Foundations of Algorithms
CSCI-665 section 5
Spring 2017

Instructor

Stanisław Radziszowski

bldg. 70B, room 3657,
(585) 475-5193, spr@cs.rit.edu
http://www.cs.rit.edu/~spr
Office hours: Tue/Thu 8-9pm, Wed 2-3pm
(if nobody comes by 8:15pm I may leave), or send email

Lectures

Tuesday/Thursday, 6:30pm - 7:45pm, room 70-2455

General Course Documents

Syllabus, outcomes, general course documents, policies, sample schedule:
college syllabus, general schedule.
This page gives the current offering's contents and schedule.

Books

T. Cormen, C. Leiserson, R. Rivest and C. Stein, Introduction to Algorithms, the MIT Press, 2009, 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

Programming, preferred C/C++ and UNIX environment. (CSCI 603, CSCI 605, and CSCI 661, with B or better in all courses) or equivalent or permission of instructor. Students who take CSCI 261 may not take CSCI 665 for credit.

Evaluation

25% Homeworks
15% first Midterm Exam, Tuesday, February 28, in class
15% second Midterm Exam, Thursday, April 6, in class
20% Experimental Project
25% Final Exam, Tuesday, May 16, 6:30pm - 8:30pm, LBR 6-2233

Topics

Many slides from the MIT Open Courseware.
Some slides prepared by Gordon Royle, University of Western Australia.

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
7. Johnson's algorithm
Linear space Hirschberg's algorithm for the LCS
Network Flow
1. Flow networks, flows, Ford-Fulkerson method, cuts
2. Max-flow Min-Cut, Edmonds-Karp heuristics
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.
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
A* algorithm
1. Search problems, estimates, under-estimates and the A* algorithm

Foundations of Algorithms CSCI-665 section 5 Spring 2017