Abstract
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.
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Hassin, R., Monnot, J., Segev, D. (2006). Approximation Algorithms and Hardness Results for Labeled Connectivity Problems. In: Královič, R., Urzyczyn, P. (eds) Mathematical Foundations of Computer Science 2006. MFCS 2006. Lecture Notes in Computer Science, vol 4162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11821069_42
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DOI: https://doi.org/10.1007/11821069_42
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