Packing cycles exactly in polynomial time

Qin Chen and Xujin Chen ()
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Qin Chen: University of Hong Kong
Xujin Chen: Chinese Academy of Sciences

Journal of Combinatorial Optimization, 2012, vol. 23, issue 2, No 2, 167-188

Abstract: 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.

Keywords: Packing and covering; Polynomial algorithm; Min-max relation; Maximum cycle packing (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10878-010-9347-1

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