11,363 research outputs found
Random Access to Grammar Compressed Strings
Grammar based compression, where one replaces a long string by a small
context-free grammar that generates the string, is a simple and powerful
paradigm that captures many popular compression schemes. In this paper, we
present a novel grammar representation that allows efficient random access to
any character or substring without decompressing the string.
Let be a string of length compressed into a context-free grammar
of size . We present two representations of
achieving random access time, and either
construction time and space on the pointer machine model, or
construction time and space on the RAM. Here, is the inverse of
the row of Ackermann's function. Our representations also efficiently
support decompression of any substring in : we can decompress any substring
of length in the same complexity as a single random access query and
additional time. Combining these results with fast algorithms for
uncompressed approximate string matching leads to several efficient algorithms
for approximate string matching on grammar-compressed strings without
decompression. For instance, we can find all approximate occurrences of a
pattern with at most errors in time , where is the number of occurrences of in . Finally, we
generalize our results to navigation and other operations on grammar-compressed
ordered trees.
All of the above bounds significantly improve the currently best known
results. To achieve these bounds, we introduce several new techniques and data
structures of independent interest, including a predecessor data structure, two
"biased" weighted ancestor data structures, and a compact representation of
heavy paths in grammars.Comment: Preliminary version in SODA 201
Approximate Nearest Neighbor Fields in Video
We introduce RIANN (Ring Intersection Approximate Nearest Neighbor search),
an algorithm for matching patches of a video to a set of reference patches in
real-time. For each query, RIANN finds potential matches by intersecting rings
around key points in appearance space. Its search complexity is reversely
correlated to the amount of temporal change, making it a good fit for videos,
where typically most patches change slowly with time. Experiments show that
RIANN is up to two orders of magnitude faster than previous ANN methods, and is
the only solution that operates in real-time. We further demonstrate how RIANN
can be used for real-time video processing and provide examples for a range of
real-time video applications, including colorization, denoising, and several
artistic effects.Comment: A CVPR 2015 oral pape
Fully-Functional Suffix Trees and Optimal Text Searching in BWT-runs Bounded Space
Indexing highly repetitive texts - such as genomic databases, software
repositories and versioned text collections - has become an important problem
since the turn of the millennium. A relevant compressibility measure for
repetitive texts is r, the number of runs in their Burrows-Wheeler Transforms
(BWTs). One of the earliest indexes for repetitive collections, the Run-Length
FM-index, used O(r) space and was able to efficiently count the number of
occurrences of a pattern of length m in the text (in loglogarithmic time per
pattern symbol, with current techniques). However, it was unable to locate the
positions of those occurrences efficiently within a space bounded in terms of
r. In this paper we close this long-standing problem, showing how to extend the
Run-Length FM-index so that it can locate the occ occurrences efficiently
within O(r) space (in loglogarithmic time each), and reaching optimal time, O(m
+ occ), within O(r log log w ({\sigma} + n/r)) space, for a text of length n
over an alphabet of size {\sigma} on a RAM machine with words of w =
{\Omega}(log n) bits. Within that space, our index can also count in optimal
time, O(m). Multiplying the space by O(w/ log {\sigma}), we support count and
locate in O(dm log({\sigma})/we) and O(dm log({\sigma})/we + occ) time, which
is optimal in the packed setting and had not been obtained before in compressed
space. We also describe a structure using O(r log(n/r)) space that replaces the
text and extracts any text substring of length ` in almost-optimal time
O(log(n/r) + ` log({\sigma})/w). Within that space, we similarly provide direct
access to suffix array, inverse suffix array, and longest common prefix array
cells, and extend these capabilities to full suffix tree functionality,
typically in O(log(n/r)) time per operation.Comment: submitted version; optimal count and locate in smaller space: O(r log
log_w(n/r + sigma)
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