  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 $8$\% with approximation accuracy as
good as the state of the art heuristic.
  This work has been supported in part by CONICYT-PCHA/Doctorado
Nacional/$2014-63140074$ 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 $690941$; Millennium Institute for Foundational Research on Data
(IMFD); FONDECYT-CONICYT grant number $1170497$; and for O. Pedreira, Xunta de
Galicia/FEDER-UE refs. CSI ED431G/01 and GRC: ED431C 2017/58.
