Summary

Ever played the Kevin Bacon game? This class will show you how it works by giving you an introduction to the design and analysis of algorithms, enabling you to discover how individuals are connected.

Expected Learning

By the end of this class you will understand key concepts needed to devise new algorithms for graphs and other important data structures and to evaluate the efficiency of these algorithms.

Syllabus

Lesson 1: A Social Network Magic Trick

Objective: Become familiar with Algorithm Analysis.

• Eulerian Path
• Correctness of Naïve
• Russian Peasants Algorithm
• Measuring Time
• Steps for Naive, Steps for Russian
• Divide and Conquer

Lesson 2: Growth Rates in Social Networks

Objective: Use mathematical tools to analyze how things are connected.

• Chain, Ring and Grid Networks
• Big Theta
• Planar Graphs
• Nodes, Edges, Regions
• Growth Rate of Edges in Planar Graph
• Hypercube
• Randomly Generated Graphs
• N Squared
• Tangled Hypercube

Lesson 3: Basic Graph Algorithms

Objective: Find the quickest route to Kevin Bacon.

• Properties of Social Networks
• Clustering Coefficient
• Connected Components
• Running Time of Connected Components
• Checking Pairwise Connectivity
• Pairwise Shortest Path
• Depth vs. Breadth First Search
• Recursion Replacement
• Marvel "Social" Network
• Finding Bridge Edges

Lesson 4: It’s Who You Know

Objective: Learn to keep track of your Best Friends using heaps.

• Degree Centrality
• Top K Via Partitioning
• Three Partitioning Cases
• Properties of a Heap
• Patch Up a Heap
• Down Heapify
• Heap Sort

Lesson 5: Strong and Weak Bonds

Objective: Work with Social Networks that have edge weights.

• Make a Tree
• Strength of Connections
• Weighted Social Networks
• How to Find the Shortest Path
• Dijkstra’s Shortest Path Algorithm
• Floyd-Warshall Intro
• Randomizing Clustering Coefficient
• Bounds on the Estimate

Lesson 6: Hardness of Network Problems

Objective: Explore what it means for a Social Network problem to be
"harder" than other.

• Tetristan
• Exponential Running Time
• Degrees of Hardness
• Reduction: Long and Simple Path
• Polynomial Time Decidable Problems
• Non-deterministic Polynomial Time Decidable Problem
• Clique Problem in NP
• Find the Strangers
• Graph Coloring is NP-Complete

Lesson 7: Review and Application

• Interview with Peter Winker (Professor, Dartmouth College) on Names and Boxes Problem && Puzzles and Algorithms

• Interview with Tina Eliassi-Rad (Professor, Rutgers University) on
  Statistical Measures in Network && Social Networks in Security and Protests

• Interview with Andrew Goldberg (Principal Researcher, Microsoft Research) on Practical Algorithms

• Interview with Vukosi Marivate (Graduate Student, Rutgers University) on Social Algorithms

• Interview with Duncan Watts (Principal Researcher, Microsoft) on Pathway That Can Use Two Nodes

• Intro to Graph Search Animation

Required Knowledge

This class assumes an understanding of programming at the level of CS101, including the ability to read and write short programs in Python; it also assumes a comfort level with mathematical notation at the level of high school Algebra II or the SATs.