IE 635 Combinatorial Optimization

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IE 635 Combinatorial Optimization

• Time Tu, Thr 1300 1430
• Room ??1? (1120)
• Instructor Prof. Sungsoo Park (E2-2, Rm. 4112,
  Tel 3121, sspark_at_kaist.ac.kr)
• Office hour Tu, Thr 1430 1600 or by
  appointment
• TA Hwayong Choi (ganarisg_at_kaist.ac.kr, Rm.
  4114, Tel 3161)
• Office hour Tu, Thr 1430 1600 or by
  appointment
• Text  "Combinatorial Optimization" by W. Cook,
  W. Cunningham, W Pulleyblank, A. Schrijver, and
  class Handouts
• Grading guideline Midterm 30 - 40, Final 40 -
  60, Homework 10 - 20
• Home page http//solab.kaist.ac.kr/

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• General combinatorial optimization problem
• Let N 1, , n , finite. c ( c1, ,
  cn )
• c(F) ?j ? F cj , F ? N.
• Given collection of subsets ? of N, find max,
  min c(F) F ? ? .
• 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

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• 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.

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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
• 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)

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• Top 10 list by W. Pulleyblank ( 2000, Triennial
  Mathematical Programming Symposium, Atlanta)
• Eulers Theorem, 1736
• Max-flow Min-cut Theorem, 1956
• Edmonds Matching Algorithm and Polyhedron, 1965
• Edmonds Matroid Intersection, 1965
• Cooks 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
• Lovaszs Shannon Capacity of Pentagon, 1979
• Goemans, Williamson, .878 Approximation for Max
  Cut (semidefinite programming), 1994