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  Rotations of periodic strings and short superstrings

Breslauer, D., Jiang, T., & Jiang, Z.(1996). Rotations of periodic strings and short superstrings (MPI-I-1996-1-019). Saarbrücken: Max-Planck-Institut für Informatik.

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MPI-I-96-1-019.pdf (Any fulltext), 198KB
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Breslauer, Dany1, Author              
Jiang, Tao2, Author
Jiang, Zhigen2, Author
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1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              
2External Organizations, ou_persistent22              

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 Abstract: This paper presents two simple approximation algorithms for the shortest superstring problem, with approximation ratios $2 {2\over 3}$ ($\approx 2.67$) and $2 {25\over 42}$ ($\approx 2.596$), improving the best previously published $2 {3\over 4}$ approximation. The framework of our improved algorithms is similar to that of previous algorithms in the sense that they construct a superstring by computing some optimal cycle covers on the distance graph of the given strings, and then break and merge the cycles to finally obtain a Hamiltonian path, but we make use of new bounds on the overlap between two strings. We prove that for each periodic semi-infinite string $\alpha = a_1 a_2 \cdots$ of period $q$, there exists an integer $k$, such that for {\em any} (finite) string $s$ of period $p$ which is {\em inequivalent} to $\alpha$, the overlap between $s$ and the {\em rotation} $\alpha[k] = a_k a_{k+1} \cdots$ is at most $p+{1\over 2}q$. Moreover, if $p \leq q$, then the overlap between $s$ and $\alpha[k]$ is not larger than ${2\over 3}(p+q)$. In the previous shortest superstring algorithms $p+q$ was used as the standard bound on overlap between two strings with periods $p$ and $q$.

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Language(s): eng - English
 Dates: 1996
 Publication Status: Published in print
 Pages: 13 p.
 Publishing info: Saarbrücken : Max-Planck-Institut für Informatik
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 Rev. Type: -
 Identifiers: Report Nr.: MPI-I-1996-1-019
BibTex Citekey: BreslauerJiangZhigen97
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Title: Research Report / Max-Planck-Institut für Informatik
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