261 research outputs found
Deterministic sub-linear space LCE data structures with efficient construction
Given a string of symbols, a longest common extension query
asks for the length of the longest common prefix of the
th and th suffixes of . LCE queries have several important
applications in string processing, perhaps most notably to suffix sorting.
Recently, Bille et al. (J. Discrete Algorithms 25:42-50, 2014, Proc. CPM 2015:
65-76) described several data structures for answering LCE queries that offers
a space-time trade-off between data structure size and query time. In
particular, for a parameter , their best deterministic
solution is a data structure of size which allows LCE queries to be
answered in time. However, the construction time for all
deterministic versions of their data structure is quadratic in . In this
paper, we propose a deterministic solution that achieves a similar space-time
trade-off of query time using
space, but significantly improve the construction time to
.Comment: updated titl
New characterizations of minimum spanning trees and of saliency maps based on quasi-flat zones
We study three representations of hierarchies of partitions: dendrograms
(direct representations), saliency maps, and minimum spanning trees. We provide
a new bijection between saliency maps and hierarchies based on quasi-flat zones
as used in image processing and characterize saliency maps and minimum spanning
trees as solutions to constrained minimization problems where the constraint is
quasi-flat zones preservation. In practice, these results form a toolkit for
new hierarchical methods where one can choose the most convenient
representation. They also invite us to process non-image data with
morphological hierarchies
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