back to CSI 7160 home

Lecture Contents

Chapters/sections refer to the textbook by Kreher and Stinson, "Combinatorial Algorithms".
Tentative schedule (it will be updated if changes occur):
days and tasks  Lecture Contents: textbook
sections
Sep 06 Introduction to the course.
What are combinatorial structures, combinatorial algorithms and combinatorial problems?
Course outline.
Parts of Chapter 1.
Sep 13 Combinatorial Generation: (ranking, unranking, successor) for
  • all subsets (lexicographical and Gray code orderings)
  • k-subsets (lexicographical)
  • 2.1,2.2,2.3.1
    Sep 20 (A1 out) Combinatorial Generation: (ranking, unranking, successor) for
  • k-subsets (revolving door ordering)
  • permutations (lexicographical ordering)
  • 2.3.3,2.4.1
    Sep 27 Combinatorial Generation: (ranking, unranking, successor) for
  • permutations (Trotter-Johnson ordering)

  • Exhaustive Generation:
  • Introduction to backtracking, a general backtracking algorithm.
  • 2.4.2, 4.1,4.2
    Oct 04 Exhaustive Generation:
  • Generating all cliques. Average-case analysis of the algorithm.
  • Estimating the size of a backtrack tree.
  • 4.3,4.3.1, 4.4
    Oct 11
    (A1 in/A2 out)
    (Exhaustive Generation) -
    Oct 18 (Exhaustive Generation/Heuristic Search) -
    Oct 25
    (project
    proposal in.)
    (Heuristic Search) -
    Nov 1
    (A2 in/A3 out)
    (Heuristic search) -
    Nov 8 (Computing isomorphism) -
    Nov 15 (Computing isomorphism) -
    Nov 22
    (A3 in)
    (Topic to be announced) -
    Nov 29
    (project in/
    presentation in)
    project presentations -