Distance Approximating Trees: Complexity and Algorithms
نویسندگان
چکیده
Let Δ ≥ 1 and δ ≥ 0 be real numbers. A tree T = (V,E′) is a distance (Δ, δ)–approximating tree of a graph G = (V,E) if dH(u, v) ≤ Δ dG(u, v) + δ and dG(u, v) ≤ Δ dH(u, v) + δ hold for every u, v ∈ V . The distance (Δ, δ)-approximating tree problem asks for a given graph G to decide whether G has a distance (Δ, δ)-approximating tree. In this paper, we consider unweighted graphs and show that the distance (Δ, 0)approximating tree problem is NP-complete for any Δ ≥ 5 and the distance (1, 1)-approximating tree problem is polynomial time solvable.
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