Geometric Spanners for Weighted Point Sets

@article{Abam2010GeometricSF,
  title={Geometric Spanners for Weighted Point Sets},
  author={Mohammad Ali Abam and Mark de Berg and Mohammad Farshi and Joachim Gudmundsson and Michiel H. M. Smid},
  journal={Algorithmica},
  year={2010},
  volume={61},
  pages={207-225}
}
Let (S,d) be a finite metric space, where each element p∈S has a non-negative weight w (p). We study spanners for the set S with respect to the following weighted distance function: $$\mathbf{d}_{\omega}(p,q)=\left\{\begin{array}{ll}0&\mbox{ if $p=q$,}\\ \operatorname {w}(p)+\mathbf{d}(p,q)+ \operatorname {w}(q)&\mbox{ if $p\neq q$.}\end{array}\right.$$ We present a general method for turning spanners with respect to the d-metric into spanners with respect to the d ω -metric. For any given ε>0… CONTINUE READING