Parallel Peeling Algorithms
Abstract
The analysis of several algorithms and data structures can be framed as a peeling process on a random hypergraph: vertices with degree less than k are removed until there are no vertices of degree less than k left. The remaining hypergraph is known as the kcore. In this paper, we analyze parallel peeling processes, where in each round, all vertices of degree less than k are removed. It is known that, below a specific edge density threshold, the kcore is empty with high probability. We show that, with high probability, below this threshold, only (log log n)/log(k1)(r1) + O(1) rounds of peeling are needed to obtain the empty kcore for runiform hypergraphs. Interestingly, we show that above this threshold, Omega(log n) rounds of peeling are required to find the nonempty kcore. Since most algorithms and data structures aim to peel to an empty kcore, this asymmetry appears fortunate. We verify the theoretical results both with simulation and with a parallel implementation using graphics processing units (GPUs). Our implementation provides insights into how to structure parallel peeling algorithms for efficiency in practice.
 Publication:

arXiv eprints
 Pub Date:
 February 2013
 arXiv:
 arXiv:1302.7014
 Bibcode:
 2013arXiv1302.7014J
 Keywords:

 Computer Science  Data Structures and Algorithms
 EPrint:
 Appears in SPAA 2014. Minor typo corrections relative to previous version