An Efficient Multiway Mergesort for GPU Architectures

Sorting is a primitive operation that is a building block for countless algorithms. As such, it is important to design sorting algorithms that approach peak performance on a range of hardware architectures. Graphics Processing Units (GPUs) are particularly attractive architectures as they provides massive parallelism and computing power. However, the intricacies of their compute and memory hierarchies make designing GPU-efficient algorithms challenging. In this work we present GPU Multiway Mergesort (MMS), a new GPU-efficient multiway mergesort algorithm. MMS employs a new partitioning technique that exposes the parallelism needed by modern GPU architectures. To the best of our knowledge, MMS is the first sorting algorithm for the GPU that is asymptotically optimal in terms of global memory accesses and that is completely free of shared memory bank conflicts. We realize an initial implementation of MMS, evaluate its performance on three modern GPU architectures, and compare it to competitive implementations available in state-of-the-art GPU libraries. Despite these implementations being highly optimized, MMS compares favorably, achieving performance improvements for most random inputs. Furthermore, unlike MMS, state-of-the-art algorithms are susceptible to bank conflicts. We find that for certain inputs that cause these algorithms to incur large numbers of bank conflicts, MMS can achieve up to a 37.6% speedup over its fastest competitor. Overall, even though its current implementation is not fully optimized, due to its efficient use of the memory hierarchy, MMS outperforms the fastest comparison-based sorting implementations available to date

Distributed Graph Clustering using Modularity and Map Equation

We study large-scale, distributed graph clustering. Given an undirected graph, our objective is to partition the nodes into disjoint sets called clusters. A cluster should contain many internal edges while being sparsely connected to other clusters. In the context of a social network, a cluster could be a group of friends. Modularity and map equation are established formalizations of this internally-dense-externally-sparse principle. We present two versions of a simple distributed algorithm to optimize both measures. They are based on Thrill, a distributed big data processing framework that implements an extended MapReduce model. The algorithms for the two measures, DSLM-Mod and DSLM-Map, differ only slightly. Adapting them for similar quality measures is straight-forward. We conduct an extensive experimental study on real-world graphs and on synthetic benchmark graphs with up to 68 billion edges. Our algorithms are fast while detecting clusterings similar to those detected by other sequential, parallel and distributed clustering algorithms. Compared to the distributed GossipMap algorithm, DSLM-Map needs less memory, is up to an order of magnitude faster and achieves better quality.Comment: 14 pages, 3 figures; v3: Camera ready for Euro-Par 2018, more details, more results; v2: extended experiments to include comparison with competing algorithms, shortened for submission to Euro-Par 201

Sparse Allreduce: Efficient Scalable Communication for Power-Law Data

Many large datasets exhibit power-law statistics: The web graph, social networks, text data, click through data etc. Their adjacency graphs are termed natural graphs, and are known to be difficult to partition. As a consequence most distributed algorithms on these graphs are communication intensive. Many algorithms on natural graphs involve an Allreduce: a sum or average of partitioned data which is then shared back to the cluster nodes. Examples include PageRank, spectral partitioning, and many machine learning algorithms including regression, factor (topic) models, and clustering. In this paper we describe an efficient and scalable Allreduce primitive for power-law data. We point out scaling problems with existing butterfly and round-robin networks for Sparse Allreduce, and show that a hybrid approach improves on both. Furthermore, we show that Sparse Allreduce stages should be nested instead of cascaded (as in the dense case). And that the optimum throughput Allreduce network should be a butterfly of heterogeneous degree where degree decreases with depth into the network. Finally, a simple replication scheme is introduced to deal with node failures. We present experiments showing significant improvements over existing systems such as PowerGraph and Hadoop