3,489 research outputs found
A new iterative algorithm for computing a quality approximate median of strings based on edit operations
This paper presents a new algorithm that can be used to compute an approximation to the median of a set of strings. The approximate median is obtained through the successive improvements of a partial solution. The edit distance from the partial solution to all the strings in the set is computed in each iteration, thus accounting for the frequency of each of the edit operations in all the positions of the approximate median. A goodness index for edit operations is later computed by multiplying their frequency by the cost. Each operation is tested, starting from that with the highest index, in order to verify whether applying it to the partial solution leads to an improvement. If successful, a new iteration begins from the new approximate median. The algorithm finishes when all the operations have been examined without a better solution being found. Comparative experiments involving Freeman chain codes encoding 2D shapes and the Copenhagen chromosome database show that the quality of the approximate median string is similar to benchmark approaches but achieves a much faster convergence.This work is partially supported by the Spanish CICYT under project DPI2006-15542-C04-01, the Spanish MICINN through project TIN2009-14205-CO4-01 and by the Spanish research program Consolider Ingenio 2010: MIPRCV (CSD2007-00018)
Pivot Selection for Median String Problem
The Median String Problem is W[1]-Hard under the Levenshtein distance, thus,
approximation heuristics are used. Perturbation-based heuristics have been
proved to be very competitive as regards the ratio approximation
accuracy/convergence speed. However, the computational burden increase with the
size of the set. In this paper, we explore the idea of reducing the size of the
problem by selecting a subset of representative elements, i.e. pivots, that are
used to compute the approximate median instead of the whole set. We aim to
reduce the computation time through a reduction of the problem size while
achieving similar approximation accuracy. We explain how we find those pivots
and how to compute the median string from them. Results on commonly used test
data suggest that our approach can reduce the computational requirements
(measured in computed edit distances) by \% with approximation accuracy as
good as the state of the art heuristic.
This work has been supported in part by CONICYT-PCHA/Doctorado
Nacional/ through a Ph.D. Scholarship; Universidad Cat\'{o}lica
de la Sant\'{i}sima Concepci\'{o}n through the research project DIN-01/2016;
European Union's Horizon 2020 under the Marie Sk\l odowska-Curie grant
agreement ; Millennium Institute for Foundational Research on Data
(IMFD); FONDECYT-CONICYT grant number ; and for O. Pedreira, Xunta de
Galicia/FEDER-UE refs. CSI ED431G/01 and GRC: ED431C 2017/58
Boosting Perturbation-Based Iterative Algorithms to Compute the Median String
[Abstract] The most competitive heuristics for calculating the median string are those that use perturbation-based iterative algorithms. Given the complexity of this problem, which under many formulations is NP-hard, the computational cost involved in the exact solution is not affordable. In this work, the heuristic algorithms that solve this problem are addressed, emphasizing its initialization and the policy to order possible editing operations. Both factors have a significant weight in the solution of this problem. Initial string selection influences the algorithm’s speed of convergence, as does the criterion chosen to select the modification to be made in each iteration of the algorithm. To obtain the initial string, we use the median of a subset of the original dataset; to obtain this subset, we employ the Half Space Proximal (HSP) test to the median of the dataset. This test provides sufficient diversity within the members of the subset while at the same time fulfilling the centrality criterion. Similarly, we provide an analysis of the stop condition of the algorithm, improving its performance without substantially damaging the quality of the solution. To analyze the results of our experiments, we computed the execution time of each proposed modification of the algorithms, the number of computed editing distances, and the quality of the solution obtained. With these experiments, we empirically validated our proposal.This work was supported in part by the Comisión Nacional de Investigación Científica y Tecnológica - Programa de Formación de Capital Humano Avanzado (CONICYT-PCHA)/Doctorado Nacional/2014-63140074 through the Ph.D. Scholarship, in part by the European Union's Horizon 2020 under the Marie Sklodowska-Curie under Grant 690941, in part by the Millennium Institute for Foundational Research on Data (IMFD), and in part by the FONDECYT-CONICYT under Grant 1170497. The work of ÓSCAR PEDREIRA was supported in part by the Xunta de Galicia/FEDER-UE refs under Grant CSI ED431G/01 and Grant GRC: ED431C 2017/58, in part by the Office of the Vice President for Research and Postgraduate Studies of the Universidad Católica de Temuco, VIPUCT Project 2020EM-PS-08, and in part by the FEQUIP 2019-INRN-03 of the Universidad Católica de TemucoXunta de Galicia; ED431G/01Xunta de Galicia; ED431C 2017/58Chile. Comisión Nacional de Investigación Científica y Tecnológica; 2014-63140074Chile. Comisión Nacional de Investigación Científica y Tecnológica; 1170497Universidad Católica de Temuco (Chile); 2020EM-PS-08Universidad Católica de Temuco (Chile); 2019-INRN-0
Single-Step Quantum Search Using Problem Structure
The structure of satisfiability problems is used to improve search algorithms
for quantum computers and reduce their required coherence times by using only a
single coherent evaluation of problem properties. The structure of random k-SAT
allows determining the asymptotic average behavior of these algorithms, showing
they improve on quantum algorithms, such as amplitude amplification, that
ignore detailed problem structure but remain exponential for hard problem
instances. Compared to good classical methods, the algorithm performs better,
on average, for weakly and highly constrained problems but worse for hard
cases. The analytic techniques introduced here also apply to other quantum
algorithms, supplementing the limited evaluation possible with classical
simulations and showing how quantum computing can use ensemble properties of NP
search problems.Comment: 39 pages, 12 figures. Revision describes further improvement with
multiple steps (section 7). See also
http://www.parc.xerox.com/dynamics/www/quantum.htm
The IceCube Neutrino Observatory Part VI: Ice Properties, Reconstruction and Future Developments
Papers on ice properties, reconstruction and future developments submitted to
the 33nd International Cosmic Ray Conference (Rio de Janeiro 2013) by the
IceCube Collaboration.Comment: 28 pages, 38 figures; Papers submitted to the 33nd International
Cosmic Ray Conference, Rio de Janeiro 2013; version 2 corrects errors in the
author lis
On Complexity of 1-Center in Various Metrics
We consider the classic 1-center problem: Given a set P of n points in a
metric space find the point in P that minimizes the maximum distance to the
other points of P. We study the complexity of this problem in d-dimensional
-metrics and in edit and Ulam metrics over strings of length d. Our
results for the 1-center problem may be classified based on d as follows.
Small d: We provide the first linear-time algorithm for 1-center
problem in fixed-dimensional metrics. On the other hand, assuming the
hitting set conjecture (HSC), we show that when , no
subquadratic algorithm can solve 1-center problem in any of the
-metrics, or in edit or Ulam metrics.
Large d. When , we extend our conditional lower bound
to rule out sub quartic algorithms for 1-center problem in edit metric
(assuming Quantified SETH). On the other hand, we give a
-approximation for 1-center in Ulam metric with running time
.
We also strengthen some of the above lower bounds by allowing approximations
or by reducing the dimension d, but only against a weaker class of algorithms
which list all requisite solutions. Moreover, we extend one of our hardness
results to rule out subquartic algorithms for the well-studied 1-median problem
in the edit metric, where given a set of n strings each of length n, the goal
is to find a string in the set that minimizes the sum of the edit distances to
the rest of the strings in the set
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