Over the past decade, there has been increasing interest in distributed/parallel algorithms for processing large-scale graphs. By now, we have quite fast algorithms---usually sublogarithmic-time and often poly(łogłog n)-time, or even faster---for a number of fundamental graph problems in the massively parallel computation (MPC) model. This model is a widely-adopted theoretical abstraction of MapReduce style settings, where a number of machines communicate in an all-to-all manner to process large-scale data. Contributing to this line of work on MPC graph algorithms, we present poly(łog k) ε poly(łogłog n) round MPC algorithms for computing O(k^1+o(1) )-spanners in the strongly sublinear regime of local memory. To the best of our knowledge, these are the first sublogarithmic-time MPC algorithms for spanner construction.
As primary applications of our spanners, we get two important implications, as follows: -For the MPC setting, we get an O(łog^2łog n)-round algorithm for O(łog^1+o(1) n) approximation of all pairs shortest paths (APSP) in the near-linear regime of local memory. To the best of our knowledge, this is the first sublogarithmic-time MPC algorithm for distance approximations. -Our result above also extends to the Congested Clique model of distributed computing, with the same round complexity and approximation guarantee. This gives the first sub-logarithmic algorithm for approximating APSP in weighted graphs in the Congested Clique model.
more »
« less
Scalable Knowledge Graph Analytics at 136 Petaflop/s
We are motivated by newly proposed methods for data mining large-scale corpora of scholarly publications, such as the full biomedical literature, which may consist of tens of millions of papers spanning decades of research. In this setting, analysts seek to discover how concepts relate to one another. They construct graph representations from annotated text databases and then formulate the relationship-mining problem as one of computing all-pairs shortest paths (APSP), which becomes a significant bottleneck. In this context, we present a new high-performance algorithm and implementation of the Floyd-Warshall algorithm for distributed-memory parallel computers accelerated by GPUs, which we call DSNAPSHOT (Distributed Accelerated Semiring All-Pairs Shortest Path). For our largest experiments, we ran DSNAPSHOT on a connected input graph with millions of vertices using 4, 096nodes (24,576GPUs) of the Oak Ridge National Laboratory's Summit supercomputer system. We find DSNAPSHOT achieves a sustained performance of 136×1015 floating-point operations per second (136petaflop/s) at a parallel efficiency of 90% under weak scaling and, in absolute speed, 70% of the best possible performance given our computation (in the single-precision tropical semiring or “min-plus” algebra). Looking forward, we believe this novel capability will enable the mining of scholarly knowledge corpora when embedded and integrated into artificial intelligence-driven natural language processing workflows at scale.
more »
« less
- Award ID(s):
- 1710371
- NSF-PAR ID:
- 10294656
- Date Published:
- Journal Name:
- SC20: International Conference for High Performance Computing, Networking, Storage and Analysis
- Page Range / eLocation ID:
- 1 to 13
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
null (Ed.)We present an optimized Floyd-Warshall (Floyd-Warshall) algorithm that computes the All-pairs shortest path (APSP) for GPU accelerated clusters. The Floyd-Warshall algorithm due to its structural similarities to matrix-multiplication is well suited for highly parallel GPU architectures. To achieve high parallel efficiency, we address two key algorithmic challenges: reducing high communication overhead and addressing limited GPU memory. To reduce high communication costs, we redesign the parallel (a) to expose more parallelism, (b) aggressively overlap communication and computation with pipelined and asynchronous scheduling of operations, and (c) tailored MPI-collective. To cope with limited GPU memory, we employ an offload model, where the data resides on the host and is transferred to GPU on-demand. The proposed optimizations are supported with detailed performance models for tuning. Our optimized parallel Floyd-Warshall implementation is up to 5x faster than a strong baseline and achieves 8.1 PetaFLOPS/sec on 256~nodes of the Summit supercomputer at Oak Ridge National Laboratory. This performance represents 70% of the theoretical peak and 80% parallel efficiency. The offload algorithm can handle 2.5x larger graphs with a 20% increase in overall running time.more » « less
-
