31,144 research outputs found
Symmetry properties of the Novelli-Pak-Stoyanovskii algorithm
The number of standard Young tableaux of a fixed shape is famously given by
the hook-length formula due to Frame, Robinson and Thrall. A bijective proof of
Novelli, Pak and Stoyanovskii relies on a sorting algorithm akin to
jeu-de-taquin which transforms an arbitrary filling of a partition into a
standard Young tableau by exchanging adjacent entries. Recently, Krattenthaler
and M\"uller defined the complexity of this algorithm as the average number of
performed exchanges, and Neumann and the author proved it fulfils some nice
symmetry properties. In this paper we recall and extend the previous results
and provide new bijective proofs.Comment: 13 pages, 3 figure, submitted to FPSAC 2014 Chicag
Parallel Performance of MPI Sorting Algorithms on Dual-Core Processor Windows-Based Systems
Message Passing Interface (MPI) is widely used to implement parallel
programs. Although Windowsbased architectures provide the facilities of
parallel execution and multi-threading, little attention has been focused on
using MPI on these platforms. In this paper we use the dual core Window-based
platform to study the effect of parallel processes number and also the number
of cores on the performance of three MPI parallel implementations for some
sorting algorithms
Cooperative protein transport in cellular organelles
Compartmentalization into biochemically distinct organelles constantly
exchanging material is one of the hallmarks of eukaryotic cells. In the most
naive picture of inter-organelle transport driven by concentration gradients,
concentration differences between organelles should relax. We determine the
conditions under which cooperative transport, i.e. based on molecular
recognition, allows for the existence and maintenance of distinct organelle
identities. Cooperative transport is also shown to control the flux of material
transiting through a compartmentalized system, dramatically increasing the
transit time under high incoming flux. By including chemical processing of the
transported species, we show that this property provides a strong functional
advantage to a system responsible for protein maturation and sorting.Comment: 9 pages, 5 figure
Efficient Implementations of Molecular Dynamics Simulations for Lennard-Jones Systems
Efficient implementations of the classical molecular dynamics (MD) method for
Lennard-Jones particle systems are considered. Not only general algorithms but
also techniques that are efficient for some specific CPU architectures are also
explained. A simple spatial-decomposition-based strategy is adopted for
parallelization. By utilizing the developed code, benchmark simulations are
performed on a HITACHI SR16000/J2 system consisting of IBM POWER6 processors
which are 4.7 GHz at the National Institute for Fusion Science (NIFS) and an
SGI Altix ICE 8400EX system consisting of Intel Xeon processors which are 2.93
GHz at the Institute for Solid State Physics (ISSP), the University of Tokyo.
The parallelization efficiency of the largest run, consisting of 4.1 billion
particles with 8192 MPI processes, is about 73% relative to that of the
smallest run with 128 MPI processes at NIFS, and it is about 66% relative to
that of the smallest run with 4 MPI processes at ISSP. The factors causing the
parallel overhead are investigated. It is found that fluctuations of the
execution time of each process degrade the parallel efficiency. These
fluctuations may be due to the interference of the operating system, which is
known as OS Jitter.Comment: 33 pages, 19 figures, add references and figures are revise
Idempotent permutations
Together with a characteristic function, idempotent permutations uniquely
determine idempotent maps, as well as their linearly ordered arrangement
simultaneously. Furthermore, in-place linear time transformations are possible
between them. Hence, they may be important for succinct data structures,
information storing, sorting and searching.
In this study, their combinatorial interpretation is given and their
application on sorting is examined. Given an array of n integer keys each in
[1,n], if it is allowed to modify the keys in the range [-n,n], idempotent
permutations make it possible to obtain linearly ordered arrangement of the
keys in O(n) time using only 4log(n) bits, setting the theoretical lower bound
of time and space complexity of sorting. If it is not allowed to modify the
keys out of the range [1,n], then n+4log(n) bits are required where n of them
is used to tag some of the keys.Comment: 32 page
The Quest for Optimal Sorting Networks: Efficient Generation of Two-Layer Prefixes
Previous work identifying depth-optimal -channel sorting networks for
is based on exploiting symmetries of the first two layers.
However, the naive generate-and-test approach typically applied does not scale.
This paper revisits the problem of generating two-layer prefixes modulo
symmetries. An improved notion of symmetry is provided and a novel technique
based on regular languages and graph isomorphism is shown to generate the set
of non-symmetric representations. An empirical evaluation demonstrates that the
new method outperforms the generate-and-test approach by orders of magnitude
and easily scales until
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