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IE 635 Combinatorial Optimization
Time: Tu, Thr 13:00 β 14:30 Room: μ°μ
1μ€ (1120) Instructor: Prof. Sungsoo Park (E2-2, Rm. 4112, Tel: 3121, Office hour: Tu, Thr 14:30 β16:30 or by appointment TA : Kiho Suh ( , Rm. 4113, Tel: 3161) Office hour: Mon, Wed 14:00 β16:00 or by appointment Text: Β "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
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General combinatorial optimization problem :
Let π= 1,β¦,π , finite. π= π 1 ,β¦, π π π πΉ = πβπΉ π π , πΉβπ. Given collection of subsets Ξ of π, find {max, min} π πΉ :πΉβΞ . Application areas: basic structures arising in many application areas; production, logistics, routing, scheduling (facility, manpower), location, network design and operation, circuit design, bioinformatics, β¦) 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, β¦ (knapsack problem, bin packing problem, TSP, network design, complexity theory, β¦ ) Investigate relationship with linear programming (integer programming), NP-completeness Combinatorial Optimization 2014
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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 didnβt take IE531. Read Appendix in the text for quick review. Background in Integer Programming: helpful but not necessary here. Combinatorial Optimization 2014
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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
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Top 10 list by W. Pulleyblank ( 2000, Triennial Mathematical Programming Symposium, Atlanta)
Eulerβs Theorem, 1736 Max-flow Min-cut Theorem, 1956 Edmondβs Matching Algorithm and Polyhedron, 1965 Edmondβs Matroid Intersection, 1965 Cookβs 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 Lovaszβs Shannon Capacity of Pentagon, 1979 Goemans, Williamson, .878 Approximation for Max Cut (semidefinite programming), 1994 Combinatorial Optimization 2014
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