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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Bibliographic Details
Published in:Theory of computing systems Vol. 64; no. 3; pp. 522 - 541
Main Authors: Kiyomi, Masashi, Ono, Hirotaka, Otachi, Yota, Schweitzer, Pascal, Tarui, Jun
Format: Journal Article
Language:English
Published: New York Springer US 01.04.2020
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:1432-4350
1433-0490
DOI:10.1007/s00224-018-09908-6