Parallel Algorithms for Hierarchical Nucleus Decomposition

Nucleus decompositions have been shown to be a useful tool for finding dense subgraphs. The coreness value of a clique represents its density based on the number of other cliques it is adjacent to. One useful output of nucleus decomposition is to generate a hierarchy among dense subgraphs at different resolutions. However, existing parallel algorithms for nucleus decomposition do not generate this hierarchy, and only compute the coreness values. This paper presents a scalable parallel algorithm for hierarchy construction, with practical optimizations, such as interleaving the coreness computation with hierarchy construction and using a concurrent union-find data structure in an innovative way to generate the hierarchy. We also introduce a parallel approximation algorithm for nucleus decomposition, which achieves much lower span in theory and better performance in practice. We prove strong theoretical bounds on the work and span (parallel time) of our algorithms. On a 30-core machine with two-way hyper-threading on real-world graphs, our parallel hierarchy construction algorithm achieves up to a 58.84x speedup over the state-of-the-art sequential hierarchy construction algorithm by Sariyuce et al. and up to a 30.96x self-relative parallel speedup. On the same machine, our approximation algorithm achieves a 3.3x speedup over our exact algorithm, while generating coreness estimates with a multiplicative error of 1.33x on average

ConnectIt: A Framework for Static and Incremental Parallel Graph Connectivity Algorithms

Connected components is a fundamental kernel in graph applications due to its usefulness in measuring how well-connected a graph is, as well as its use as subroutines in many other graph algorithms. The fastest existing parallel multicore algorithms for connectivity are based on some form of edge sampling and/or linking and compressing trees. However, many combinations of these design choices have been left unexplored. In this paper, we design the ConnectIt framework, which provides different sampling strategies as well as various tree linking and compression schemes. ConnectIt enables us to obtain several hundred new variants of connectivity algorithms, most of which extend to computing spanning forest. In addition to static graphs, we also extend ConnectIt to support mixes of insertions and connectivity queries in the concurrent setting. We present an experimental evaluation of ConnectIt on a 72-core machine, which we believe is the most comprehensive evaluation of parallel connectivity algorithms to date. Compared to a collection of state-of-the-art static multicore algorithms, we obtain an average speedup of 37.4x (2.36x average speedup over the fastest existing implementation for each graph). Using ConnectIt, we are able to compute connectivity on the largest publicly-available graph (with over 3.5 billion vertices and 128 billion edges) in under 10 seconds using a 72-core machine, providing a 3.1x speedup over the fastest existing connectivity result for this graph, in any computational setting. For our incremental algorithms, we show that our algorithms can ingest graph updates at up to several billion edges per second. Finally, to guide the user in selecting the best variants in ConnectIt for different situations, we provide a detailed analysis of the different strategies in terms of their work and locality

Parallel Index-Based Structural Graph Clustering and Its Approximation

SCAN (Structural Clustering Algorithm for Networks) is a well-studied, widely used graph clustering algorithm. For large graphs, however, sequential SCAN variants are prohibitively slow, and parallel SCAN variants do not effectively share work among queries with different SCAN parameter settings. Since users of SCAN often explore many parameter settings to find good clusterings, it is worthwhile to precompute an index that speeds up queries. This paper presents a practical and provably efficient parallel index-based SCAN algorithm based on GS*-Index, a recent sequential algorithm. Our parallel algorithm improves upon the asymptotic work of the sequential algorithm by using integer sorting. It is also highly parallel, achieving logarithmic span (parallel time) for both index construction and clustering queries. Furthermore, we apply locality-sensitive hashing (LSH) to design a novel approximate SCAN algorithm and prove guarantees for its clustering behavior. We present an experimental evaluation of our algorithms on large real-world graphs. On a 48-core machine with two-way hyper-threading, our parallel index construction achieves 50--151$\times$ speedup over the construction of GS*-Index. In fact, even on a single thread, our index construction algorithm is faster than GS*-Index. Our parallel index query implementation achieves 5--32$\times$ speedup over GS*-Index queries across a range of SCAN parameter values, and our implementation is always faster than ppSCAN, a state-of-the-art parallel SCAN algorithm. Moreover, our experiments show that applying LSH results in faster index construction while maintaining good clustering quality

Parallel Integer Sort: Theory and Practice

Integer sorting is a fundamental problem in computer science. This paper studies parallel integer sort both in theory and in practice. In theory, we show tighter bounds for a class of existing practical integer sort algorithms, which provides a solid theoretical foundation for their widespread usage in practice and strong performance. In practice, we design a new integer sorting algorithm, \textsf{DovetailSort}, that is theoretically-efficient and has good practical performance. In particular, \textsf{DovetailSort} overcomes a common challenge in existing parallel integer sorting algorithms, which is the difficulty of detecting and taking advantage of duplicate keys. The key insight in \textsf{DovetailSort} is to combine algorithmic ideas from both integer- and comparison-sorting algorithms. In our experiments, \textsf{DovetailSort} achieves competitive or better performance than existing state-of-the-art parallel integer and comparison sorting algorithms on various synthetic and real-world datasets

Fast, Parallel, and Cache-Friendly Suffix Array Construction

String indexes such as the suffix array (SA) and the closely related longest common prefix (LCP) array are fundamental objects in bioinformatics and have a wide variety of applications. Despite their importance in practice, few scalable parallel algorithms for constructing these are known, and the existing algorithms can be highly non-trivial to implement and parallelize. In this paper we present CaPS-SA, a simple and scalable parallel algorithm for constructing these string indexes inspired by samplesort. Due to its design, CaPS-SA has excellent memory-locality and thus incurs fewer cache misses and achieves strong performance on modern multicore systems with deep cache hierarchies. We show that despite its simple design, CaPS-SA outperforms existing state-of-the-art parallel SA and LCP-array construction algorithms on modern hardware. Finally, motivated by applications in modern aligners where the query strings have bounded lengths, we introduce the notion of a bounded-context SA and show that CaPS-SA can easily be extended to exploit this structure to obtain further speedups

Parallel Graph Algorithms in Constant Adaptive Rounds: Theory meets Practice

We study fundamental graph problems such as graph connectivity, minimum spanning forest (MSF), and approximate maximum (weight) matching in a distributed setting. In particular, we focus on the Adaptive Massively Parallel Computation (AMPC) model, which is a theoretical model that captures MapReduce-like computation augmented with a distributed hash table. We show the first AMPC algorithms for all of the studied problems that run in a constant number of rounds and use only $O(n^\epsilon)$ space per machine, where $0 < \epsilon < 1$. Our results improve both upon the previous results in the AMPC model, as well as the best-known results in the MPC model, which is the theoretical model underpinning many popular distributed computation frameworks, such as MapReduce, Hadoop, Beam, Pregel and Giraph. Finally, we provide an empirical comparison of the algorithms in the MPC and AMPC models in a fault-tolerant distriubted computation environment. We empirically evaluate our algorithms on a set of large real-world graphs and show that our AMPC algorithms can achieve improvements in both running time and round-complexity over optimized MPC baselines