Work-Efficient Parallel GPU Methods for Single-Source Shortest Paths

Abstract

Finding the shortest paths from a single source to all other vertices is a fundamental method used in a variety of higher-level graph algorithms. We present three parallelfriendly and work-efficient methods to solve this Single-Source Shortest Paths (SSSP) problem: Workfront Sweep, Near-Far and Bucketing. These methods choose different approaches to balance the tradeoff between saving work and organizational overhead.In practice, all of these methods do much less work than traditional Bellman-Ford methods, while adding only a modest amount of extra work over serial methods. These methods are designed to have a sufficient parallel workload to fill modern massively-parallel machines, and select reorganizational schemes that map well to these architectures. We show that in general our Near-Far method has the highest performance on modern GPUs, outperforming other parallel methods.We also explore a variety of parallel load-balanced graph traversal strategies and apply them towards our SSSP solver. Our work-saving methods always outperform a traditional GPU Bellman-Ford implementation, achieving rates up to 14x higher on low-degree graphs and 340x higher on scalefree graphs. We also see significant speedups (20-60x) when compared against a serial implementation on graphs with adequately high degree.

A GPU-based solution for fast calculation of the betweenness centrality in large weighted networks

“…In addition to the edge-parallel strategy, other techniques have also been developed to solve this problem (Davidson et al, 2014;Hong et al, 2011). Hong et al proposed the warp-centric concept, in which a warp rather than a thread is allocated to each node.…”

“…As a result, each thread does less work for high-degree nodes, thereby greatly reducing the waiting time. Other techniques for addressing the load-imbalance problem include Cooperative Blocks, CTA + Warp + Scan and load-balanced partitioning (Davidson et al, 2014;Wang et al, 2016). These methods attempt to assign threads to edges that need to be inspected by means of the design of several novel data structures and algorithms, which ensure excellent within-block and interblock load balance.…”

“…d-Stepping is another frequently employed parallel SSSP algorithm, in which vertices are grouped into buckets and all vertices in a bucket are processed simultaneously. However, as described in Davidson et al (2014), there are three main characteristics that make -stepping difficult to implement efficiently on a GPU; e.g., it requires dynamic arrays, which are poorly supported in the CUDA framework. Because of this, we base our SSSP algorithm on the parallel Dijkstra algorithm.…”

“…First, we apply the compressed sparse row (CSR) format, which is widely used in graph algorithms, to store the input graph (Bell & Garland, 2009;Davidson et al, 2014). This format is space efficient because both a vertex and an edge consume one entry, and it is convenient for performing the traversal task on a GPU.…”

“…In weighted networks, the Dijkstra algorithm should be used to solve the single-source shortest path (SSSP) problem rather than the breadth-first search (BFS) algorithm. In previous work, many efforts have been devoted to developing a GPU version of the SSSP problem using the well-known Dijkstra algorithm (Martin, Torres & Gavilanes, 2009;Ortega-Arranz et al, 2013;Delling et al, 2011;Davidson et al, 2014). Although such algorithms have been successfully developed and presented, establishing a parallel version of the BC algorithm for weighted networks is nontrivial because the original SSSP algorithm must be modified in many critical aspects for this task, and to the best of our knowledge, a suitable fast solution is still lacking.…”