11,956 research outputs found
Fully dynamic data structure for LCE queries in compressed space
A Longest Common Extension (LCE) query on a text of length asks for
the length of the longest common prefix of suffixes starting at given two
positions. We show that the signature encoding of size [Mehlhorn et al., Algorithmica 17(2):183-198,
1997] of , which can be seen as a compressed representation of , has a
capability to support LCE queries in time,
where is the answer to the query, is the size of the Lempel-Ziv77
(LZ77) factorization of , and is an integer that can be handled
in constant time under word RAM model. In compressed space, this is the fastest
deterministic LCE data structure in many cases. Moreover, can be
enhanced to support efficient update operations: After processing
in time, we can insert/delete any (sub)string of length
into/from an arbitrary position of in time, where . This yields
the first fully dynamic LCE data structure. We also present efficient
construction algorithms from various types of inputs: We can construct
in time from uncompressed string ; in
time from grammar-compressed string
represented by a straight-line program of size ; and in time from LZ77-compressed string with factors. On top
of the above contributions, we show several applications of our data structures
which improve previous best known results on grammar-compressed string
processing.Comment: arXiv admin note: text overlap with arXiv:1504.0695
Indexing large genome collections on a PC
Motivation: The availability of thousands of invidual genomes of one species
should boost rapid progress in personalized medicine or understanding of the
interaction between genotype and phenotype, to name a few applications. A key
operation useful in such analyses is aligning sequencing reads against a
collection of genomes, which is costly with the use of existing algorithms due
to their large memory requirements.
Results: We present MuGI, Multiple Genome Index, which reports all
occurrences of a given pattern, in exact and approximate matching model,
against a collection of thousand(s) genomes. Its unique feature is the small
index size fitting in a standard computer with 16--32\,GB, or even 8\,GB, of
RAM, for the 1000GP collection of 1092 diploid human genomes. The solution is
also fast. For example, the exact matching queries are handled in average time
of 39\,s and with up to 3 mismatches in 373\,s on the test PC with
the index size of 13.4\,GB. For a smaller index, occupying 7.4\,GB in memory,
the respective times grow to 76\,s and 917\,s.
Availability: Software and Suuplementary material:
\url{http://sun.aei.polsl.pl/mugi}
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