Approximation Algorithms and Hardness Results for Labeled Connectivity Problems

  • Refael Hassin
  • Jérôme Monnot
  • Danny Segev
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4162)


Let G = (V,E) be a connected multigraph, whose edges are associated with labels specified by an integer-valued function \({\mathcal{L}} : E \rightarrow \mathbb{N}\). In addition, each label ℓ ∈ ℕ to which at least one edge is mapped 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 \(\{ e \in E : {\mathcal {L}}( e ) \in I \}\) 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, where s and t are provided as part of the input.

The main contributions of this paper are improved approximation algorithms and hardness results for MinLST and MinLP. As a secondary objective, we make a concentrated effort to relate the algorithmic methods utilized in approximating these problems to a number of well-known techniques, originally studied in the context of integer covering.


Vertex Cover Approximation Factor Hardness Result Connected Subgraph Approximation Guarantee 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Refael Hassin
    • 1
  • Jérôme Monnot
    • 2
  • Danny Segev
    • 1
  1. 1.School of Mathematical SciencesTel-Aviv UniversityIsrael
  2. 2.CNRS LAMSADEUniversité Paris-DauphineFrance

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