Approximation of the Degree-Constrained Minimum Spanning Hierarchies

Miklós Molnár 1 Sylvain Durand 1, 2 Massinissa Merabet 1
1 MAORE - Méthodes Algorithmes pour l'Ordonnancement et les Réseaux
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : Degree-constrained spanning problems are well known and are mainly used to solve capacity constrained routing problems. The degree-constrained spanning tree problems are NP-hard and computing the minimum cost spanning tree is not approximable. Often, applications (such as some degree-constrained communications) do not need trees as solutions. Recently, a more flexible, connected, graph related structure called hierarchy was proposed to span a set of vertices under constraints. This structure permits a new formulation of some degree-constrained spanning problems. In this paper we show that although the newly for- mulated problem is still NP-hard, it is approximable with a constant ratio. In the worst case, this ratio is bounded by 3/2. We provide a sim- ple heuristic and prove its approximation ratio is the best possible for any algorithm based on a minimum spanning tree.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-01056259
Contributor : Sylvain Durand <>
Submitted on : Monday, August 18, 2014 - 12:41:06 PM
Last modification on : Wednesday, January 29, 2020 - 5:22:33 PM

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Miklós Molnár, Sylvain Durand, Massinissa Merabet. Approximation of the Degree-Constrained Minimum Spanning Hierarchies. SIROCCO: Structural Information and Communication Complexity, Jul 2014, Takayama, Japan. pp.96-107, ⟨10.1007/978-3-319-09620-9_9⟩. ⟨lirmm-01056259⟩

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