Space-Efficient Algorithms for Longest Increasing Subsequence

Given a sequence of integers, we want to find a longest increasing subsequence of the sequence. It is known that this problem can be solved in O n log n time and space. Our goal in this paper is to reduce the space consumption while keeping the time complexity small. For n ≤ s ≤ n , we present algor...

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Vydáno v:	Theory of computing systems Ročník 64; číslo 3; s. 522 - 541
Hlavní autoři:	Kiyomi, Masashi, Ono, Hirotaka, Otachi, Yota, Schweitzer, Pascal, Tarui, Jun
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.04.2020 Springer Nature B.V
Témata:	Algorithms Complexity Computer Science Computing time Integers Special Issue on Theoretical Aspects of Computer Science Theory of Computation Space-efficient algorithm Patience sorting Longest increasing subsequence
ISSN:	1432-4350, 1433-0490
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Abstract	Given a sequence of integers, we want to find a longest increasing subsequence of the sequence. It is known that this problem can be solved in O n log n time and space. Our goal in this paper is to reduce the space consumption while keeping the time complexity small. For n ≤ s ≤ n , we present algorithms that use O s log n bits and O 1 s ⋅ n 2 ⋅ log n time for computing the length of a longest increasing subsequence, and O 1 s ⋅ n 2 ⋅ log 2 n time for finding an actual subsequence. We also show that the time complexity of our algorithms is optimal up to polylogarithmic factors in the framework of sequential access algorithms with the prescribed amount of space.
AbstractList	Given a sequence of integers, we want to find a longest increasing subsequence of the sequence. It is known that this problem can be solved in O n log n time and space. Our goal in this paper is to reduce the space consumption while keeping the time complexity small. For n ≤ s ≤ n , we present algorithms that use O s log n bits and O 1 s ⋅ n 2 ⋅ log n time for computing the length of a longest increasing subsequence, and O 1 s ⋅ n 2 ⋅ log 2 n time for finding an actual subsequence. We also show that the time complexity of our algorithms is optimal up to polylogarithmic factors in the framework of sequential access algorithms with the prescribed amount of space. Given a sequence of integers, we want to find a longest increasing subsequence of the sequence. It is known that this problem can be solved in Onlogn time and space. Our goal in this paper is to reduce the space consumption while keeping the time complexity small. For n≤s≤n, we present algorithms that use Oslogn bits and O1s⋅n2⋅logn time for computing the length of a longest increasing subsequence, and O1s⋅n2⋅log2n time for finding an actual subsequence. We also show that the time complexity of our algorithms is optimal up to polylogarithmic factors in the framework of sequential access algorithms with the prescribed amount of space.
Author	Schweitzer, Pascal Tarui, Jun Kiyomi, Masashi Ono, Hirotaka Otachi, Yota
Author_xml	– sequence: 1 givenname: Masashi surname: Kiyomi fullname: Kiyomi, Masashi organization: Yokohama City University – sequence: 2 givenname: Hirotaka surname: Ono fullname: Ono, Hirotaka organization: Nagoya University – sequence: 3 givenname: Yota orcidid: 0000-0002-0087-853X surname: Otachi fullname: Otachi, Yota email: otachi@cs.kumamoto-u.ac.jp organization: Kumamoto University – sequence: 4 givenname: Pascal surname: Schweitzer fullname: Schweitzer, Pascal organization: TU Kaiserslautern – sequence: 5 givenname: Jun surname: Tarui fullname: Tarui, Jun organization: The University of Electro-Communications
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Snippet	Given a sequence of integers, we want to find a longest increasing subsequence of the sequence. It is known that this problem can be solved in O n log n time... Given a sequence of integers, we want to find a longest increasing subsequence of the sequence. It is known that this problem can be solved in Onlogn time and...
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SubjectTerms	Algorithms Complexity Computer Science Computing time Integers Special Issue on Theoretical Aspects of Computer Science Theory of Computation
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Title	Space-Efficient Algorithms for Longest Increasing Subsequence
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