Task-based Augmented Contour Trees with Fibonacci Heaps

This paper presents a new algorithm for the fast, shared memory, multi-core computation of augmented contour trees on triangulations. In contrast to most existing parallel algorithms our technique computes augmented trees, enabling the full extent of contour tree based applications including data segmentation. Our approach completely revisits the traditional, sequential contour tree algorithm to re-formulate all the steps of the computation as a set of independent local tasks. This includes a new computation procedure based on Fibonacci heaps for the join and split trees, two intermediate data structures used to compute the contour tree, whose constructions are efficiently carried out concurrently thanks to the dynamic scheduling of task parallelism. We also introduce a new parallel algorithm for the combination of these two trees into the output global contour tree. Overall, this results in superior time performance in practice, both in sequential and in parallel thanks to the OpenMP task runtime. We report performance numbers that compare our approach to reference sequential and multi-threaded implementations for the computation of augmented merge and contour trees. These experiments demonstrate the run-time efficiency of our approach and its scalability on common workstations. We demonstrate the utility of our approach in data segmentation applications

Parallel Construction of Wavelet Trees on Multicore Architectures

The wavelet tree has become a very useful data structure to efficiently represent and query large volumes of data in many different domains, from bioinformatics to geographic information systems. One problem with wavelet trees is their construction time. In this paper, we introduce two algorithms that reduce the time complexity of a wavelet tree's construction by taking advantage of nowadays ubiquitous multicore machines. Our first algorithm constructs all the levels of the wavelet in parallel in $O(n)$ time and $O(n\lg\sigma + \sigma\lg n)$ bits of working space, where $n$ is the size of the input sequence and $\sigma$ is the size of the alphabet. Our second algorithm constructs the wavelet tree in a domain-decomposition fashion, using our first algorithm in each segment, reaching $O(\lg n)$ time and $O(n\lg\sigma + p\sigma\lg n/\lg\sigma)$ bits of extra space, where $p$ is the number of available cores. Both algorithms are practical and report good speedup for large real datasets.Comment: This research has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sk{\l}odowska-Curie Actions H2020-MSCA-RISE-2015 BIRDS GA No. 69094

Engineering Parallel String Sorting

We discuss how string sorting algorithms can be parallelized on modern multi-core shared memory machines. As a synthesis of the best sequential string sorting algorithms and successful parallel sorting algorithms for atomic objects, we first propose string sample sort. The algorithm makes effective use of the memory hierarchy, uses additional word level parallelism, and largely avoids branch mispredictions. Then we focus on NUMA architectures, and develop parallel multiway LCP-merge and -mergesort to reduce the number of random memory accesses to remote nodes. Additionally, we parallelize variants of multikey quicksort and radix sort that are also useful in certain situations. Comprehensive experiments on five current multi-core platforms are then reported and discussed. The experiments show that our implementations scale very well on real-world inputs and modern machines.Comment: 46 pages, extension of "Parallel String Sample Sort" arXiv:1305.115

Algorithms in the Ultra-Wide Word Model

The effective use of parallel computing resources to speed up algorithms in current multi-core parallel architectures remains a difficult challenge, with ease of programming playing a key role in the eventual success of various parallel architectures. In this paper we consider an alternative view of parallelism in the form of an ultra-wide word processor. We introduce the Ultra-Wide Word architecture and model, an extension of the word-RAM model that allows for constant time operations on thousands of bits in parallel. Word parallelism as exploited by the word-RAM model does not suffer from the more difficult aspects of parallel programming, namely synchronization and concurrency. For the standard word-RAM algorithms, the speedups obtained are moderate, as they are limited by the word size. We argue that a large class of word-RAM algorithms can be implemented in the Ultra-Wide Word model, obtaining speedups comparable to multi-threaded computations while keeping the simplicity of programming of the sequential RAM model. We show that this is the case by describing implementations of Ultra-Wide Word algorithms for dynamic programming and string searching. In addition, we show that the Ultra-Wide Word model can be used to implement a nonstandard memory architecture, which enables the sidestepping of lower bounds of important data structure problems such as priority queues and dynamic prefix sums. While similar ideas about operating on large words have been mentioned before in the context of multimedia processors [Thorup 2003], it is only recently that an architecture like the one we propose has become feasible and that details can be worked out.Comment: 28 pages, 5 figures; minor change

GraphMineSuite: Enabling High-Performance and Programmable Graph Mining Algorithms with Set Algebra

We propose GraphMineSuite (GMS): the first benchmarking suite for graph mining that facilitates evaluating and constructing high-performance graph mining algorithms. First, GMS comes with a benchmark specification based on extensive literature review, prescribing representative problems, algorithms, and datasets. Second, GMS offers a carefully designed software platform for seamless testing of different fine-grained elements of graph mining algorithms, such as graph representations or algorithm subroutines. The platform includes parallel implementations of more than 40 considered baselines, and it facilitates developing complex and fast mining algorithms. High modularity is possible by harnessing set algebra operations such as set intersection and difference, which enables breaking complex graph mining algorithms into simple building blocks that can be separately experimented with. GMS is supported with a broad concurrency analysis for portability in performance insights, and a novel performance metric to assess the throughput of graph mining algorithms, enabling more insightful evaluation. As use cases, we harness GMS to rapidly redesign and accelerate state-of-the-art baselines of core graph mining problems: degeneracy reordering (by up to >2x), maximal clique listing (by up to >9x), k-clique listing (by 1.1x), and subgraph isomorphism (by up to 2.5x), also obtaining better theoretical performance bounds