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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
Sep 09 Introduction to the course.
What are combinatorial structures, combinatorial algorithms and combinatorial problems?
Course outline.
Parts of Chapter 1.
Sep 16 (A1 out) Combinatorial Generation: (ranking, unranking, successor) for 
  • all subsets (lexicographical and Gray code orderings)
  • k-subsets (lexicographical) 
  • 2.1,2.2,2.3.1 
    Sep 23  Combinatorial Generation: (ranking, unranking, successor) for 
  • k-subsets (revolving door ordering) 
  • permutations (lexicographical ordering, Trotter-Johnson ordering)
  • 2.3.3,2.4.1,2.4.2
    Oct 30 Exhaustive Generation:
  • Introduction to backtracking, a general backtracking algorithm. 
  • Generating all cliques. Average-case analysis of the algorithm.
  • 4.1,4.2,4.3,4.3.1
    Oct  7 (A1 in/A2 out) Exhaustive Generation:
  • Estimating the size of a backtrack tree.
  • Exact cover
  • 4.4, 4.5
    Oct  14
    Exhaustive Generation: branch and bound
    Bounding functions (maximum clique,Knapsack)
    Branch-and-bound and TSP
    4.6, 4.6.1, 4.6.3,4.7
    Oct 21 Heuristic Search 5
    Oct 28
    proposal in, A2 in/A3 out)
    Heuristic Search 5
    Nov 04 Heuristic search 5
    Nov 11 Computing isomorphism 7
    Nov 18 Computing isomorphism/Isomorph-free generation 7/papers
    Nov 25
    (A3 in)
    Isomorph-free generation papers
    Extra day TBA project presentations -