Design and Analysis of Algorithms

Educational level: this is a tertiary (university) resource.
Completion status: this resource is ~25% complete.
Subject classification: this is a mathematics resource.

Donald Knuth lists, in the preface of The Art of Computer Programming Vol 3, the following as the important questions of design and analysis of algorithms[1]:

  • How are good algorithms discovered?
  • How can given algorithms and programs be improved?
  • How can the efficiency of algorithms be analyzed mathematically?
  • How can a person chose rationally between different algorithms for the same task?
  • In what senses can algorithms be proved "best possible"?
  • How does the theory of computing interact with practical considerations?
  • How can external memories like tapes, drums, or disks be used efficiently with large databases?
Edsger Dijkstra invented the shortest-path algorithm that bears his name. He also made contributions to formal specification and verification, algorithm design, programming languages, program design, operating systems, and distributed processing. Much of his writing is free to access at the E.W. Dijkstra Archive.

Course Outline edit

Introduction edit

Mathematical Foundations edit

Sorting edit

Divide and Conquer Methods edit

Greedy Methods edit

Pattern Matching edit

Backtracking edit

Graph Algorithms edit

Dynamic Programming edit

NP-Completeness edit

Approximation algorithms edit

Maximum Bipartite Matching edit

Problems Sets edit

solve the recurrence equuation for t(n)=2t(n-1)+n2^n+n^2

Exams edit

Textbooks edit

Free textbooks:

  • Algorithms by S. Dasgupta, C.H. Papadimitriou, and U.V. Vazirani

Supplementary Materials edit

Related Websites edit

References edit

  1. Donald Knuth. The Art of Computer Programming, Volume 3: Sorting and Searching, Third Edition. Addison-Wesley, 1997. ISBN 0-201-89685-0. Preface, pp.v.

See also edit