IE 635 Combinatorial Optimization

1. IE 635 Combinatorial Optimization Time: Tu, Thr13:00 – 14:30 Room: 산업1실 (1120) Instructor: Prof. Sungsoo Park (E2-2, Rm.4112, Tel:3121, sspark@kaist.ac.kr) Office hour: Tu, Thr14:30 –16:30 or by appointment TA: KihoSuh ( emffp1410@kaist.ac.kr , Rm. 4113, Tel: 3161) Office hour: Mon, Wed14:00 –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 30 - 40%, Final 40 - 60%, Homework 10 - 20% Home page: http://solab.kaist.ac.kr/

2. General combinatorial optimization problem : Let , finite. . Given collection of subsets of , find {max, min} . • 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

3. We will focus on logic and ideas of algorithms. But real implementations need more knowledge (data structures representing graphs, etc) • Needed Backgrounds : IE531 Linear Programmingis 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.

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, 2003 (3 volumes, 1881p)

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, 1954. 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