Distance approximating trees: complexity and algorithms

Authors:
Feodor F. Dragan;Chenyu Yan
Affiliations:
Department of Computer Science, Kent State University, Kent, OH;Department of Computer Science, Kent State University, Kent, OH
Venue:
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
Year:
2006

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Abstract

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.