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Packing cycles exactly in polynomial time

Author

Listed:
  • Qin Chen

    (University of Hong Kong)

  • Xujin Chen

    (Chinese Academy of Sciences)

Abstract

Let G=(V,E) be an undirected graph in which every vertex v∈V is assigned a nonnegative integer w(v). A w-packing is a collection of cycles (repetition allowed) in G such that every v∈V is contained at most w(v) times by the members of . Let 〈w〉=2|V|+∑ v∈V ⌈log (w(v)+1)⌉ denote the binary encoding length (input size) of the vector (w(v): v∈V) T . We present an efficient algorithm which finds in O(|V|8〈w〉2+|V|14) time a w-packing of maximum cardinality in G provided packing and covering cycles in G satisfy the ℤ+-max-flow min-cut property.

Suggested Citation

  • Qin Chen & Xujin Chen, 2012. "Packing cycles exactly in polynomial time," Journal of Combinatorial Optimization, Springer, vol. 23(2), pages 167-188, February.
  • Handle: RePEc:spr:jcomop:v:23:y:2012:i:2:d:10.1007_s10878-010-9347-1
    DOI: 10.1007/s10878-010-9347-1
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    References listed on IDEAS

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    1. EDMONDS, Jack & GILES, Rick, 1977. "A min-max relation for submodular functions on graphs," LIDAM Reprints CORE 301, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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