Property Testing of Planarity in the CONGEST model
Abstract
We give a distributed algorithm in the {\sf CONGEST} model for property testing of planarity with onesided error in general (unboundeddegree) graphs. Following CensorHillel et al. (DISC 2016), who recently initiated the study of property testing in the distributed setting, our algorithm gives the following guarantee: For a graph $G = (V,E)$ and a distance parameter $\epsilon$, if $G$ is planar, then every node outputs {\sf accept\/}, and if $G$ is $\epsilon$far from being planar (i.e., more than $\epsilon\cdot E$ edges need to be removed in order to make $G$ planar), then with probability $11/{\rm poly}(n)$ at least one node outputs {\sf reject}. The algorithm runs in $O(\logV\cdot{\rm poly}(1/\epsilon))$ rounds, and we show that this result is tight in terms of the dependence on $V$. Our algorithm combines several techniques of graph partitioning and local verification of planar embeddings. Furthermore, we show how a main subroutine in our algorithm can be applied to derive additional results for property testing of cyclefreeness and bipartiteness, as well as the construction of spanners, in minorfree (unweighted) graphs.
 Publication:

arXiv eprints
 Pub Date:
 May 2018
 arXiv:
 arXiv:1805.10657
 Bibcode:
 2018arXiv180510657L
 Keywords:

 Computer Science  Distributed;
 Parallel;
 and Cluster Computing