Constructing Uniquely Realizable Graphs

@article{Pak2013ConstructingUR,
  title={Constructing Uniquely Realizable Graphs},
  author={Igor Pak and Dan Vilenchik},
  journal={Discrete & Computational Geometry},
  year={2013},
  volume={50},
  pages={1051-1071}
}
In the Graph Realization Problem (GRP), one is given a graph G, a set of non-negative edge-weights, and an integer d. The goal is to find, if possible, a realization of G in the Euclidian space R, such that the distance between any two vertices is the assigned edge weight. The problem has many applications in mathematics and computer science, but is NP-hard when the dimension d is fixed. Characterizing tractable instances of GRP is a classical problem, first studied by Menger in 1931. We… CONTINUE READING

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