Algorithms, VCSG 800
Fall 2011

Instructor

Stanislaw Radziszowski

bldg. 70B, room 3657,
(585) 475-5193, spr@cs.rit.edu
http://www.cs.rit.edu/~spr
Office hours: M 5-6pm, TR 8-9pm (if nobody comes by 8:15pm I may go home), or send email

Lectures

Tuesday/Thursday, 6-8pm, room 70-3560

Books

• T. Cormen, C. Leiserson, R. Rivest and C. Stein, Introduction to Algorithms, the MIT Press, 2001 (2009), second (third) edition, required textbook.
• J. Kleinberg and E. Tardos, Algorithm Design, Addison-Wesley, 2006 (past textbook, optional).
• S. Dasgupta, C. Papadimitriou and U. Vazirani, Algorithms, McGraw-Hill, 2007 (past textbook, optional).
• D. Knuth, The Art of Computer Programming, vols. 1, 2, 3, Addison-Wesley, 1981 (The Book, optional).
• A. Aho, J. Hopcroft and J. Ullman, The Design and Analysis of Computer Algorithms , Addison-Wesley, 1976 (old good times, optional).
• D. Kreher and D. Stinson, Combinatorial Algorithms, Generation, Enumeration and Search, CRC Press, 1999 (complementary reading).
• D. Harel, Algorithmics, The Spirit of Computing , Addison Wesley, 1992 (optional).
• G. Brassard and P. Bratley, Fundamentals of Algorithmics, Prentice Hall, 1996 (optional).

Prerequisites

Evaluation

• 30% Homeworks
• 20% Midterm Exam, Tuesday, October 11, 2011, in class
• 20% Experimental Project on the LCS problem
• 30% Final Exam, Tuesday, 6-8pm, November 15, 2011

Topics

• Introduction and complexity (MIT lectures 1, 2 and 3)
  1. Computational problems, algorithms, input size
  2. Asymptotic notation complexity.
  3. Recurrences, master theorem
  4. Divide and conquer
• Dynamic programming (MIT lecture 15)
  1. Longest common subsequence
  2. Matrix-chain multiplication
• Greedy algorithms (MIT lecture 16)
  1. Definition of graph, basic graph terminology
  2. Minimum spanning trees - Prim
  3. Minimum spanning trees - Kruskal
  4. Priority queues, heaps, find-union algorithms
• Path algorithms (MIT lectures 17, 18 and 19)
  1. Breadth-first search, applications of breadth-first search.
  2. Depth-first search, topological sort
  3. Dijkstra's algorithm
  4. Relaxation, Bellman-Ford
  5. Matrix multiplication method
  6. Floyd-Warshall algorithm
• Network Flow
  1. Flow networks, flows, Ford-Fulkerson method, cuts
  2. Max-flow Min-Cut, Edmonds-Karp heuristics
• P and NP
  1. Complexity classes P and NP, P!=NP conjecture
  2. Reducibility, NP-completeness
• Attemps to solve traveling salesman and other NP-hard problems
  1. Approximation Algorithms, Nearest Neighbour methods
  2. Iterative improvement, Hill-climbing, Simulated annealing, Genetic Algorithms

  
  (not done last quarter)

• String processing
  1. Pattern-matching, Rabin-Karp algorithm, Knuth-Morris-Pratt algorithm and the Boyer-Moore algorithm.
  2. Great website with implementations and comments on various string algorithms.
• A* algorithm
  1. Search problems, estimates, under-estimates and the A* algorithm