Constant Approximation Algorithms for Embedding Graph Metrics into Trees and Outerplanar Graphs

Victor Chepoi (1) , Feodor F. Dragan (2) , Ilan Newman (3) , Yuri Rabinovich (3) , Yann Vaxès (1)

1 LIF - Laboratoire d'informatique Fondamentale de Marseille
2 Kent State University
3 Department of Computer Science [Haifa]

We present a simple factor 6 algorithm for approximating the optimal multiplicative distortion of embedding (unweighted) graph metrics into tree metrics (thus improving and simplifying the factor 100 and 27 algorithms of B\v{a}doiu et al. (2007) and B\v{a}doiu et al. (2008)). We also present a constant factor algorithm for approximating the optimal distortion of embedding graph metrics into outerplanar metrics. For this, we introduce a notion of metric relaxed minor and show that if $G$ contains an $\alpha$-metric relaxed $H$-minor, then the distortion of any embedding of $G$ into any metric induced by a $H$-minor free graph is $\geq \alpha$. Then, for $H=K_{2,3}$, we present an algorithm which either finds an $\alpha$-relaxed minor, or produces an $O(\alpha)$-embedding into an outerplanar metric.

Domaines: Informatique [cs]

Victor Chepoi, Feodor F. Dragan, Ilan Newman, Yuri Rabinovich, Yann Vaxès. Constant Approximation Algorithms for Embedding Graph Metrics into Trees and Outerplanar Graphs. 13th International Workshop, APPROX 2010, Sep 2010, Barcelone, Spain. pp.95--109, ⟨10.1007/978-3-642-15369-3_8⟩. ⟨hal-01195589⟩