1,876 research outputs found
Parallel Batch-Dynamic Graph Connectivity
In this paper, we study batch parallel algorithms for the dynamic
connectivity problem, a fundamental problem that has received considerable
attention in the sequential setting. The most well known sequential algorithm
for dynamic connectivity is the elegant level-set algorithm of Holm, de
Lichtenberg and Thorup (HDT), which achieves amortized time per
edge insertion or deletion, and time per query. We
design a parallel batch-dynamic connectivity algorithm that is work-efficient
with respect to the HDT algorithm for small batch sizes, and is asymptotically
faster when the average batch size is sufficiently large. Given a sequence of
batched updates, where is the average batch size of all deletions, our
algorithm achieves expected amortized work per
edge insertion and deletion and depth w.h.p. Our algorithm
answers a batch of connectivity queries in expected
work and depth w.h.p. To the best of our knowledge, our algorithm
is the first parallel batch-dynamic algorithm for connectivity.Comment: This is the full version of the paper appearing in the ACM Symposium
on Parallelism in Algorithms and Architectures (SPAA), 201
Theoretically Efficient Parallel Graph Algorithms Can Be Fast and Scalable
There has been significant recent interest in parallel graph processing due
to the need to quickly analyze the large graphs available today. Many graph
codes have been designed for distributed memory or external memory. However,
today even the largest publicly-available real-world graph (the Hyperlink Web
graph with over 3.5 billion vertices and 128 billion edges) can fit in the
memory of a single commodity multicore server. Nevertheless, most experimental
work in the literature report results on much smaller graphs, and the ones for
the Hyperlink graph use distributed or external memory. Therefore, it is
natural to ask whether we can efficiently solve a broad class of graph problems
on this graph in memory.
This paper shows that theoretically-efficient parallel graph algorithms can
scale to the largest publicly-available graphs using a single machine with a
terabyte of RAM, processing them in minutes. We give implementations of
theoretically-efficient parallel algorithms for 20 important graph problems. We
also present the optimizations and techniques that we used in our
implementations, which were crucial in enabling us to process these large
graphs quickly. We show that the running times of our implementations
outperform existing state-of-the-art implementations on the largest real-world
graphs. For many of the problems that we consider, this is the first time they
have been solved on graphs at this scale. We have made the implementations
developed in this work publicly-available as the Graph-Based Benchmark Suite
(GBBS).Comment: This is the full version of the paper appearing in the ACM Symposium
on Parallelism in Algorithms and Architectures (SPAA), 201
A Logic for Non-Deterministic Parallel Abstract State Machines
We develop a logic which enables reasoning about single steps of
non-deterministic parallel Abstract State Machines (ASMs). Our logic builds
upon the unifying logic introduced by Nanchen and St\"ark for reasoning about
hierarchical (parallel) ASMs. Our main contribution to this regard is the
handling of non-determinism (both bounded and unbounded) within the logical
formalism. Moreover, we do this without sacrificing the completeness of the
logic for statements about single steps of non-deterministic parallel ASMs,
such as invariants of rules, consistency conditions for rules, or step-by-step
equivalence of rules.Comment: arXiv admin note: substantial text overlap with arXiv:1602.0748
Parallel Minimum Cuts in Near-linear Work and Low Depth
We present the first near-linear work and poly-logarithmic depth algorithm
for computing a minimum cut in a graph, while previous parallel algorithms with
poly-logarithmic depth required at least quadratic work in the number of
vertices. In a graph with vertices and edges, our algorithm computes
the correct result with high probability in work and
depth. This result is obtained by parallelizing a data
structure that aggregates weights along paths in a tree and by exploiting the
connection between minimum cuts and approximate maximum packings of spanning
trees. In addition, our algorithm improves upon bounds on the number of cache
misses incurred to compute a minimum cut
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Parallel data compression
Data compression schemes remove data redundancy in communicated and stored data and increase the effective capacities of communication and storage devices. Parallel algorithms and implementations for textual data compression are surveyed. Related concepts from parallel computation and information theory are briefly discussed. Static and dynamic methods for codeword construction and transmission on various models of parallel computation are described. Included are parallel methods which boost system speed by coding data concurrently, and approaches which employ multiple compression techniques to improve compression ratios. Theoretical and empirical comparisons are reported and areas for future research are suggested
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