We give a distributed algorithm in the CONGEST model for property testing of planarity with one-sided error in general (unbounded-degree) graphs. Following Censor-Hillel et al. (Proceedings of the 30th International Symposium on Distributed Computing, pp. 43–56, 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 ϵ, if G is planar, then every node outputs accept, and if G is ϵ-far from being planar (i.e., more than ϵ· | E| edges need to be removed in order to make G planar), then with probability 1 - 1 / poly (n) at least one node outputs reject. The algorithm runs in O(log | V| · poly (1 / ϵ)) 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 cycle-freeness and bipartiteness, as well as the construction of spanners, in minor-free (unweighted) graphs.
|Number of pages||18|
|State||Published - Feb 2021|
Bibliographical noteFunding Information:
This article extends work presented at PODC 2018 . Reut Levi is partially supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No. 819702). Reut Levi was also supported by ERC advanced grant 834735. Moti Medina was partially supported by the Israel Science Foundation Grant No. 867/19. Dana Ron was partially supported by the Israel Science Foundation Grants No. 671/13 and 1146/18 and the Kadar family prize.
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
- Distributed graph algorithms
- Distributed property testing
- Planarity testing