The Design and Analysis of Algorithms

I Lectures.- 1 Algorithms and Their Complexity.- 2 Topological Sort and MST.- 3 Matroids and Independence.- 4 Depth-First and Breadth-First Search.- 5 Shortest Paths and Transitive Closure.- 6 Kleene Algebra.- 7 More on Kleene Algebra.- 8 Binomial Heaps.- 9 Fibonacci Heaps.- 10 Union-Find.- 11 Analysis of Union-Find.- 12 Splay Trees.- 13 Random Search Trees.- 14 Planar and Plane Graphs.- 15 The Planar Separator Theorem.- 16 Max Flow.- 17 More on Max Flow.- 18 Still More on Max Flow.- 19 Matching.- 20 More on Matching.- 21 Reductions and NP-Completeness.- 22 More on Reductions and NP-Completeness.- 23 More NP-Complete Problems.- 24 Still More NP-Complete Problems.- 25 Cook's Theorem.- 26 Counting Problems and #P.- 27 Counting Bipartite Matchings.- 28 Parallel Algorithms and NC.- 29 Hypercubes and the Gray Representation.- 30 Integer Arithmetic in NC.- 31 Csanky's Algorithm.- 32 Chistov's Algorithm.- 33 Matrix Rank.- 34 Linear Equations and Polynomial GCDs.- 35 The Fast Fourier Transform (FFT).- 36 Luby's Algorithm.- 37 Analysis of Luby's Algorithm.- 38 Miller's Primality Test.- 39 Analysis of Miller's Primality Test.- 40 Probabilistic Tests with Polynomials.- II Homework Exercises.- Homework 1.- Homework 2.- Homework 3.- Homework 4.- Homework 5.- Homework 6.- Homework 7.- Homework 8.- Homework 9.- Homework 10.- Miscellaneous Exercises.- III Homework Solutions.- Homework 1 Solutions.- Homework 2 Solutions.- Homework 3 Solutions.- Homework 4 Solutions.- Homework 5 Solutions.- Homework 6 Solutions.- Homework 7 Solutions.- Homework 8 Solutions.- Homework 9 Solutions.- Homework 10 Solutions.- Solutions to Miscellaneous Exercises.