Recognizing and Embedding Outerplanar Distributed Computer Networks

Abstract

A new distributed algorithm for outerplanar network recognition and embedding is presented. The algorithm requires 2n-2 time and transmits at most 5m messages of O(lg n) length, where m is the number of links and n is the number of nodes in the network. In addition, if the network is indeed outerplanar, the algorithm will run in 2n-2 time and transmit at most 10n-15 messages. This time bound is the best one could ever achieve with a depth-first-search based algorithm. The previously best known algorithm achieves O(n) time and message bounds by using messages of O(n) length and running on a stronger model, making multiple passes over the network.