There are nearly one hundred parallel and distributed graph processing packages. Selecting the best package for a given problem is difficult; some packages require GPUs, some are optimized for distributed or shared memory, and some require proprietary compilers or perform better on different hardware. Furthermore, performance may vary wildly depending on the graph itself. This complexity makes selecting the optimal implementation manually infeasible. We develop an approach to predict the performance of parallel graph processing using both regression models and binary classification by labeling configurations as either well-performing or not. We demonstrate our approach on six graph processing packages: GraphMat, the Graph500, the Graph Algorithm Platform Benchmark Suite, GraphBIG, Galois, and PowerGraph and on four algorithms: PageRank, single-source shortest paths, triangle counting, and breadth first search. Given a graph, our method can estimate execution time or suggest an implementation and thread count expected to perform well. Our method correctly identifies well-performing configurations in 97% of test cases.more » « less
-
In the era of big data and cloud computing, large amounts of data are generated from user applications and need to be processed in the datacenter. Data-parallel computing frameworks, such as Apache Spark, are widely used to perform such data processing at scale. Specifically, Spark leverages distributed memory to cache the intermediate results, represented as Resilient Distributed Datasets (RDDs). This gives Spark an advantage over other parallel frameworks for implementations of iterative machine learning and data mining algorithms, by avoiding repeated computation or hard disk accesses to retrieve RDDs. By default, caching decisions are left at the programmer’s discretion, and the LRU policy is used for evicting RDDs when the cache is full. However, when the objective is to minimize total work, LRU is woefully inadequate, leading to arbitrarily suboptimal caching decisions. In this paper, we design an algorithm for multi-stage big data processing platforms to adaptively determine and cache the most valuable intermediate datasets that can be reused in the future. Our solution automates the decision of which RDDs to cache: this amounts to identifying nodes in a direct acyclic graph (DAG) representing computations whose outputs should persist in the memory. Our experiment results show that our proposed cache optimization solution can improve the performance of machine learning applications on Spark decreasing the total work to recompute RDDs by 12%.more » « less
-
Given a user-specified minimum degree threshold γ, a γ-quasi-clique is a subgraph where each vertex connects to at least γ fraction of the other vertices. Quasi-clique is a natural definition for dense structures, so finding large and hence statistically significant quasi-cliques is useful in applications such as community detection in social networks and discovering significant biomolecule structures and pathways. However, mining maximal quasi-cliques is notoriously expensive, and even a recent algorithm for mining large maximal quasi-cliques is flawed and can lead to a lot of repeated searches. This paper proposes a parallel solution for mining maximal quasi-cliques that is able to fully utilize CPU cores. Our solution utilizes divide and conquer to decompose the workloads into independent tasks for parallel mining, and we addressed the problem of (i) drastic load imbalance among different tasks and (ii) difficulty in predicting the task running time and the time growth with task subgraph size, by (a) using a timeout-based task decomposition strategy, and by (b) utilizing a priority task queue to schedule long-running tasks earlier for mining and decomposition to avoid stragglers. Unlike our conference version in PVLDB 2020 where the solution was built on a distributed graph mining framework called G-thinker, this paper targets a single-machine multi-core environment which is more accessible to an average end user. A general framework called T-thinker is developed to facilitate the programming of parallel programs for algorithms that adopt divide and conquer, including but not limited to our quasi-clique mining algorithm. Additionally, we consider the problem of directly mining large quasi-cliques from dense parts of a graph, where we identify the repeated search issue of a recent method and address it using a carefully designed concurrent trie data structure. Extensive experiments verify that our parallel solution scales well with the number of CPU cores, achieving 26.68× runtime speedup when mining a graph with 3.77M vertices and 16.5M edges with 32 mining threads. Additionally, mining large quasi-cliques from dense parts can provide an additional speedup of up to 89.46×.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/SC41405.2020.00010
