This document outlines the syllabus for a course on analysis of algorithms and complexity. The course will cover foundational topics like asymptotic analysis and randomized algorithms, as well as specific algorithms like sorting, searching trees, and graph algorithms. It will also cover advanced techniques like dynamic programming, greedy algorithms, and amortized analysis. Later topics will include NP-completeness, multi-threaded algorithms, and approaches for dealing with NP-complete problems. The requirements include exams, homework assignments, and a project, and the course will be taught in English.

1. Analysis of Algorithms and Complexity
Andres Mendez-Vazquez
Email: amendez@gdl.cinvestav.mx
Office Hours
3:00-4:00 PM Monday and
Wednesday Room 365
Contents
1 Overview 1
2 Texts 1
3 Prerequisites 2
4 Course Requirements 2
4.1 English . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
4.2 Exams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
4.3 Homework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
5 Subjects 3
1 Overview
In this class, you will learn to analyze and understand the computational complexity of different data structures and
algorithms in Computer Science. For this, we will learn to use the asymptotic notation to analyze and understand their
computational complexity. Examples of these methods are minimum spanning trees, greedy algorithms, probabilistic
algorithms, etc. Finally, we will look at the fact that the universe of polynomial algorithms is smaller than the universe
of the non-polynomial algorithms. For this, we will learn when an algorithm is Non-Polynomial (NP) by transforming
it to an already well known NP-Complete algorithm.
2 Texts
The required text for this course is:
• Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein, Introduction to Algorithms,
Third Edition (MIT Press, 2009).
In addition you can consult the following texts:
• S. Dasgupta, C. H. Papadimitriou, and U. V. Vazirani, Algorithms, First Edition (McGraw-Hill Education, 2006).
• Rajeev Motwani and Prabhakar Raghavan, Randomized Algorithms, Cambridge University Press, New York,
NY, USA.
• R. Sedgewick, K. Wayne, Algorithms (Addison-Wesley Professional, 2011).
1

2. 3 PREREQUISITES 2
• Russ Miller and Laurence Boxer. 2005. Algorithms Sequential and Parallel: A Unified Approach (Charles River
Media Computer Engineering (Hardcover)). Charles River Media, Inc., Rockland, MA, USA.
• Mark de Berg, Otfried Cheong, Marc van Kreveld, and Mark Overmars. 2008. Computational Geometry:
Algorithms and Applications (3rd edition). Telos, Santa Clara, CA, USA.
In addition to a lot of papers.
3 Prerequisites
Discrete mathematics, basic probability and data structures.
4 Course Requirements
The requirements of the course are
Requirement % of Grade Date
1. Midterm #1 15% Jan 31
2. MIDTERM #2 15% Feb 31
3. MIDTERM #3 15% March 28
3. Final 15% April 30
4. HOMEWORKS 20% TBA
5. Project 20% TBA
4.1 English
We will use English to teach the class. However you can ask in Spanish, I reserve the right to answer in English or
Spanish.
4.2 Exams
We will have three exams in this course, and you have five hours per test. Blank pages will be provided.
No makeup test unless medical issues with letter by the doctor.
4.3 Homework
We will have homework with four problems in each. You will use the format of IEEE style latex class at single column
for the homeworks. No other format will be accepted. It needs to have the following format:
1. Name and date must be at the first page.
2. Each problem must be stated before the solution.
It will no accepted in other way. They will be uploaded in the web place for the class. The programming assignments
need to work in order to be graded.
-
Late Homeworks will have 0 automatically.

3. 5 SUBJECTS 3
5 Subjects
In this course, we will cover the following subjects:
1. Foundations
(a) The Role of Algorithms in Computing
(b) Growth of Functions
(c) Divide-and- Conquer
(d) Recurrences
(e) Probabilistic Analysis and Randomized Algorithms
2. Sorting
(a) Heapsort
i. For Priority Queues
(b) Quicksort
i. Definition
ii. Expected time complexity
(c) Sorting in Linear Time
i. Counting Sort
ii. Radix Sort
iii. Bucket Sort
(d) Lower bounds for sorting under comparisons
3. Median and Order Statistics
(a) Definition
(b) Expected time for the i-th statistics
(c) The Worst Case for the i-th statistics
4. Basic Data Structures
(a) Elementary Data Structures
(b) Hash Table
i. Definition
(c) Binary Search Trees
i. Definition
ii. Insertion and Deletions
iii. Rotations
(d) Red-Black Trees
i. Well balanced trees
5. Advanced Techniques
(a) Dynamic Programming
i. Introduction
ii. Optimality of the subproblems
iii. Avoiding the recursion

4. 5 SUBJECTS 4
iv. Examples:
A. Longest Common subsequence
B. Matrix Chain Multiplication
(b) Greedy Algorithms
i. Introduction
ii. Defining the Greedy Choice
iii. Examples:
A. Knapsack Problem
B. Scheduling
C. Hoffman Codes
(c) Amortized Analysis
i. Introduction
ii. Aggregated Method
iii. Accounting Method
iv. Potential Method
v. Examples:
A. Dynamic Tables
B. Move-to-Front
6. Advanced Data Structures
(a) Skip Lists - A probabilistic Data Structure
(b) B-Trees - Fast Access to indexes
(c) Fibonacci Heaps - Better Priority Queues
7. Graph Algorithms
(a) Elementary Graph Algorithms
(b) Minimum Spanning Trees
i. Prim and Kruskal
(c) Single-Source Shortest Paths
i. Bellman-Ford
ii. Dijkstra’s Algorithms
(d) All-Pairs Shortest Paths
i. Dynamic Programming Solution
ii. Floyd-Warshall
iii. Johnson’s Algorithm
(e) Maximum Flow
i. Introduction
ii. Ford-Fulkerson
iii. Edmond-Karp
8. Selected Topics
(a) Multi-threaded Algorithms
i. Introduction
ii. Multi-Threading Model

5. 5 SUBJECTS 5
iii. Hierarchy of Complexities
iv. Example
A. Parallel Fibonacci
B. Parallel Matrix Multiplication
C. Parallel Merge Sort
(b) Matrix Based Algorithms
i. The Holy Grail - The Strassen’s Algorithm
ii. Lower Upper Decomposition
iii. Applications
(c) String Matching
i. Introduction
ii. Rabin-Karp
(d) Computational Geometry
i. Representation
ii. Segment Intersection
iii. Convex Hull
9. NP-Completeness
(a) Definitions
(b) Encodings
(c) Polynomial Time Verification
(d) Polynomial Reduction
(e) NP-Hard
(f) NP-Complete proofs
(g) A family of NP-Problems
10. Dealing with NP-Problems
(a) Backtracking
(b) Branch-and-Bound
(c) Approximation Algorithms
i. Approximation Ratios
ii. Problems
A. Vertex Cover
B. Traveling Salesman Problem
C. Set Covering Problem