**The Design and Analysis of Algorithms**

**Book Description:**

These are my lecture notes from CS681: Design and Analysis of Algo rithms, a one-semester graduate course I taught at Cornell for three consec utive fall semesters from ’88 to ’90. The course serves a dual purpose: to cover core material in algorithms for graduate students in computer science preparing for their PhD qualifying exams, and to introduce theory students to some advanced topics in the design and analysis of algorithms. The material is thus a mixture of core and advanced topics. At first I meant these notes to supplement and not supplant a textbook, but over the three years they gradually took on a life of their own. In addition to the notes, I depended heavily on the texts • A. V. Aho, J. E. Hopcroft, and J. D. Ullman, The Design and Analysis of Computer Algorithms. Addison-Wesley, 1975. • M. R. Garey and D. S. Johnson, Computers and Intractibility: A Guide to the Theory of NP-Completeness. w. H. Freeman, 1979. • R. E. Tarjan, Data Structures and Network Algorithms. SIAM Regional Conference Series in Applied Mathematics 44, 1983. and still recommend them as excellent references.

**Table of contents :**

Algorithms and Their Complexity

Topological Sort and MST

Matroids and Independence

Depth-First and Breadth-First Search

Shortest Paths and Transitive Closure

Kleene Algebra

More on Kleene Algebra

Binomial Heaps

Fibonacci Heaps

Union-Find

Analysis of Union-Find

Splay Trees

Random Search Trees

Planar and Plane Graphs

The Planar Separator Theorem

Max Flow

More on Max Flow

Still More on Max Flow

Matching

More on Matching

Reductions and NP-Completeness

More on Reductions and NP-Completeness

More NP-Complete Problems

Still More NP-Complete Problems

Cook’s Theorem

Counting Problems and #P

Counting Bipartite Matchings

Parallel Algorithms and NC

Hypercubes and the Gray Representation

Integer Arithmetic in NC

Csanky’s Algorithm

Chistov’s Algorithm

Matrix Rank

Linear Equations and Polynomial GCDs

The Fast Fourier Transform (FFT)

Luby’s Algorithm

Analysis of Luby’s Algorithm

Miller’s Primality Test

Analysis of Miller’s Primality Test

Probabilistic Tests with Polynomials

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**The Design and Analysis of Algorithms**

Author(s): Dexter C. Kozen

Series: Texts and Monographs in Computer Science

Publisher: Springer, Year: 1992

ISBN: 978-1-4612-8757-5,978-1-4612-4400-4

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