46,103 research outputs found
To Index or Not to Index: Optimizing Exact Maximum Inner Product Search
Exact Maximum Inner Product Search (MIPS) is an important task that is widely
pertinent to recommender systems and high-dimensional similarity search. The
brute-force approach to solving exact MIPS is computationally expensive, thus
spurring recent development of novel indexes and pruning techniques for this
task. In this paper, we show that a hardware-efficient brute-force approach,
blocked matrix multiply (BMM), can outperform the state-of-the-art MIPS solvers
by over an order of magnitude, for some -- but not all -- inputs.
In this paper, we also present a novel MIPS solution, MAXIMUS, that takes
advantage of hardware efficiency and pruning of the search space. Like BMM,
MAXIMUS is faster than other solvers by up to an order of magnitude, but again
only for some inputs. Since no single solution offers the best runtime
performance for all inputs, we introduce a new data-dependent optimizer,
OPTIMUS, that selects online with minimal overhead the best MIPS solver for a
given input. Together, OPTIMUS and MAXIMUS outperform state-of-the-art MIPS
solvers by 3.2 on average, and up to 10.9, on widely studied
MIPS datasets.Comment: 12 pages, 8 figures, 2 table
An efficient multi-scale Green's Functions Reaction Dynamics scheme
Molecular Dynamics - Green's Functions Reaction Dynamics (MD-GFRD) is a
multiscale simulation method for particle dynamics or particle-based
reaction-diffusion dynamics that is suited for systems involving low particle
densities. Particles in a low-density region are just diffusing and not
interacting. In this case one can avoid the costly integration of microscopic
equations of motion, such as molecular dynamics (MD), and instead turn to an
event-based scheme in which the times to the next particle interaction and the
new particle positions at that time can be sampled. At high (local)
concentrations, however, e.g. when particles are interacting in a nontrivial
way, particle positions must still be updated with small time steps of the
microscopic dynamical equations. The efficiency of a multi-scale simulation
that uses these two schemes largely depends on the coupling between them and
the decisions when to switch between the two scales. Here we present an
efficient scheme for multi-scale MD-GFRD simulations. It has been shown that
MD-GFRD schemes are more efficient than brute-force molecular dynamics
simulations up to a molar concentration of . In this paper, we
show that the choice of the propagation domains has a relevant impact on the
computational performance. Domains are constructed using a local optimization
of their sizes and a minimal domain size is proposed. The algorithm is shown to
be more efficient than brute-force Brownian dynamics simulations up to a molar
concentration of and is up to an order of magnitude more
efficient compared with previous MD-GFRD schemes
Faster tuple lattice sieving using spherical locality-sensitive filters
To overcome the large memory requirement of classical lattice sieving
algorithms for solving hard lattice problems, Bai-Laarhoven-Stehl\'{e} [ANTS
2016] studied tuple lattice sieving, where tuples instead of pairs of lattice
vectors are combined to form shorter vectors. Herold-Kirshanova [PKC 2017]
recently improved upon their results for arbitrary tuple sizes, for example
showing that a triple sieve can solve the shortest vector problem (SVP) in
dimension in time , using a technique similar to
locality-sensitive hashing for finding nearest neighbors.
In this work, we generalize the spherical locality-sensitive filters of
Becker-Ducas-Gama-Laarhoven [SODA 2016] to obtain space-time tradeoffs for near
neighbor searching on dense data sets, and we apply these techniques to tuple
lattice sieving to obtain even better time complexities. For instance, our
triple sieve heuristically solves SVP in time . For
practical sieves based on Micciancio-Voulgaris' GaussSieve [SODA 2010], this
shows that a triple sieve uses less space and less time than the current best
near-linear space double sieve.Comment: 12 pages + references, 2 figures. Subsumed/merged into Cryptology
ePrint Archive 2017/228, available at https://ia.cr/2017/122
Approximating the least hypervolume contributor: NP-hard in general, but fast in practice
The hypervolume indicator is an increasingly popular set measure to compare
the quality of two Pareto sets. The basic ingredient of most hypervolume
indicator based optimization algorithms is the calculation of the hypervolume
contribution of single solutions regarding a Pareto set. We show that exact
calculation of the hypervolume contribution is #P-hard while its approximation
is NP-hard. The same holds for the calculation of the minimal contribution. We
also prove that it is NP-hard to decide whether a solution has the least
hypervolume contribution. Even deciding whether the contribution of a solution
is at most (1+\eps) times the minimal contribution is NP-hard. This implies
that it is neither possible to efficiently find the least contributing solution
(unless ) nor to approximate it (unless ).
Nevertheless, in the second part of the paper we present a fast approximation
algorithm for this problem. We prove that for arbitrarily given \eps,\delta>0
it calculates a solution with contribution at most (1+\eps) times the minimal
contribution with probability at least . Though it cannot run in
polynomial time for all instances, it performs extremely fast on various
benchmark datasets. The algorithm solves very large problem instances which are
intractable for exact algorithms (e.g., 10000 solutions in 100 dimensions)
within a few seconds.Comment: 22 pages, to appear in Theoretical Computer Scienc
Sampling Sparse Signals on the Sphere: Algorithms and Applications
We propose a sampling scheme that can perfectly reconstruct a collection of
spikes on the sphere from samples of their lowpass-filtered observations.
Central to our algorithm is a generalization of the annihilating filter method,
a tool widely used in array signal processing and finite-rate-of-innovation
(FRI) sampling. The proposed algorithm can reconstruct spikes from
spatial samples. This sampling requirement improves over
previously known FRI sampling schemes on the sphere by a factor of four for
large . We showcase the versatility of the proposed algorithm by applying it
to three different problems: 1) sampling diffusion processes induced by
localized sources on the sphere, 2) shot noise removal, and 3) sound source
localization (SSL) by a spherical microphone array. In particular, we show how
SSL can be reformulated as a spherical sparse sampling problem.Comment: 14 pages, 8 figures, submitted to IEEE Transactions on Signal
Processin
Dynamical model of DNA-protein interaction: effect of protein charge distribution and mechanical properties
The mechanical model based on beads and springs, which we recently proposed
to study non-specific DNA-protein interactions [J. Chem. Phys. 130, 015103
(2009)], was improved by describing proteins as sets of interconnected beads
instead of single beads. In this paper, we first compare the results obtained
with the updated model with those of the original one and then use it to
investigate several aspects of the dynamics of DNA sampling, which could not be
accounted for by the original model. These aspects include the effect on the
speed of DNA sampling of the regularity and/or randomness of the protein charge
distribution, the charge and location of the search site, and the shape and
deformability of the protein. We also discuss the efficiency of facilitated
diffusion, that is, the extent to which the combination of 1D sliding along the
DNA and 3D diffusion in the cell can lead to faster sampling than pure 3D
diffusion of the protein.Comment: accepted in JC
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