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Approximation algorithms and hardness results for labeled connectivity problems

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Abstract

Let G=(V,E) be a connected multigraph, whose edges are associated with labels specified by an integer-valued function ℒ:E→ℕ. In addition, each label ℓ∈ℕ has a non-negative cost c(ℓ). The minimum label spanning tree problem (MinLST) asks to find a spanning tree in G that minimizes the overall cost of the labels used by its edges. Equivalently, we aim at finding a minimum cost subset of labels I⊆ℕ such that the edge set {e∈E:ℒ(e)∈I} forms a connected subgraph spanning all vertices. Similarly, in the minimum label s – t path problem (MinLP) the goal is to identify an s–t path minimizing the combined cost of its labels. The main contributions of this paper are improved approximation algorithms and hardness results for MinLST and MinLP.

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Authors and Affiliations

  1. School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv, 69978, Israel

    Refael Hassin & Danny Segev

  2. CNRS LAMSADE, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775, Paris, Cedex 16, France

    Jérôme Monnot

Authors
  1. Refael Hassin
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  2. Jérôme Monnot
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  3. Danny Segev
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Correspondence to Danny Segev.

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Hassin, R., Monnot, J. & Segev, D. Approximation algorithms and hardness results for labeled connectivity problems. J Comb Optim 14, 437–453 (2007). https://doi.org/10.1007/s10878-007-9044-x

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