NDLI: Output-Sensitive Algorithms for Finding the Nested Common Intervals of Two General Sequences

Content Provider	IEEE Xplore Digital Library
Author	Biing-Feng Wang
Copyright Year	2004
Abstract	The focus of this paper is the problem of finding all nested common intervals of two general sequences. Depending on the treatment one wants to apply to duplicate genes, Blin et al. introduced three models to define nested common intervals of two sequences: the uniqueness, the free-inclusion, and the bijection models. We consider all the three models. For the uniqueness and the bijection models, we give O(n + N_out)-time algorithms, where N_out denotes the size of the output. For the free-inclusion model, we give an O(n^1+ε + N_out)-time algorithm, where ε >; 0 is an arbitrarily small constant. We also present an upper bound on the size of the output for each model. For the uniqueness and the free-inclusion models, we show that N_out = O(n²). Let C = Σ_gϵΓ o₁(g)o₂(5), where Γ is the set of distinct genes, and o₁(g) and o₂(g) are, respectively, the numbers of copies of g in the two given sequences. For the bijection model, we show that N_out = O(Cn). In this paper, we also study the problem of finding all approximate nested common intervals of two sequences on the bijection model. An O(δn + N_out)-time algorithm is presented, where δ denotes the maximum number of allowed gaps. In addition, we show that for this problem N_out is O(δn³).
Sponsorship	IEEE Computer Society
Page Count	12
File Size	323255
Starting Page	548
Ending Page	559
File Format	PDF
ISSN	15455963
Volume Number	9
Issue Number	2
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Approximation algorithms Algorithm design and analysis Bioinformatics Biological system modeling Computational modeling Genomics Computational biology conserved gene clusters. Algorithms data structures common intervals comparative genomics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Genetics Biotechnology

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