Tree Contraction, Connected Components, Minimum Spanning Trees: a GPU Path to Vertex Fitting

Standard parallel computing operations are considered in the context of algorithms for solving 3D graph problems which have applications, e.g., in vertex finding in HEP. Exploiting GPUs for tree-accumulation and graph algorithms is challenging: GPUs offer extreme computational power and high memory-access bandwidth, combined with a model of fine-grained parallelism perhaps not suiting the irregular distribution of linked representations of graph data structures. Achieving data-race free computations may demand serialization through atomic transactions, inevitably producing poor parallel performance. A Minimum Spanning Tree algorithm for GPUs is presented, its implementation discussed, and its efficiency evaluated on GPU and multicore architectures