Packing cycles exactly in polynomial time

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 ?+-max-flow min-cut property.