Approximation algorithms and hardness results for labeled connectivity problems

Let G=(V,E) be a connected multigraph, whose edges are associated with labels specified by an integer-valued function E → ℕ. In addition, each label l ε ℕ 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.