Geld: Load-balanced D-Core Decomposition for Consumer GPUs

D-core decomposition (DCD) identifies groups of nodes with strong cohesion \dmsat different levels of granularity, supporting e.g. clustering and community detection in directed graphs. Given the inefficiency of computing DCD, the computational power of GPUs is an attractive target. However, existing algorithms are ill-suited due to their restrictive programming model, as well as memory constraints in the widely available consumer-level GPUs. In particular, we show that any trivial adaptation of peeling algorithms, state-of-the-art for DCD, suffers from workload imbalance, redundant operations, and repeated atomic operations. To address these challenges, we propose a novel dynamic strategy to balance the computation on nodes with varying vertex degree and an enumeration-based lightweight memory footprint with greatly reduced thread contention. We conduct extensive experiments on 12 datasets showing that Geld achieves an average speedup of 31× over GPU peeling DCD, 6× over GPU H-Index DCD, 22× over the best existing parallel DCD algorithm with 33% memory efficiency, and 3 orders of magnitude over the best serial DCD algorithm.