Fast Algorithms for Bounded-Range LIS Approximation
Name
Sawettamalya-pachara-meng-eecs-2022-thesis.pdf
Description
Thesis PDF
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Author(s)
Sawettamalya, Pachara
Advisor(s)
Rubinfeld, Ronitt
Date Issued
May 2022
Publisher
Massachusetts Institute of Technology
Abstract
We introduce an improvement to additive approximation of Longest Increasing Subsequence (LIS) of a sequence with a bounded number of unique elements. In particular, for a sequence ๐ of length ๐ with ๐ unique elements and ๐ additive error paramenter, we present an algorithm that approximate the size of ๐โs LIS within ยฑ๐๐ using ๐(๐๐โปยฒ) ยท ๐๐๐๐ฆ(log ๐ โปยน) samples and ๐(๐๐โปยฒ) ยท ๐๐๐๐ฆ(log ๐, log ๐ โปยน) runtime. Our approache introduces small adjustments to the previously known algorithm for this problem, due to [5], resulting in a polynomial runtime algorithm which uses less queries by a factor of ๐ โปยน. Similar approaches can also be applied to estimating edit distance to monotonicity in 2-dimenstional array and ๐ฟโ edit distance of a sequence within sublinear time using ๐๐๐๐ฆ(๐, ๐โปยน) queries.
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Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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