eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-10-04
16:1
16:15
10.4230/LIPIcs.DISC.2018.16
article
Detecting Cliques in CONGEST Networks
Czumaj, Artur
1
Konrad, Christian
2
Department of Computer Science and Centre for Discrete Mathematics and its Applications (DIMAP), University of Warwick, UK
Department of Computer Science, University of Bristol, UK
The problem of detecting network structures plays a central role in distributed computing. One of the fundamental problems studied in this area is to determine whether for a given graph H, the input network contains a subgraph isomorphic to H or not. We investigate this problem for H being a clique K_l in the classical distributed CONGEST model, where the communication topology is the same as the topology of the underlying network, and with limited communication bandwidth on the links.
Our first and main result is a lower bound, showing that detecting K_l requires Omega(sqrt{n} / b) communication rounds, for every 4 <=l <=sqrt{n}, and Omega(n / (l b)) rounds for every l >= sqrt{n}, where b is the bandwidth of the communication links. This result is obtained by using a reduction to the set disjointness problem in the framework of two-party communication complexity. We complement our lower bound with a two-party communication protocol for listing all cliques in the input graph, which up to constant factors communicates the same number of bits as our lower bound for K_4 detection. This demonstrates that our lower bound cannot be improved using the two-party communication framework.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol121-disc2018/LIPIcs.DISC.2018.16/LIPIcs.DISC.2018.16.pdf
Lower bounds
CONGEST
subgraph detection
two-party communication