Syllabus for ICS 263

1. Recursion
   • integer multiplication [Karatsuba]
   • Divide-and-Conquer and Master theorems
   • matrix multiplication [Strassen, Pan], FFT
   • closest pairs of points
   • median selection
2. Evaluation of relations
   • transitive closure vs. matrix multiplication
   • Boolean matrix multiplication [4 Russians]
   • "easy" relations
3. Dynamic programming
   • multiplying matrices
   • LCS
   • Fibonacci numbers
   • Nim, including use of stack programming
   • incremental and stack programming - convex hull, maximum rectangle
4. Greedy algorithms
   • scheduling
   • MST
5. Trees
   • Huffman trees
   • optimal binary search trees
   • Hu-Tucker algorithm
   • tree isomorphism
   • Union-Find algorithms
6. Pattern matching
   • failure functions [KMP]
   • sublinear search [Boyer-Moore]
   • position trees
   • longest repeated factors [KMR]
   • maximal palindromes [Manacher]
7. NP-completeness
   • P and NP
   • reducibility, NP-completeness, Cook's theorem
   • reductions
8. Approximation algorithms
   • epsilon approximation
   • fully polynomial approximation algorithms
   • pseudo-polynomial algorithms
   • online algorithms and competitive analysis
9. Randomization, probabilistic algorithms
   • Sherwood - searching ordered linked list stored in arrays
   • Las Vegas - 8 queens
   • Monte Carlo - matrix multiplication verification
   • primality testing, public-key encryption