  Core decomposition is a well-established graph mining problem with various
applications that involves partitioning the graph into hierarchical subgraphs.
Solutions to this problem have been developed using both bottom-up and top-down
approaches from the perspective of vertex convergence dependency. However,
existing algorithms have not effectively harnessed GPU performance to expedite
core decomposition, despite the growing need for enhanced performance.
Moreover, approaching performance limitations of core decomposition from two
different directions within a parallel synchronization structure has not been
thoroughly explored. This paper introduces an efficient GPU acceleration
framework, PICO, for the Peel and Index2core paradigms of k-core decomposition.
We propose PeelOne, a Peel-based algorithm designed to simplify the parallel
logic and minimize atomic operations by eliminating vertices that are
'under-core'. We also propose an Index2core-based algorithm, named HistoCore,
which addresses the issue of extensive redundant computations across both
vertices and edges. Extensive experiments on NVIDIA RTX 3090 GPU show that
PeelOne outperforms all other Peel-based algorithms, and HistoCore outperforms
all other Index2core-based algorithms. Furthermore, HistoCore even outperforms
PeelOne by 1.1x - 3.2x speedup on six datasets, which breaks the stereotype
that the Index2core paradigm performs much worse than the Peel in a shared
memory parallel setting.
