CS 5114: Theory of Algorithms (Fall 2018)

CS 5114 is a traditional introduction to the theory of algorithms for computer science graduate students. It covers methods to construct algorithms and to analyze algorithms mathematically for correctness and efficiency (e.g., running time and space used). The course starts with definitions of algorithmic efficiency, discusses powerful paradigms for algorithm design, defines the theory of NP-completeness, and presents current approaches for coping with intractability, including approximation and randomized algorithms. The course provides a foundation for research in the design and analysis of algorithms itself or on problems with significant algorithmic content.

Instructor

T. M. Murali

Please include "CS 5114" and a brief topic in the subject line of all email messages that you send me.

Class Meeting Times

Course Description and Syllabus

Homework Assignments

Homework 1, PDF, LaTeX (Assigned on August 27, 2018; due by the start of class on September 3, 2018).
Homework 2, PDF, LaTeX (Assigned on September 10, 2018; due by the start of class on September 19, 2018).
Homework 3, PDF, LaTeX (Assigned on September 19, 2018; due by the start of class on September 26, 2018).
Homework 4, PDF, LaTeX (Assigned on October 1, 2018; due by the start of class October 8, 2018).
Homework 5, PDF, LaTeX (Assigned on October 22, 2018; due by the start of class on October 29, 2018).
Homework 6, PDF, LaTeX (Assigned on November 5, 2018; due by the start of class on November 12, 2018)
Homework 7, PDF, LaTeX (Assigned on November 26, 2018; due by the start of class on December 3, 2018)

Schedule

This schedule is subject to continuous change throughout the semester. Please refer to this webpage for the most up-to-date information, for reading assignments, and for homeworks. I will announce every homework and examination via Canvas. All chapters below refer to the textbook, "Algorithm Design" by Kleinberg and Tardos, unless specified otherwise.

Date	Topic	Reading	Homework
Mon, Aug 20, 2018	Introduction and Course Logistics, Stable Matching	Chapter 1, 2.3
Wed, Aug 22, 2018	Analysis of Algorithms	Chapter 2.1-2.4
Mon, Aug 27, 2018	Review of priority queues and graph searches	Chapters 2.5, 3.1-3.3	Homework 1 assigned
Wed, Aug 29, 2018	Class cancelled
Mon, Sep 3, 2018	Labour Day, no class
Wed, Sep 5, 2018	Review of priority queues and graph searches, same lecture as the previous class Linear-time graph algorithms	Chapters 2.5, 3.1-3.3 Chapter 3.4	Homework 1 due
Mon, Sep 10, 2018	Greedy Graph Algorithms	Chapter 4.4-4.6	Homework 2 assigned
Wed, Sep 12, 2018	Greedy Graph Algorithms, same lecture as the previous class
Mon, Sep 17, 2018	Greedy Graph Algorithms, same lecture as the previous class
Wed, Sep 19, 2018	Applications of MST Divide and Conquer	Chapter 4.7 Chapter 5.1-5.2	Homework 2 due Homework 3 assigned
Mon, Sep 24, 2018	Divide and Conquer, same lecture as the previous class	Chapter 5.4
Wed, Sep 26, 2018	Dynamic Programming Unweighted and weighted interval scheduling	Chapter 4.1, Chapter 6.1-6.2	Homework 3 due
Mon, Oct 1, 2018	Dynamic Programming, same lecture as the previous class Segmented least squares	Chapter 6.3	Homework 4 assigned
Wed, Oct 3, 2018	Dynamic Programming, same lecture as the previous class RNA secondary structure	Chapter 6.5
Mon, Oct 8, 2018	Dynamic Programming, same lecture as the previous class Sequence alignment	Chapter 6.6-6.7	Homework 4 due Midterm examination assigned PDF, LaTeX
Wed, Oct 10, 2018	Dynamic Programming, same lecture as the previous class Sequence alignment	Chapter 6.7
Mon, Oct 15, 2018	Dynamic Programming, same lecture as the previous class Shortest paths in graphs	Chapter 6.8	Midterm examination due
Wed, Oct 17, 2018	Network Flow Ford-Fulkerson algorithm	Chapter 7.1-7.2 On the history of the transportation and maximum flow problems
Mon, Oct 22, 2018	Network Flow, same lecture as the previous class Ford-Fulkerson algorithm		Homework 5 assigned
Wed, Oct 24, 2018	Network Flow, same lecture as the previous class Scaling algorithm, Edmonds-Karp algorithm	Chapter 7.3
Mon, Oct 29, 2018	Applications of Network Flow Maximum matching	Chapter 7.5	Homework 5 due
Wed, Oct 31, 2018	Applications of Network Flow, same lecture as the previous class Edge-disjoint paths, Image segmentation	Chapter 7.6, 7.10
Mon, Nov 5, 2018	Applications of Network Flow, same lecture as the previous class Circulation with demands, Airline scheduling	Chapter 7.7, 7.9	Homework 6 assigned
Wed, Nov 7, 2018	NP and Computational Intractability	Chapter 8.1-8.2
Mon, Nov 12, 2018	NP and Computational Intractability, same lecture as previous class NP-Complete Problems	Chapter 8.3-8.4 Chapter 8.5	Homework 6 due
Wed, Nov 14, 2018	NP-Complete Problems, same lecture as the previous class	Chapter 8.6-8.7
Mon, Nov 26, 2018	NP-Complete Problems, same lecture as the previous class Coping with NP-completeness	Chapter 10.1	Homework 7 assigned
Wed, Nov 28, 2018	Coping with NP-completeness, same lecture as the previous class	Chapter 10.2, 11.1
Mon, Dec 3, 2018	Coping with NP-completeness, same lecture as the previous class	Chapter 11.3, 11.8	Homework 7 due
Tue, Dec 4, 2018	Final examination assigned PDF, LaTeX
Wed, Dec 5, 2018	No class
Wed, Dec 12, 2018	4pm, Final examination due