{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/144937"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/144937","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Fast Algorithms for Bounded-Range LIS Approximation","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 𝑓 of length 𝑛 with 𝑟 unique elements and 𝜖 additive error paramenter, we present an algorithm that approximate the size of 𝑓’s LIS within ±𝜖𝑛 using 𝑂(𝑟𝜖⁻²) · 𝑝𝑜𝑙𝑦(log 𝜖 ⁻¹) samples and 𝑂(𝑟𝜖⁻²) · 𝑝𝑜𝑙𝑦(log 𝑟, log 𝜖 ⁻¹) 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 𝜖 ⁻¹. Similar approaches can also be applied to estimating edit distance to monotonicity in 2-dimenstional array and 𝐿₁ edit distance of a sequence within sublinear time using 𝑝𝑜𝑙𝑦(𝑟, 𝜖⁻¹) queries.","abstract_html":"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 𝑓 of length 𝑛 with 𝑟 unique elements and 𝜖 additive error paramenter, we present an algorithm that approximate the size of 𝑓’s LIS within ±𝜖𝑛 using 𝑂(𝑟𝜖⁻²) · 𝑝𝑜𝑙𝑦(log 𝜖 ⁻¹) samples and 𝑂(𝑟𝜖⁻²) · 𝑝𝑜𝑙𝑦(log 𝑟, log 𝜖 ⁻¹) 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 𝜖 ⁻¹. Similar approaches can also be applied to estimating edit distance to monotonicity in 2-dimenstional array and 𝐿₁ edit distance of a sequence within sublinear time using 𝑝𝑜𝑙𝑦(𝑟, 𝜖⁻¹) queries.","abstract_has_math":false,"creators":["Sawettamalya, Pachara"],"institution":"Massachusetts Institute of Technology","degree_name":"Master","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. 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In particular, for a sequence 𝑓 of length 𝑛 with 𝑟 unique elements and 𝜖 additive error paramenter, we present an algorithm that approximate the size of 𝑓’s LIS within ±𝜖𝑛 using 𝑂(𝑟𝜖⁻²) · 𝑝𝑜𝑙𝑦(log 𝜖 ⁻¹) samples and 𝑂(𝑟𝜖⁻²) · 𝑝𝑜𝑙𝑦(log 𝑟, log 𝜖 ⁻¹) 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 𝜖 ⁻¹. Similar approaches can also be applied to estimating edit distance to monotonicity in 2-dimenstional array and 𝐿₁ edit distance of a sequence within sublinear time using 𝑝𝑜𝑙𝑦(𝑟, 𝜖⁻¹) queries."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["M.Eng."]},{"key":"dc:title","label":"Title","values":["Fast Algorithms for Bounded-Range LIS Approximation"]}]}],"canonical_facts":{"dc:contributor.advisor":["Rubinfeld, Ronitt"],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science"],"dc:creator":["Sawettamalya, Pachara"],"dc:date.accessioned":["2022-08-29T16:22:14Z"],"dc:date.available":["2022-08-29T16:22:14Z"],"dc:date.issued":["2022-05"],"dc:description.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 𝑓 of length 𝑛 with 𝑟 unique elements and 𝜖 additive error paramenter, we present an algorithm that approximate the size of 𝑓’s LIS within ±𝜖𝑛 using 𝑂(𝑟𝜖⁻²) · 𝑝𝑜𝑙𝑦(log 𝜖 ⁻¹) samples and 𝑂(𝑟𝜖⁻²) · 𝑝𝑜𝑙𝑦(log 𝑟, log 𝜖 ⁻¹) 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 𝜖 ⁻¹. Similar approaches can also be applied to estimating edit distance to monotonicity in 2-dimenstional array and 𝐿₁ edit distance of a sequence within sublinear time using 𝑝𝑜𝑙𝑦(𝑟, 𝜖⁻¹) queries."],"dc:description.degree":["M.Eng."],"dc:identifier.uri":["https://hdl.handle.net/1721.1/144937"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["In Copyright - Educational Use Permitted","Copyright MIT"],"dc:rights.uri":["http://rightsstatements.org/page/InC-EDU/1.0/"],"dc:title":["Fast Algorithms for Bounded-Range LIS Approximation"],"dc:type":["Thesis"],"thesis:degree_name":["Master","Master of Engineering in Electrical Engineering and Computer Science"]},"updated_at":"2026-07-22T22:20:58Z"}