Fractional packing in ideal clutters

Abstract

This paper presents a generic scheme for fractional packing in ideal clutters. Consider an ideal clutter with a nonnegative capacity function on its vertices. It follows from ideality that for any nonnegative capacity the total multiplicity of an optimal fractional packing is equal to the minimum capacity of a vertex cover. Our scheme finds an optimal packing using at most n edges with positive multiplicities, performing minimization for the clutter at most n times and minimization for its blocker at most n 2 times, where n denotes the cardinality of the vertex set. Applied to the clutter of dijoins (directed cut covers), the scheme provides the first combinatorial polynomial-time algorithm for fractional packing of dijoins.

Um arcabouço generalizado para empacotamento de ramificações e outras estruturas combinatórias

“…Ressaltamos que este algoritmo foi estendido por Barahona [Bar04] para o problema do empacotamento fracionário de T -junções e, por Matsuoka [Mat12], para o problema do empacotamento fracionário em clutters ideais.…”