Design and Analysis of Algorithms
CSCI 5454, Spring 2013
Time: Monday and Wednesday, 1:00pm - 2:15pm
Room: ECCS 1B12

Instructor: Aaron Clauset
Office: ECOT 743
Office hours: Wednesdays, 10:00-11:30am
Email: look it up
Syllabus

Description
Course work and grading
Schedule and lecture notes
Problem sets

Description
Algorithms are the heart of computer science, and their essential nature is to automate some aspect of the collecting, organizing and processing of information. Today, information of all kinds is increasingly available in enormous quantities. However, our ability to make sense of all this information, to manage, organize and search it, and to use it for practical purposes, e.g., self-driving cars, adaptive computation, search algorithms for the Internet or for social networks, artificial intelligence, and many scientific applications, relies on the design of efficient algorithms, that is, algorithms that are fast, use little memory and provide guarantees on their performance.

This graduate-level course will cover topics related to algorithm design and analysis. Topics will include divide and conquer algorithms, greedy algorithms, graph algorithms, algorithms for social networks, computational biology, optimization algorithms, randomization and algorithm analysis. We will not cover any of these topics exhaustively. Rather, the focus will be on algorithmic thinking, performance guarantees and boundary cases, efficient solutions to practical problems and understanding how to analyze algorithms. Advanced topics will cover a selection of modern algorithms, many of which come from real-world applications.

Prerequisites
Undergraduate algorithms (CSCI 3104), data structures (CSCI 2270), discrete mathematics (CSCI 2824) and two semesters of calculus, or equivalents. This class assumes familiarity with asymptotic analysis (Big-O, etc.), recurrence relations and the correct implementation of basic algorithms. Students without the required background may struggle to keep up with the lectures and assignments. There will be a brief survey at the beginning of the semester to help me get an idea of the class's preparation.

Text
Required:
Introduction to Algorithms (3rd ed.), by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest and Clifford Stein ("CLRS"; available at the CU Bookstore).

Optional:
Algorithm Design, by J. Kleinberg and E. Tardos, and
Algorithms, by S. Dasgupta, C. Papadimitriou and U. Vazirani

Course work and grading
See the syllabus for description of the required coursework, including descriptions of the problem sets, crowd-source lecture and independent project assignments.

5454-002 (or by permission): Grades will be assigned based on attendance (0.2), crowd-source lecture or independent project (0.3), and problem sets (0.5).
5454-5454: Grades will be assigned based on the project (0.4) and problem sets (0.6).

Tentative Schedule
Week 1: Overview, why algorithms? (Lecture 0)
Week 2: Divide and conquer (Lecture 1 and Lecture 2)
Week 3: Randomized data structures (Lecture 3 and Lecture 4)
Week 4: Greedy algorithms (Lecture 5)
Week 5: Graph algorithms (Lecture 6 and Lecture 7)
Week 6: Minimum spanning trees (Lecture 8)
Week 7: Network flow (Lectures 9 and 10)
Week 8: Phylogenetic trees (Lectures 11 and 12)
Week 9: Optimization (Lecture 13) and Graph Clustering (Lectures 14 and 15)
Week 10: Stable matchings (Lecture 16) and
Crowd-source lecture (i) disjoint sets and union find (Lecture 17)
Week 11: Spring Break
Week 12: Crowd-source lectures:
(i) knapsack problems (Lecture 18) and (ii) sequence alignment (Lecture 19)
Week 13: Crowd-source lectures:
(i) randomized min-cut (Lecture 20) and (ii) Sudoku and latin square solvers (Lecure 21)
Week 14: Crowd-source lectures:
(i) Byzantine agreement (Lecture 22) and (ii) fair division algorithms (Lecture 23)
Week 15: Crowd-source lectures:
(i) NP-hard problems (Lecture 23) and (ii) approximation algorithms (Lecture 24)
Week 16: Crowd-source lectures:
(i) link prediction in social networks (Lecture 24) and (ii) PageRank algorithm (Lecture 25)

Problem Sets
Problem set 1 (assigned January 14; due February 4)
Problem set 2 (assigned February 5; due February 25)
Problem set 3 (assigned February 26; due March 18)
Problem set 4 (assigned March 19; due April 8)
Problem set 5 (assigned April 9; due April 29)

Readings
Week 3: William Pugh, Skip Lists: A Probabilistic Alternative To Balanced Trees

Resources
Advice on writing proofs, by Cathy O'Neil.
Mathematics for Computer Scientists; advice by Eric Lehman (Google), F. Thomson Leighton (MIT) and Albert R Meyer (MIT)
TeXShop (LaTeX installation for Mac OS X)
LaTeX resources and guides (here, here, here and here).
Algorithms Course Materials by Jeff Erickson (UIUC)