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David M. Mount wrote:Copyright, David M. Mount, 2004, Dept. of Computer Science, University of Maryland, College Park, MD, 20742. These lecture notes were prepared by David Mount for the course CMSC 451, Design and Analysis of Computer Algorithms, at the University of Maryland. Permission to use, copy, modify, and distribute these notes for educational purposes and without fee is hereby granted, provided that this copyright notice appear in all copies.

Document Excerpts:

Programming is a very complex task, and there are a number of aspects of programming that make it so complex. The first is that most programming projects are very large, requiring the coordinated efforts of many people. (This is the topic a course like software engineering.) The next is that many programming projects involve storing and accessing large quantities of data efficiently. (This is the topic of courses on data structures and databases.) The last is that many programming projects involve solving complex computational problems, for which simplistic or naive solutions may not be efficient enough. The complex problems may involve numerical data (the subject of courses on numerical analysis), but often they involve discrete data. This is where the topic of algorithm design and analysis is important.

Although the algorithms discussed in this course will often represent only a tiny fraction of the code that is generated in a large software system, this small fraction may be very important for the success of the overall project. An unfortunately common approach to this problem is to first design an inefficient algorithm and data structure to solve the problem, and then take this poor design and attempt to fine-tune its performance. The problem is that if the underlying design is bad, then often no amount of fine-tuning is going to make a substantial difference.

The focus of this course is on how to design good algorithms, and how to analyze their efficiency. This is among the most basic aspects of good programming.

Course Overview:

This course will consist of a number of major sections. The first will be a short review of some preliminary material, including asymptotics, summations, and recurrences and sorting. These have been covered in earlier courses, and so we will breeze through them pretty quickly. We will then discuss approaches to designing optimization algorithms, including dynamic programming and greedy algorithms. The next major focus will be on graph algorithms. This will include a review of breadth-first and depth-first search and their application in various problems related to connectivity in graphs. Next we will discuss minimum spanning trees, shortest paths, and network flows. We will briefly discuss algorithmic problems arising from geometric settings, that is, computational geometry.

Most of the emphasis of the first portion of the course will be on problems that can be solved efficiently, in the latter portion we will discuss intractability and NP-hard problems. These are problems for which no efficient solution is known. Finally, we will discuss methods to approximate NP-hard problems, and how to prove how close these approximations are to the optimal solutions.