4,147 research outputs found
A survey on algorithmic aspects of modular decomposition
The modular decomposition is a technique that applies but is not restricted
to graphs. The notion of module naturally appears in the proofs of many graph
theoretical theorems. Computing the modular decomposition tree is an important
preprocessing step to solve a large number of combinatorial optimization
problems. Since the first polynomial time algorithm in the early 70's, the
algorithmic of the modular decomposition has known an important development.
This paper survey the ideas and techniques that arose from this line of
research
Quantum Computing: Pro and Con
I assess the potential of quantum computation. Broad and important
applications must be found to justify construction of a quantum computer; I
review some of the known quantum algorithms and consider the prospects for
finding new ones. Quantum computers are notoriously susceptible to making
errors; I discuss recently developed fault-tolerant procedures that enable a
quantum computer with noisy gates to perform reliably. Quantum computing
hardware is still in its infancy; I comment on the specifications that should
be met by future hardware. Over the past few years, work on quantum computation
has erected a new classification of computational complexity, has generated
profound insights into the nature of decoherence, and has stimulated the
formulation of new techniques in high-precision experimental physics. A broad
interdisciplinary effort will be needed if quantum computers are to fulfill
their destiny as the world's fastest computing devices. (This paper is an
expanded version of remarks that were prepared for a panel discussion at the
ITP Conference on Quantum Coherence and Decoherence, 17 December 1996.)Comment: 17 pages, LaTeX, submitted to Proc. Roy. Soc. Lond. A, minor
correction
Efficient implementation of the Hardy-Ramanujan-Rademacher formula
We describe how the Hardy-Ramanujan-Rademacher formula can be implemented to
allow the partition function to be computed with softly optimal
complexity and very little overhead. A new implementation
based on these techniques achieves speedups in excess of a factor 500 over
previously published software and has been used by the author to calculate
, an exponent twice as large as in previously reported
computations.
We also investigate performance for multi-evaluation of , where our
implementation of the Hardy-Ramanujan-Rademacher formula becomes superior to
power series methods on far denser sets of indices than previous
implementations. As an application, we determine over 22 billion new
congruences for the partition function, extending Weaver's tabulation of 76,065
congruences.Comment: updated version containing an unconditional complexity proof;
accepted for publication in LMS Journal of Computation and Mathematic
Reliable Quantum Computers
The new field of quantum error correction has developed spectacularly since
its origin less than two years ago. Encoded quantum information can be
protected from errors that arise due to uncontrolled interactions with the
environment. Recovery from errors can work effectively even if occasional
mistakes occur during the recovery procedure. Furthermore, encoded quantum
information can be processed without serious propagation of errors. Hence, an
arbitrarily long quantum computation can be performed reliably, provided that
the average probability of error per quantum gate is less than a certain
critical value, the accuracy threshold. A quantum computer storing about 10^6
qubits, with a probability of error per quantum gate of order 10^{-6}, would be
a formidable factoring engine. Even a smaller, less accurate quantum computer
would be able to perform many useful tasks. (This paper is based on a talk
presented at the ITP Conference on Quantum Coherence and Decoherence, 15-18
December 1996.)Comment: 24 pages, LaTeX, submitted to Proc. Roy. Soc. Lond. A, minor
correction
Harmonic and Refined Harmonic Shift-Invert Residual Arnoldi and Jacobi--Davidson Methods for Interior Eigenvalue Problems
This paper concerns the harmonic shift-invert residual Arnoldi (HSIRA) and
Jacobi--Davidson (HJD) methods as well as their refined variants RHSIRA and
RHJD for the interior eigenvalue problem. Each method needs to solve an inner
linear system to expand the subspace successively. When the linear systems are
solved only approximately, we are led to the inexact methods. We prove that the
inexact HSIRA, RHSIRA, HJD and RHJD methods mimic their exact counterparts well
when the inner linear systems are solved with only low or modest accuracy. We
show that (i) the exact HSIRA and HJD expand subspaces better than the exact
SIRA and JD and (ii) the exact RHSIRA and RHJD expand subspaces better than the
exact HSIRA and HJD. Based on the theory, we design stopping criteria for inner
solves. To be practical, we present restarted HSIRA, HJD, RHSIRA and RHJD
algorithms. Numerical results demonstrate that these algorithms are much more
efficient than the restarted standard SIRA and JD algorithms and furthermore
the refined harmonic algorithms outperform the harmonic ones very
substantially.Comment: 15 pages, 4 figure
Introduction to Quantum Information Processing
As a result of the capabilities of quantum information, the science of
quantum information processing is now a prospering, interdisciplinary field
focused on better understanding the possibilities and limitations of the
underlying theory, on developing new applications of quantum information and on
physically realizing controllable quantum devices. The purpose of this primer
is to provide an elementary introduction to quantum information processing, and
then to briefly explain how we hope to exploit the advantages of quantum
information. These two sections can be read independently. For reference, we
have included a glossary of the main terms of quantum information.Comment: 48 pages, to appear in LA Science. Hyperlinked PDF at
http://www.c3.lanl.gov/~knill/qip/prhtml/prpdf.pdf, HTML at
http://www.c3.lanl.gov/~knill/qip/prhtm
Modeling the growth of fingerprints improves matching for adolescents
We study the effect of growth on the fingerprints of adolescents, based on
which we suggest a simple method to adjust for growth when trying to recover a
juvenile's fingerprint in a database years later. Based on longitudinal data
sets in juveniles' criminal records, we show that growth essentially leads to
an isotropic rescaling, so that we can use the strong correlation between
growth in stature and limbs to model the growth of fingerprints proportional to
stature growth as documented in growth charts. The proposed rescaling leads to
a 72% reduction of the distances between corresponding minutiae for the data
set analyzed. These findings were corroborated by several verification tests.
In an identification test on a database containing 3.25 million right index
fingers at the Federal Criminal Police Office of Germany, the identification
error rate of 20.8% was reduced to 2.1% by rescaling. The presented method is
of striking simplicity and can easily be integrated into existing automated
fingerprint identification systems
- …