Dartmouth logo Dartmouth College Computer Science
Technical Report series
CS home
TR home
TR search TR listserv
By author: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
By number: 2017, 2016, 2015, 2014, 2013, 2012, 2011, 2010, 2009, 2008, 2007, 2006, 2005, 2004, 2003, 2002, 2001, 2000, 1999, 1998, 1997, 1996, 1995, 1994, 1993, 1992, 1991, 1990, 1989, 1988, 1987, 1986

A 2-2/3 Approximation for the Shortest Superstring Problem
Chris Armen, Clifford Stein
Dartmouth PCS-TR95-262


Given a collection of strings S={s_1, ..., s_n} over an alphabet \Sigma, a superstring \alpha of S is a string containing each s_i as a substring; that is, for each i, 1<=i<=n, \alpha contains a block of |s_i| consecutive characters that match s_i exactly. The shortest superstring problem is the problem of finding a superstring \alpha of minimum length.

The shortest superstring problem has applications in both data compression and computational biology. In data compression, the problem is a part of a general model of string compression proposed by Gallant, Maier and Storer (JCSS '80). Much of the recent interest in the problem is due to its application to DNA sequence assembly.

The problem has been shown to be NP-hard; in fact, it was shown by Blum et al.(JACM '94) to be MAX SNP-hard. The first O(1)-approximation was also due to Blum et al., who gave an algorithm that always returns a superstring no more than 3 times the length of an optimal solution. Several researchers have published results that improve on the approximation ratio; of these, the best previous result is our algorithm ShortString, which achieves a 2 3/4-approximation (WADS '95).

We present our new algorithm, G-ShortString, which achieves a ratio of 2 2/3. It generalizes the ShortString algorithm, but the analysis differs substantially from that of ShortString. Our previous work identified classes of strings that have a nested periodic structure, and which must be present in the worst case for our algorithms. We introduced machinery to descibe these strings and proved strong structural properties about them. In this paper we extend this study to strings that exhibit a more relaxed form of the same structure, and we use this understanding to obtain our improved result.

PS.Z compressed postscript .ps.Z (144KB) , PDF PDF (308KB) (derived from the ps.Z)

Bibliographic citation for this report: [plain text] [BIB] [BibTeX] [Refer]

Or copy and paste:
   Chris Armen and Clifford Stein, "A 2-2/3 Approximation for the Shortest Superstring Problem." Dartmouth Computer Science Technical Report PCS-TR95-262, June 1995.

Notify me about new tech reports.

Search the technical reports.

To receive paper copy of a report, by mail, send your address and the TR number to reports AT cs.dartmouth.edu

Copyright notice: The documents contained in this server are included by the contributing authors as a means to ensure timely dissemination of scholarly and technical work on a non-commercial basis. Copyright and all rights therein are maintained by the authors or by other copyright holders, notwithstanding that they have offered their works here electronically. It is understood that all persons copying this information will adhere to the terms and constraints invoked by each author's copyright. These works may not be reposted without the explicit permission of the copyright holder.

Technical reports collection maintained by David Kotz.