Topics in Advanced Algorithms -
CSCI-761, Spring 2019
bldg. 70B, room 3657,
(585) 475-5193, firstname.lastname@example.org
office hours: TR 6:20pm-8pm, or send email
Tuesday/Thursday, 5:00pm-6:15pm, room 70-1455
General Course Documents
College course document, and
common RIT policies and calendar.
This course will explore the possibilities and limitations of
effective computations in combinatorics.
The first half of the course will cover classical algorithms
in combinatorial computing, together with the problems of
generation, enumeration and manipulation of various types
of combinatorial objects (graphs and finite set systems).
The second part will concentrate on computational techniques
for the search of different combinatorial configurations:
Ramsey numbers, t-designs, Turan coverings, Folkman colorings
and others. A number of topics suitable for further independent
study, project or thesis development will be discussed.
Students will write a term paper, either
theoretical based on literature or reporting student's own
implementation or experiments with a chosen combinatorial problem.
Depending on the size of the group, some or all students will
give a presentation to the class.
Combinatorial Algorithms. Generation, Enumeration, and Search,
by Donald L. Kreher and Douglas R. Stinson, CRC Press, 1999.
- Handbook of Combinatorics by
R. Graham, M. Grotschel and L. Lovasz,
MIT Press, 1995 (complementary reference monograph).
- Introductory Combinatorics by
Kenneth Bogart, third edition,
HBJ Publ., 2000 (complementary combinatorial background).
papers and presentations.
Other Journal articles.
CSCI-665 or ((CSCI-261 or CSCI-264) and permission of the
- 5% class participation
- 40% homeworks, programming exercises
- 25% midterm exam, Thursday, March 7, 5:00pm-6:15pm, 70-1455
- 30% final exam, Thursday, May 2, 7pm-9:30pm, room TBA
- Overview of types of objects
- Generation: subsets, Gray codes, permutations
- Trees, ranking
- Naive and enhanced backtracking
- Generating cliques
- Knapsack and traveling salesman problems
- Satisfiability problem, SAT-solvers
- Estimating size of backtrack tree
Heuristic searches for combinatorial configurations
- Hill climbing
- Simulated annealing
- Tabu search
- Genetic Algorithms
- Reduced basis
- Solving systems of integer equations
- Solving subset-sum problem
Computations in Ramsey theory
- Ramsey, Folkman and van der Waerden numbers
- Constructing critical configurations
- Computing, analyzing, and using automorphism groups of configurations
Computations in design theory
- Constructing balanced incomplete block design
- Constructing Steiner triple systems
- Constructing t-designs and coverings