Parallel Peeling Algorithms

Justin Thaler, Michael Mitzenmacher, Jiayang Jiang

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 k-core. 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 k-core is empty
with high probability. We show that, with high probability, below this threshold,
only 1 / log((k-1)(r-1)) log log n + O(1) rounds of peeling are needed to obtain
the empty k-core for r-uniform hypergraphs. Interestingly, we show
that above this threshold, Ω(log n) rounds of peeling are required to find the non-empty
k-core. Since most algorithms and data structures aim to peel to an empty k-core,
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.

Guest: Michael Mitzenmacher
Host: Stefan Schmid

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