TY - GEN
T1 - Possibilities and impossibilities for distributed subgraph detection
AU - Fischer, Orr
AU - Kuhn, Fabian
AU - Gonen, Tzlil
AU - Oshman, Rotem
N1 - Publisher Copyright: © 2018 Copyright held by the owner/author(s).
PY - 2018/7/11
Y1 - 2018/7/11
N2 - In the distributed subgraph detection problem, we are given a fixed subgraph H, and the network must decide whether the network graph contains a copy of H or not. Subgraph detection can be solved in a constant number of rounds if message size is unbounded, but in the CONGEST model, where each message has bounded size, it can have high round complexity. Distributed subgraph detection has received significant attention recently, with new upper and lower bounds, but several fundamental questions remain open. In this paper we prove new possibility and impossibility results for subgraph detection in the CONGEST model. We show for the first time that some subgraphs require superlinear — in fact, nearly quadratic — running time, even in small-diameter networks. We also study cycle-detection, and show that any even cycle can be detected in sublinear time (in contrast to odd cycles, which require linear time). For the special case of triangle-detection, we show that deterministic algorithms require Ω(log n) total communication even in graphs of degree 2, and that one-round randomized algorithms must send Ω(∆) bits in graphs of degree ∆, improving on the recent results of [Abboud et. al.]. Finally, we extend a recent lower bound of [Izumi, Le Gall] on listing all triangles to cliques of any size.
AB - In the distributed subgraph detection problem, we are given a fixed subgraph H, and the network must decide whether the network graph contains a copy of H or not. Subgraph detection can be solved in a constant number of rounds if message size is unbounded, but in the CONGEST model, where each message has bounded size, it can have high round complexity. Distributed subgraph detection has received significant attention recently, with new upper and lower bounds, but several fundamental questions remain open. In this paper we prove new possibility and impossibility results for subgraph detection in the CONGEST model. We show for the first time that some subgraphs require superlinear — in fact, nearly quadratic — running time, even in small-diameter networks. We also study cycle-detection, and show that any even cycle can be detected in sublinear time (in contrast to odd cycles, which require linear time). For the special case of triangle-detection, we show that deterministic algorithms require Ω(log n) total communication even in graphs of degree 2, and that one-round randomized algorithms must send Ω(∆) bits in graphs of degree ∆, improving on the recent results of [Abboud et. al.]. Finally, we extend a recent lower bound of [Izumi, Le Gall] on listing all triangles to cliques of any size.
UR - http://www.scopus.com/inward/record.url?scp=85051121614&partnerID=8YFLogxK
U2 - https://doi.org/10.1145/3210377.3210401
DO - https://doi.org/10.1145/3210377.3210401
M3 - منشور من مؤتمر
T3 - Annual ACM Symposium on Parallelism in Algorithms and Architectures
SP - 153
EP - 162
BT - SPAA 2018 - Proceedings of the 30th ACM Symposium on Parallelism in Algorithms and Architectures
T2 - 30th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2018
Y2 - 16 July 2018 through 18 July 2018
ER -