15,012 research outputs found
Distributed Formal Concept Analysis Algorithms Based on an Iterative MapReduce Framework
While many existing formal concept analysis algorithms are efficient, they
are typically unsuitable for distributed implementation. Taking the MapReduce
(MR) framework as our inspiration we introduce a distributed approach for
performing formal concept mining. Our method has its novelty in that we use a
light-weight MapReduce runtime called Twister which is better suited to
iterative algorithms than recent distributed approaches. First, we describe the
theoretical foundations underpinning our distributed formal concept analysis
approach. Second, we provide a representative exemplar of how a classic
centralized algorithm can be implemented in a distributed fashion using our
methodology: we modify Ganter's classic algorithm by introducing a family of
MR* algorithms, namely MRGanter and MRGanter+ where the prefix denotes the
algorithm's lineage. To evaluate the factors that impact distributed algorithm
performance, we compare our MR* algorithms with the state-of-the-art.
Experiments conducted on real datasets demonstrate that MRGanter+ is efficient,
scalable and an appealing algorithm for distributed problems.Comment: 17 pages, ICFCA 201, Formal Concept Analysis 201
Parallel Algorithms for Generating Random Networks with Given Degree Sequences
Random networks are widely used for modeling and analyzing complex processes.
Many mathematical models have been proposed to capture diverse real-world
networks. One of the most important aspects of these models is degree
distribution. Chung--Lu (CL) model is a random network model, which can produce
networks with any given arbitrary degree distribution. The complex systems we
deal with nowadays are growing larger and more diverse than ever. Generating
random networks with any given degree distribution consisting of billions of
nodes and edges or more has become a necessity, which requires efficient and
parallel algorithms. We present an MPI-based distributed memory parallel
algorithm for generating massive random networks using CL model, which takes
time with high probability and space per processor,
where , , and are the number of nodes, edges and processors,
respectively. The time efficiency is achieved by using a novel load-balancing
algorithm. Our algorithms scale very well to a large number of processors and
can generate massive power--law networks with one billion nodes and
billion edges in one minute using processors.Comment: Accepted in NPC 201
Computing Exact Clustering Posteriors with Subset Convolution
An exponential-time exact algorithm is provided for the task of clustering n
items of data into k clusters. Instead of seeking one partition, posterior
probabilities are computed for summary statistics: the number of clusters, and
pairwise co-occurrence. The method is based on subset convolution, and yields
the posterior distribution for the number of clusters in O(n * 3^n) operations,
or O(n^3 * 2^n) using fast subset convolution. Pairwise co-occurrence
probabilities are then obtained in O(n^3 * 2^n) operations. This is
considerably faster than exhaustive enumeration of all partitions.Comment: 6 figure
Polynomial-time T-depth Optimization of Clifford+T circuits via Matroid Partitioning
Most work in quantum circuit optimization has been performed in isolation
from the results of quantum fault-tolerance. Here we present a polynomial-time
algorithm for optimizing quantum circuits that takes the actual implementation
of fault-tolerant logical gates into consideration. Our algorithm
re-synthesizes quantum circuits composed of Clifford group and T gates, the
latter being typically the most costly gate in fault-tolerant models, e.g.,
those based on the Steane or surface codes, with the purpose of minimizing both
T-count and T-depth. A major feature of the algorithm is the ability to
re-synthesize circuits with additional ancillae to reduce T-depth at
effectively no cost. The tested benchmarks show up to 65.7% reduction in
T-count and up to 87.6% reduction in T-depth without ancillae, or 99.7%
reduction in T-depth using ancillae.Comment: Version 2 contains substantial improvements and extensions to the
previous version. We describe a new, more robust algorithm and achieve
significantly improved experimental result
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