-        public static Graph ReadFile(string file)
+        public static Graph ReadFile(FileInfo file)
         {
             // create default Graph object
-            Graph graph = new Graph();
+            Graph graph = new Graph(undirected: true);
 
             // Read in graph file
-            foreach (string line in File.ReadLines(file))
+            foreach (string line in File.ReadLines(file.FullName))
             {
                 // each file line is a Node with optional edges
                 // line format:
@@ -116,11 +87,13 @@ namespace Program
                     // AddEdge(int u, int v, double weight)
                     int.TryParse(vals[i], out v);
                     double.TryParse(vals[i + 1], out weight);
-                    graph.AddEdge(u, v, weight);
+                    if (!graph[u].Edges.ContainsKey(v))
+                        graph.AddEdge(u, v, weight);
                 }
             }
             // return object when done
             return graph;
         }
+
     }
 }