TY - GEN

T1 - Property testing of planarity in the CONGEST model

AU - Levi, Reut

AU - Medina, Moti

AU - Ron, Dana

N1 - Publisher Copyright:
© 2018 Association for Computing Machinery.

PY - 2018/7/23

Y1 - 2018/7/23

N2 - 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. (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, if G is planar, then every node outputs accept, and if G is -far from being planar (i.e., more than · |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/)) 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.

AB - 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. (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, if G is planar, then every node outputs accept, and if G is -far from being planar (i.e., more than · |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/)) 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.

KW - Congest

KW - Distributed algorithms

KW - Distributed property testing

KW - Planarity testing

UR - http://www.scopus.com/inward/record.url?scp=85052445508&partnerID=8YFLogxK

U2 - 10.1145/3212734.3212748

DO - 10.1145/3212734.3212748

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AN - SCOPUS:85052445508

SN - 9781450357951

T3 - Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

SP - 347

EP - 356

BT - PODC 2018 - Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing

PB - Association for Computing Machinery

T2 - 37th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2018

Y2 - 23 July 2018 through 27 July 2018

ER -