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<!DOCTYPE html>
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<title>Vanilla Knapsack and Its Various Flavors</title>
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<meta name="description" content="This project explores different approaches to the familiar Maximum 0-1 Knapsack problem.">
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<meta name="author" content="An Phi">
<meta name="date" content="2017-05-07">
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<li class="chapter" data-level="1" data-path="methodology.html"><a href="methodology.html"><i class="fa fa-check"></i><b>1</b> Methodology</a><ul>
<li class="chapter" data-level="1.1" data-path="methodology.html"><a href="methodology.html#maximum-0-1-knapsack"><i class="fa fa-check"></i><b>1.1</b> Maximum 0-1 Knapsack</a></li>
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<li class="chapter" data-level="4" data-path="result.html"><a href="result.html"><i class="fa fa-check"></i><b>4</b> Result and Discussion</a><ul>
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<i class="fa fa-circle-o-notch fa-spin"></i><a href="./">Vanilla Knapsack and Its Various Flavors</a>
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<h1 class="title">Vanilla Knapsack and Its Various Flavors</h1>
<h4 class="author"><em>An Phi</em></h4>
<h4 class="date"><em>2017-05-07</em></h4>
</div>
<div id="introduction" class="section level1 unnumbered">
<h1>Introduction</h1>
<p>In this project, we shall explore several different algorithms (flavors) to solve Maximum 0-1 Knapsack, a classic NP-Hard problem, <em>in a reasonable amount of time</em>. In our experiments, we want to show the differences between the running time and the optimal values obtained using these various algorithms.</p>
<p>We also want to take a side-track and demonstrate how Maximum 0-1 Knapsack can be used to solve 3SAT, the iconic NP-Complete problem, via the polynomial time reduction from 3SAT to Decision 0-1 Knapsack <span class="citation">(O’Connell <a href="#ref-oconnell2013">2013</a>)</span>.</p>
<p>We are going to explore 4 different flavors of Knapsack solver, including:</p>
<ul>
<li>Maximum Value Dynamic Programming</li>
<li>Minimum Cost Dynamic Programming</li>
<li>Greedy 2-Approximation</li>
<li>Fully Polynomial-time Approximation Scheme</li>
</ul>
</div>
<h3>References</h3>
<div id="refs" class="references">
<div id="ref-oconnell2013">
<p>O’Connell, Thomas C. 2013. <em>What Is a Computer and What Can It Do?</em> 1st ed. Milton Keynes, UK: College Publications.</p>
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