1,238 research outputs found
Runtime Distributions and Criteria for Restarts
Randomized algorithms sometimes employ a restart strategy. After a certain
number of steps, the current computation is aborted and restarted with a new,
independent random seed. In some cases, this results in an improved overall
expected runtime. This work introduces properties of the underlying runtime
distribution which determine whether restarts are advantageous. The most
commonly used probability distributions admit the use of a scale and a location
parameter. Location parameters shift the density function to the right, while
scale parameters affect the spread of the distribution. It is shown that for
all distributions scale parameters do not influence the usefulness of restarts
and that location parameters only have a limited influence. This result
simplifies the analysis of the usefulness of restarts. The most important
runtime probability distributions are the log-normal, the Weibull, and the
Pareto distribution. In this work, these distributions are analyzed for the
usefulness of restarts. Secondly, a condition for the optimal restart time (if
it exists) is provided. The log-normal, the Weibull, and the generalized Pareto
distribution are analyzed in this respect. Moreover, it is shown that the
optimal restart time is also not influenced by scale parameters and that the
influence of location parameters is only linear
The Potential of Restarts for ProbSAT
This work analyses the potential of restarts for probSAT, a quite successful
algorithm for k-SAT, by estimating its runtime distributions on random 3-SAT
instances that are close to the phase transition. We estimate an optimal
restart time from empirical data, reaching a potential speedup factor of 1.39.
Calculating restart times from fitted probability distributions reduces this
factor to a maximum of 1.30. A spin-off result is that the Weibull distribution
approximates the runtime distribution for over 93% of the used instances well.
A machine learning pipeline is presented to compute a restart time for a
fixed-cutoff strategy to exploit this potential. The main components of the
pipeline are a random forest for determining the distribution type and a neural
network for the distribution's parameters. ProbSAT performs statistically
significantly better than Luby's restart strategy and the policy without
restarts when using the presented approach. The structure is particularly
advantageous on hard problems.Comment: Eurocast 201
No imminent quantum supremacy by boson sampling
It is predicted that quantum computers will dramatically outperform their
conventional counterparts. However, large-scale universal quantum computers are
yet to be built. Boson sampling is a rudimentary quantum algorithm tailored to
the platform of photons in linear optics, which has sparked interest as a rapid
way to demonstrate this quantum supremacy. Photon statistics are governed by
intractable matrix functions known as permanents, which suggests that sampling
from the distribution obtained by injecting photons into a linear-optical
network could be solved more quickly by a photonic experiment than by a
classical computer. The contrast between the apparently awesome challenge faced
by any classical sampling algorithm and the apparently near-term experimental
resources required for a large boson sampling experiment has raised
expectations that quantum supremacy by boson sampling is on the horizon. Here
we present classical boson sampling algorithms and theoretical analyses of
prospects for scaling boson sampling experiments, showing that near-term
quantum supremacy via boson sampling is unlikely. While the largest boson
sampling experiments reported so far are with 5 photons, our classical
algorithm, based on Metropolised independence sampling (MIS), allowed the boson
sampling problem to be solved for 30 photons with standard computing hardware.
We argue that the impact of experimental photon losses means that demonstrating
quantum supremacy by boson sampling would require a step change in technology.Comment: 25 pages, 9 figures. Comments welcom
The Configurable SAT Solver Challenge (CSSC)
It is well known that different solution strategies work well for different
types of instances of hard combinatorial problems. As a consequence, most
solvers for the propositional satisfiability problem (SAT) expose parameters
that allow them to be customized to a particular family of instances. In the
international SAT competition series, these parameters are ignored: solvers are
run using a single default parameter setting (supplied by the authors) for all
benchmark instances in a given track. While this competition format rewards
solvers with robust default settings, it does not reflect the situation faced
by a practitioner who only cares about performance on one particular
application and can invest some time into tuning solver parameters for this
application. The new Configurable SAT Solver Competition (CSSC) compares
solvers in this latter setting, scoring each solver by the performance it
achieved after a fully automated configuration step. This article describes the
CSSC in more detail, and reports the results obtained in its two instantiations
so far, CSSC 2013 and 2014
Restart Strategies for Constraint-Handling in Generative Design Systems
Product alternatives suggested by a generative design system often need to be evaluated on qualitative criteria. This evaluation necessitates that several feasible solutions which fulfill all technical constraints can be proposed to the user of the system. Also, as concept development is an iterative process, it is important that these solutions are generated quickly; i.e., the system must have a low convergence time. A problem, however, is that stochastic constraint-handling techniques can have highly unpredictable convergence times, spanning several orders of magnitude, and might sometimes not converge at all. A possible solution to avoid the lengthy runs is to restart the search after a certain time, with the hope that a new starting point will lead to a lower overall convergence time, but selecting an optimal restart-time is not trivial. In this paper, two strategies are investigated for such selection, and their performance is evaluated on two constraint-handling techniques for a product design problem. The results show that both restart strategies can greatly reduce the overall convergence time. Moreover, it is shown that one of the restart strategies can be applied to a wide range of constraint-handling techniques and problems, without requiring any fine-tuning of problem-specific parameters
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