# ICS 311 Spring 2015 Topics

This gives a conceptual overview of how the topics are grouped and overall sequencing. The exact coverage and sequencing for a given semester may vary.

## Part I: Introduction to Analysis

This section introduces algorithms as abstractions of programs, and motivates why we need to do analysis of algorithms rather than just run empirical tests of programs. It then introduces some mathematical and conceptual tools for doing analysis. Two useful sorting algorithms are used for illustration; we'll return to sorting later.

• #1 - Chapter 1: Introduction to Course Format and to Algorithms
• #2 - Chapter 2: Examples of Analysis with Insertion and Merge Sort
• #3 - Chapter 3: Growth of Functions and Asymptotic Concepts

## Part II: Data Structures for Dictionaries & Sets

In this section we introduce problem solving and analysis methods (chapters 3-5), some of which have been covered in ICS 241, and also review review basic data structures and algorithms (chapters 10-12) that were introduced in ICS 211. The chapters from the text are interleaved and paired up in a manner that uses the basic dictionary and set data structures and algorithms to illustrate the problem solving and analysis methods. Hopefully this is mostly review of the two prerequisite courses with some added depth.

• #4 - Chapter 10: Stacks, Queues, Lists and Trees (Review)
• #5 - Chapter 5 and Goodrich & Tamassia section: Probabilistic Analysis and Randomized Algorithms; Skip list example
• #6 - Chapter 11: Hash Tables
• #7 - Chapter 4: Divide & Conquer and Associated Analysis Methods
• #8 - Chapter 12: Binary Search Trees

## Part III: Sorting and Balanced Trees

We continue into more advanced applications of trees (chapters 6 and 13), also providing the basis for another efficient sorting algorithm. We compare additional sorting algorithms to those from Chapter 2. Sorting is one of the most fundamental and common applications of computers, so efficiency is very important. We consider the broader question of how fast any sort algorithm can be. This is an example of a powerful method of computer science: reasoning about sets of possible algorithms rather than specific algorithms.

• #9 - Chapter 6: Heapsort and Priority Queues
• #10 - Chapters 7 & 8: Quicksort, Theoretical Limits, and O(n) sorts
• #11 - Chapter 13 & Sedgewick Chapter 15: Balanced Trees

## Part IV: Problem Solving and Analysis Methods

This part introduces two further problem solving methods, dynamic programming and greedy algorithms, with example applications. We then cover another important analytic method, amortization , with examples in the analysis of the union-find representation of sets. (Chronologically, #14 graphs will be introduced in this sequence to help you get started on a programming assignment, but conceptually they belong in the next section.)

• #12 - Chapter 15: Dynamic Programming
• #13 - Chapter 16: Greedy Algorithms & Huffman Codes
• #15 - Chapter 17 - Amortization
• #16 - Chapter 21 - Sets and Union-Find (now merged into one day with #15)

## Part V: Graphs

Graphs are a very flexible data structure for which many applications exist. Equipped with various problem solving and analytic tools, we examine the most important algorithms on graphs -- including some of the most classic work in computer science -- and their applications.

• #14 - Chapter 22: Graph Representations and Basic Algorithms (covered earlier)
• #17 - Chapter 23: Minimum Spanning Trees
• #18 - Chapter 24: Single-Source Shortest Paths
• #19 - Chapter 25: All Pairs Shortest Paths
• #20 - Chapter 26: Maximum Flow

## Part VI: Selected Topics

There are a number of other important or common application areas that have their own specialized algorithms of interest: multithreading (parallel algorithms), matrix operations, linear programming, operations on polynomials, number-theory, string matching, and computational geometry. These are covered in the text, but we can't fit them all in. At the instructor's discretion, some of these topics will be covered more lightly in class (no homework) Linear Programming fills out an area not covered well above (numeric algorithms), and also has interesting connections to previous material (e.g., you can solve flow problems with a linear program). Multithreading is important with today's multi-core and GPU machines, and string matching is central to many applications.

• #21 - Sedgewick Chapters 5 and 38; Chapter 29: Linear Programming
• #22 - Chapter 27: Multithreading
• #23 - Chapter 32: String Matching

## Part VII: Complexity Theory and NP-Completeness

Finally, abstracting further from algorithms to problems, we deal with the important question of whether an efficient algorithm is known (or even possible) for a given problem, and what to do if none are known. We encounter the most important open problem in theoretical computer science, which is also of practical interest because awareness of "intractable" problems and approximation algorithms could save you considerable trouble if you encounter one of these very common problems on the job! The seminal book on this topic by Garey & Johnson is the most cited reference in computer science.

• #24 - Chapter 34 - Complexity Theory & NP-Completeness
• #25 - Chapter 35 - Approximation Algorithms

Nodari Sitchinava (based on material by Dan Suthers)