267,619 research outputs found
siEDM: an efficient string index and search algorithm for edit distance with moves
Although several self-indexes for highly repetitive text collections exist,
developing an index and search algorithm with editing operations remains a
challenge. Edit distance with moves (EDM) is a string-to-string distance
measure that includes substring moves in addition to ordinal editing operations
to turn one string into another. Although the problem of computing EDM is
intractable, it has a wide range of potential applications, especially in
approximate string retrieval. Despite the importance of computing EDM, there
has been no efficient method for indexing and searching large text collections
based on the EDM measure. We propose the first algorithm, named string index
for edit distance with moves (siEDM), for indexing and searching strings with
EDM. The siEDM algorithm builds an index structure by leveraging the idea
behind the edit sensitive parsing (ESP), an efficient algorithm enabling
approximately computing EDM with guarantees of upper and lower bounds for the
exact EDM. siEDM efficiently prunes the space for searching query strings by
the proposed method, which enables fast query searches with the same guarantee
as ESP. We experimentally tested the ability of siEDM to index and search
strings on benchmark datasets, and we showed siEDM's efficiency.Comment: 23 page
Improving the accuracy and efficiency of time-resolved electronic spectra calculations: Cellular dephasing representation with a prefactor
Time-resolved electronic spectra can be obtained as the Fourier transform of
a special type of time correlation function known as fidelity amplitude, which,
in turn, can be evaluated approximately and efficiently with the dephasing
representation. Here we improve both the accuracy of this approximation---with
an amplitude correction derived from the phase-space propagator---and its
efficiency---with an improved cellular scheme employing inverse Weierstrass
transform and optimal scaling of the cell size. We demonstrate the advantages
of the new methodology by computing dispersed time-resolved stimulated emission
spectra in the harmonic potential, pyrazine, and the NCO molecule. In contrast,
we show that in strongly chaotic systems such as the quartic oscillator the
original dephasing representation is more appropriate than either the cellular
or prefactor-corrected methods.Comment: submitte
Approximation Algorithms for Route Planning with Nonlinear Objectives
We consider optimal route planning when the objective function is a general
nonlinear and non-monotonic function. Such an objective models user behavior
more accurately, for example, when a user is risk-averse, or the utility
function needs to capture a penalty for early arrival. It is known that as
nonlinearity arises, the problem becomes NP-hard and little is known about
computing optimal solutions when in addition there is no monotonicity
guarantee. We show that an approximately optimal non-simple path can be
efficiently computed under some natural constraints. In particular, we provide
a fully polynomial approximation scheme under hop constraints. Our
approximation algorithm can extend to run in pseudo-polynomial time under a
more general linear constraint that sometimes is useful. As a by-product, we
show that our algorithm can be applied to the problem of finding a path that is
most likely to be on time for a given deadline.Comment: 9 pages, 2 figures, main part of this paper is to be appear in
AAAI'1
Faster all-pairs shortest paths via circuit complexity
We present a new randomized method for computing the min-plus product
(a.k.a., tropical product) of two matrices, yielding a faster
algorithm for solving the all-pairs shortest path problem (APSP) in dense
-node directed graphs with arbitrary edge weights. On the real RAM, where
additions and comparisons of reals are unit cost (but all other operations have
typical logarithmic cost), the algorithm runs in time
and is correct with high probability.
On the word RAM, the algorithm runs in time for edge weights in . Prior algorithms used either time for
various , or time for various
and .
The new algorithm applies a tool from circuit complexity, namely the
Razborov-Smolensky polynomials for approximately representing
circuits, to efficiently reduce a matrix product over the algebra to
a relatively small number of rectangular matrix products over ,
each of which are computable using a particularly efficient method due to
Coppersmith. We also give a deterministic version of the algorithm running in
time for some , which utilizes the
Yao-Beigel-Tarui translation of circuits into "nice" depth-two
circuits.Comment: 24 pages. Updated version now has slightly faster running time. To
appear in ACM Symposium on Theory of Computing (STOC), 201
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