661 research outputs found
Approximating solution structure of the Weighted Sentence Alignment problem
We study the complexity of approximating solution structure of the bijective
weighted sentence alignment problem of DeNero and Klein (2008). In particular,
we consider the complexity of finding an alignment that has a significant
overlap with an optimal alignment. We discuss ways of representing the solution
for the general weighted sentence alignment as well as phrases-to-words
alignment problem, and show that computing a string which agrees with the
optimal sentence partition on more than half (plus an arbitrarily small
polynomial fraction) positions for the phrases-to-words alignment is NP-hard.
For the general weighted sentence alignment we obtain such bound from the
agreement on a little over 2/3 of the bits. Additionally, we generalize the
Hamming distance approximation of a solution structure to approximating it with
respect to the edit distance metric, obtaining similar lower bounds
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
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