Distributed Algorithms for Planar Networks I: Planar Embedding

  title={Distributed Algorithms for Planar Networks I: Planar Embedding},
  author={Mohsen Ghaffari and Bernhard Haeupler},
This paper presents the first (non-trivial) distributed planar embedding algorithm. We consider this a crucial first step in a broader program to design efficient distributed algorithms for planar networks. We work in the standard distributed model in which nodes can send an O(log n)-bit message to each of their neighbors per round. In a planar network, with n nodes and diameter D, our deterministic planar embedding algorithm uses O(D dot min{log n, D) rounds to compute a combinatorial planar… CONTINUE READING