7,855 research outputs found
Parallel Weighted Random Sampling
Data structures for efficient sampling from a set of weighted items are an important building block of many applications. However, few parallel solutions are known. We close many of these gaps both for shared-memory and distributed-memory machines. We give efficient, fast, and practicable algorithms for sampling single items, k items with/without replacement, permutations, subsets, and reservoirs. We also give improved sequential algorithms for alias table construction and for sampling with replacement. Experiments on shared-memory parallel machines with up to 158 threads show near linear speedups both for construction and queries
The Parallel Complexity of Growth Models
This paper investigates the parallel complexity of several non-equilibrium
growth models. Invasion percolation, Eden growth, ballistic deposition and
solid-on-solid growth are all seemingly highly sequential processes that yield
self-similar or self-affine random clusters. Nonetheless, we present fast
parallel randomized algorithms for generating these clusters. The running times
of the algorithms scale as , where is the system size, and the
number of processors required scale as a polynomial in . The algorithms are
based on fast parallel procedures for finding minimum weight paths; they
illuminate the close connection between growth models and self-avoiding paths
in random environments. In addition to their potential practical value, our
algorithms serve to classify these growth models as less complex than other
growth models, such as diffusion-limited aggregation, for which fast parallel
algorithms probably do not exist.Comment: 20 pages, latex, submitted to J. Stat. Phys., UNH-TR94-0
On the Complexity of List Ranking in the Parallel External Memory Model
We study the problem of list ranking in the parallel external memory (PEM)
model. We observe an interesting dual nature for the hardness of the problem
due to limited information exchange among the processors about the structure of
the list, on the one hand, and its close relationship to the problem of
permuting data, which is known to be hard for the external memory models, on
the other hand.
By carefully defining the power of the computational model, we prove a
permuting lower bound in the PEM model. Furthermore, we present a stronger
\Omega(log^2 N) lower bound for a special variant of the problem and for a
specific range of the model parameters, which takes us a step closer toward
proving a non-trivial lower bound for the list ranking problem in the
bulk-synchronous parallel (BSP) and MapReduce models. Finally, we also present
an algorithm that is tight for a larger range of parameters of the model than
in prior work
Parallel Weighted Random Sampling
Data structures for efficient sampling from a set of weighted items are an important building block of many applications. However, few parallel solutions are known. We close many of these gaps both for shared-memory and distributed-memory machines. We give efficient, fast, and practicable algorithms for sampling single items, k items with/without replacement, permutations, subsets, and reservoirs. We also give improved sequential algorithms for alias table construction and for sampling with replacement. Experiments on shared-memory parallel machines with up to 158 threads show near linear speedups both for construction and queries
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