2,449 research outputs found
Faster subsequence recognition in compressed strings
Computation on compressed strings is one of the key approaches to processing
massive data sets. We consider local subsequence recognition problems on
strings compressed by straight-line programs (SLP), which is closely related to
Lempel--Ziv compression. For an SLP-compressed text of length , and an
uncompressed pattern of length , C{\'e}gielski et al. gave an algorithm for
local subsequence recognition running in time . We improve
the running time to . Our algorithm can also be used to
compute the longest common subsequence between a compressed text and an
uncompressed pattern in time ; the same problem with a
compressed pattern is known to be NP-hard
Edit Distance: Sketching, Streaming and Document Exchange
We show that in the document exchange problem, where Alice holds and Bob holds , Alice can send Bob a message of
size bits such that Bob can recover using the
message and his input if the edit distance between and is no more
than , and output "error" otherwise. Both the encoding and decoding can be
done in time . This result significantly
improves the previous communication bounds under polynomial encoding/decoding
time. We also show that in the referee model, where Alice and Bob hold and
respectively, they can compute sketches of and of sizes
bits (the encoding), and send to the referee, who can
then compute the edit distance between and together with all the edit
operations if the edit distance is no more than , and output "error"
otherwise (the decoding). To the best of our knowledge, this is the first
result for sketching edit distance using bits.
Moreover, the encoding phase of our sketching algorithm can be performed by
scanning the input string in one pass. Thus our sketching algorithm also
implies the first streaming algorithm for computing edit distance and all the
edits exactly using bits of space.Comment: Full version of an article to be presented at the 57th Annual IEEE
Symposium on Foundations of Computer Science (FOCS 2016
Optimum Search Schemes for Approximate String Matching Using Bidirectional FM-Index
Finding approximate occurrences of a pattern in a text using a full-text
index is a central problem in bioinformatics and has been extensively
researched. Bidirectional indices have opened new possibilities in this regard
allowing the search to start from anywhere within the pattern and extend in
both directions. In particular, use of search schemes (partitioning the pattern
and searching the pieces in certain orders with given bounds on errors) can
yield significant speed-ups. However, finding optimal search schemes is a
difficult combinatorial optimization problem.
Here for the first time, we propose a mixed integer program (MIP) capable to
solve this optimization problem for Hamming distance with given number of
pieces. Our experiments show that the optimal search schemes found by our MIP
significantly improve the performance of search in bidirectional FM-index upon
previous ad-hoc solutions. For example, approximate matching of 101-bp Illumina
reads (with two errors) becomes 35 times faster than standard backtracking.
Moreover, despite being performed purely in the index, the running time of
search using our optimal schemes (for up to two errors) is comparable to the
best state-of-the-art aligners, which benefit from combining search in index
with in-text verification using dynamic programming. As a result, we anticipate
a full-fledged aligner that employs an intelligent combination of search in the
bidirectional FM-index using our optimal search schemes and in-text
verification using dynamic programming outperforms today's best aligners. The
development of such an aligner, called FAMOUS (Fast Approximate string Matching
using OptimUm search Schemes), is ongoing as our future work
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