Volume 3595 of the series Lecture Notes in Computer Science pp 263-272
Finding Longest Increasing and Common Subsequences in Streaming Data
- David Liben-NowellAffiliated withDepartment of Mathematics and Computer Science, Carleton College
- , Erik VeeAffiliated withIBM Almaden Research Center
- , An ZhuAffiliated withGoogle, Inc
Abstract
We present algorithms and lower bounds for the Longest Increasing Subsequence (LIS) and Longest Common Subsequence (LCS) problems in the data-streaming model. To decide if the LIS of a given stream of elements drawn from an alphabet Σ has length at least k, we discuss a one-pass algorithm using O(k log|Σ|) space, with update time either O(log k) or O(loglog|Σ|); for |Σ| = O(1), we can achieve O(log k) space and constant-time updates. We also prove a lower bound of Ω(k) on the space requirement for this problem for general alphabets Σ, even when the input stream is a permutation of Σ. For finding the actual LIS, we give a ⌈ log (1+1/ε) ⌉-pass algorithm using O(k 1 + ε log|Σ|) space, for any ε > 0. For LCS, there is a trivial Θ(1)-approximate O(log n)-space streaming algorithm when |Σ| = O(1). For general alphabet Σ, the problem is much harder. We prove several lower bounds on the LCS problem, of which the strongest is the following: it is necessary to use Ω(n/ρ 2) space to approximate the LCS of two n-element streams to within a factor of ρ, even if the streams are permutations of each other.
- Title
- Finding Longest Increasing and Common Subsequences in Streaming Data
- Book Title
- Computing and Combinatorics
- Book Subtitle
- 11th Annual International Conference, COCOON 2005 Kunming, China, August 16–19, 2005 Proceedings
- Pages
- pp 263-272
- Copyright
- 2005
- DOI
- 10.1007/11533719_28
- Print ISBN
- 978-3-540-28061-3
- Online ISBN
- 978-3-540-31806-4
- Series Title
- Lecture Notes in Computer Science
- Series Volume
- 3595
- Series ISSN
- 0302-9743
- Publisher
- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- Additional Links
- Topics
- Industry Sectors
- eBook Packages
- Editors
-
- Lusheng Wang (1)
- Editor Affiliations
-
- 1. Department of Computer Science, City University of Hong Kong
- Authors
-
- David Liben-Nowell (2)
- Erik Vee (3)
- An Zhu (4)
- Author Affiliations
-
- 2. Department of Mathematics and Computer Science, Carleton College, USA
- 3. IBM Almaden Research Center, USA
- 4. Google, Inc, USA
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