1. IE 635 Combinatorial Optimization
Time: Tu, Thr 13:00 – 14:30
Room: 산업1실 (1120)
Instructor: Prof. Sungsoo Park (E2-2, Rm. 4112, Tel: 3121,
Office hour: Tu, Thr 14:30 –16:30 or by appointment
TA : Kiho Suh ( , Rm. 4113, Tel: 3161)
Office hour: Mon, Wed 14:00 –16:00 or by appointment
Text:  "Combinatorial Optimization" by W. Cook, W. Cunningham, W Pulleyblank, A. Schrijver, 1998, Wiley (4 books reserved in library) and class Handouts
Grading guideline : Midterm %, Final %, Homework %
Home page:
Combinatorial Optimization 2014

2. General combinatorial optimization problem :
Let 𝑁= 1,…,𝑛 , finite. 𝑐= 𝑐 1 ,…, 𝑐 𝑛
𝑐 𝐹 = 𝑗∈𝐹 𝑐 𝑗 , 𝐹⊆𝑁.
Given collection of subsets Γ of 𝑁, find {max, min} 𝑐 𝐹 :𝐹∈Γ .
Application areas: basic structures arising in many application areas; production, logistics, routing, scheduling (facility, manpower), location, network design and operation, circuit design, bioinformatics, …)
Science and Engineering
Issues: trees, connectivity of graphs, paths, cycles (TSP), network flow problems (max flow, min cost flow), matchings, chinese postman problem (T-join), matroid, submodular function optimization, semidefinite programming, …
(knapsack problem, bin packing problem, TSP, network design, complexity theory, … )
Investigate relationship with linear programming (integer programming), NP-completeness
Combinatorial Optimization 2014

3. Read Appendix in the text for quick review.
We will focus on logic and ideas of algorithms. But real implementations need more knowledge (data structures representing graphs, etc)
Needed Backgrounds :
IE531 Linear Programming is prerequisite (theory of polyhedron, (revised, bounded variable) simplex method, duality theory, theorem of the alternatives, etc). Knowledge of interior point method is not necessary. See instructor if you didn’t take IE531.
Read Appendix in the text for quick review.
Background in Integer Programming: helpful but not necessary here.
Combinatorial Optimization 2014

4. References:
Combinatorial Optimization: Networks and Matroids, E. Lawler, Holt, Rinehart and Winston, 1976 (recently republished)
Graph Theory with Applications, J. Bondy, U. Murty, North Holland, 1976, 2008
Computers and Intractability: A Guide to the Theory of NP-Completeness, M. Garey, D. Johnson, Freeman, 1979
Graphs and Algorithms, M. Gondran, M. Minoux, S. Vajda, Wiley, 1984
Theory of Linear and Integer Programming, A. Schrijver, 1986
Integer and Combinatorial Optimization, G. Nemhauser, L. Wolsey, Wiley, 1988
Optimization Algorithms for Networks and Graphs, J. Evans, E. Minieka, Dekker, 1992
Network Flows: Theory, Algorithms, and Applications, R. Ahuja, T. Magnanti, J. Orlin, Prentice-Hall, 1993
Integer Programming, L. Wolsey, Wiley, 1998
Combinatorial Optimization: Theory and Algorithms, Bernhard Korte, Jens Vygen, Springer, 2002
Combinatorial Optimization: Polyhedra and Efficiency, A. Schrijver, Springer, (3 volumes, 1881p)
Combinatorial Optimization 2014

5. Top 10 list by W. Pulleyblank ( 2000, Triennial Mathematical Programming Symposium, Atlanta)
Euler’s Theorem, 1736
Max-flow Min-cut Theorem, 1956
Edmond’s Matching Algorithm and Polyhedron, 1965
Edmond’s Matroid Intersection, 1965
Cook’s Theorem (NP-completeness), 1971
Dantzig, Fulkerson, and Johnson: 49 cities TSP, Held and Karp, Lagrangian relaxation of TSP and subgradient optimization, 1970, 1971
Lin, Kernighan, Local Search for the TSP (metaheuristic), 1973
Optimization = Seperation, 1981
Lovasz’s Shannon Capacity of Pentagon, 1979
Goemans, Williamson, .878 Approximation for Max Cut (semidefinite programming), 1994
Combinatorial Optimization 2014