Management Science and Financial Engineering

The Korean Operations Research and Management Science Society (한국경영과학회)
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On the Convex Hull of Multicuts on a Cycle

  • Lee, Kyung-Sik (School of Industrial and Management Engineering, Hankuk University of Foreign Studies)
  • Published : 2009.11.30
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Abstract

The minimum multicut problem on a cycle is to find a multicut on an undirected cycle such that the sum of weights is minimized, which is known to be polynomially solvable. This paper shows that there exists a compact polyhedral description of the set of feasible solutions to the problem whose number of variables and constraints is O($\upsilon\kappa$).

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References

  1. Balas, E., 'Disjunctive programming and a hierarchy of relaxations for discrete optimization problems,' SIAM Journal on Algebraic and Discrete Methods 6 (1985), 466-486 https://doi.org/10.1137/0606047
  2. Balas, E., 'Disjuctive programming: Properties of the convex hull of feasible points,' Discrete Applied Mathematics 89 (1998), 3-44 https://doi.org/10.1016/S0166-218X(98)00136-X
  3. Bartholdi, J. J., J. B. Orlin, and H. D. Ratliff, 'Cyclic scheduling via integer programs with circular ones,' Operations Research 28 (1980), 1074-1085 https://doi.org/10.1287/opre.28.5.1074
  4. Bentz, C, 'Exact and approximate resolution of integral multiflow and multicut problems: algorithms and complexity,' 4OR 6 (2008), 89-92 https://doi.org/10.1007/s10288-007-0040-x
  5. Dahlhaus, E., D. S. Johnson, C. H. Papadimitriou, P. D. Seymour, and M. Yannakakis, 'The complexity of multiterminal cuts,' SIAM Journal on Computing 23 (1994), 864-894 https://doi.org/10.1137/S0097539792225297
  6. Schrijver, A., Combinatorial Optimization, Springer-Verlag, Berlin, 2003