NDLI: Restricted and Swap Common Superstring: A Multivariate Algorithmic Perspective

Content Provider	Springer Nature Link
Author	Bonizzoni, Paola Dondi, Riccardo Mauri, Giancarlo Zoppis, Italo
Copyright Year	2014
Abstract	In several areas, for example in bioinformatics and in AI planning, the Shortest Common Superstring problem (SCS) and variants thereof have been successfully applied for string comparison. In this paper we consider two variants of SCS recently introduced, namely Restricted Common Superstring (RCS) and Swapped Common Superstring (SRCS). In RCS we are given a set $$S$$ of strings and a multiset $$\mathcal {M}$$ of symbols, and we look for an ordering $$\mathcal {M}_o$$ of $$\mathcal {M}$$ such that the number of input strings which are substrings of $$\mathcal {M}_o$$ is maximized. In SRCS we are given a set $$S$$ of strings and a text $$\mathcal {T}$$ , and we look for a swap ordering $$\mathcal {T}_o$$ of $$\mathcal {T}$$ (an ordering of $$\mathcal {T}$$ obtained by swapping only some pairs of adjacent symbols) such that the number of input strings which are substrings of $$\mathcal {T}_o$$ is maximized. In this paper we propose a multivariate algorithmic analysis of the complexity of the two problems, aiming at determining how different parameters influence the complexity of the two problems. We consider as interesting parameters the size of the solutions (that is the number of input strings contained in the computed superstring), the maximum length of the given input strings, the size of the alphabet over which the input strings range. First, we give two fixed-parameter algorithms, where the parameter is the size of the solution, for SRCS and lRCS (the RCS problem restricted to strings of length bounded by a parameter $$\ell $$ ). Furthermore, we complement these results by showing that SRCS and lRCS do not admit a polynomial kernel unless $$NP \subseteq coNP/Poly$$ . Then, we show that SRCS is APX-hard even when the input strings have length bounded by a constant (equal to $$10$$ ) or are over a binary alphabet.
Starting Page	914
Ending Page	939
Page Count	26
File Format	PDF
ISSN	01784617
Journal	Algorithmica
Volume Number	72
Issue Number	4
e-ISSN	14320541
Language	English
Publisher	Springer US
Publisher Date	2014-04-12
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Shortest common superstring String comparison Parameterized complexity Algorithms APX-hardness Algorithm Analysis and Problem Complexity Theory of Computation Mathematics of Computing Computer Systems Organization and Communication Networks Data Structures, Cryptology and Information Theory
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computer Science Applications

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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