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, Thr15:00 –17:00 or by appointment TA: KyoungmiHwang (emptycan82@hanmail.net, Rm. 4114, Tel: 3161) Office hour: Tu, Thr14:30 –16:30 or by appointment Text:  "Combinatorial Optimization" by W. Cook, W. Cunningham, W Pulleyblank, A. Schrijver, 1998, Wiley 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, … ) Relationship with linear programming (integer programming), NP-completeness

3. Needed Backgrounds : Linear Programming( duality, polyhedron, … IE531 level). If not enough background, see instructor. Read Appendix in the text for quick review. 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