The Design and Analysis of Algorithms (Monographs in Computer Science)

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. 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