eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-09-17
58:1
58:15
10.4230/LIPIcs.APPROX-RANDOM.2019.58
article
The Maximum Label Propagation Algorithm on Sparse Random Graphs
Knierim, Charlotte
1
Lengler, Johannes
1
Pfister, Pascal
1
Schaller, Ulysse
1
Steger, Angelika
1
ETH Zurich, Switzerland
In the Maximum Label Propagation Algorithm (Max-LPA), each vertex draws a distinct random label. In each subsequent round, each vertex updates its label to the label that is most frequent among its neighbours (including its own label), breaking ties towards the larger label. It is known that this algorithm can detect communities in random graphs with planted communities if the graphs are very dense, by converging to a different consensus for each community. In [Kothapalli et al., 2013] it was also conjectured that the same result still holds for sparse graphs if the degrees are at least C log n. We disprove this conjecture by showing that even for degrees n^epsilon, for some epsilon>0, the algorithm converges without reaching consensus. In fact, we show that the algorithm does not even reach almost consensus, but converges prematurely resulting in orders of magnitude more communities.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol145-approx-random2019/LIPIcs.APPROX-RANDOM.2019.58/LIPIcs.APPROX-RANDOM.2019.58.pdf
random graphs
distributed algorithms
label propagation algorithms
consensus
community detection