Abstract
In this paper we study the following problem: Given n strings s1, s 2,..., sn, each of length m, find a substring ti of length L for each s i, and a string s of length L, such that maxi = 1n d(s, ti) is minimized, where d(·, ·) is the Hamming distance. The problem was raised in [6] in an application of genetic drug target search and is a key open problem in many applications [7]. The authors of [6] showed that it is NP-hard and can be trivially approximated within ratio 2. A non-trivial approximation algorithm with ratio better than 2 was found in [7]. A major open question in this area is whether there exists a polynomial time approximation scheme (PTAS) for this problem. In this paper, we answer this question positively. We also apply our method to two related problems.
Supported in part by NSERC Research Grant OGP0046506.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. Ben-Dor, G. Lancia, J. Perone, and R. Ravi, Banishing Bias from Consensus Sequences, Combinatorial Pattern Matching, 8th Annual Symposium, Springer-Verlag, Berlin, 1997.
S. Crooke and B. Lebleu (editors), Antisense Research and Applications, CRC Press, 1993.
M. Frances and A. Litman, On covering problems of codes, Theory of Computing Systems, vol. 30, pp. 113–119, 1997.
L. Gçasieniec, J. Jansson, and A. Lingas, Efficient approximation algorithms for the Hamming center problem, Proceedings of the Tenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 905–906, San Francisco, 1999.
E. M. Hillis, C. Moritz, and B. K. Mable, Molecular Systematics, 2nd ed., Sinauer Associates Inc., Sunderland, 1996.
K. Lanctot, M. Li, B. Ma, S. Wang, and L. Zhang, Distinguish string search problems, Proceedings of the Tenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 633–642, San Francisco, 1999.
M. Li, B. Ma, and L. Wang, Finding similar regions in many strings, Proceedings of the Thirty-first Annual ACM Symposium on Theory of Computing, pp. 473–482, Atlanta, 1999.
B. Ma, Some approximation algorithms on strings and trees, Ph.D. Thesis, Peking University, 1999.
A. Macario and E. Macario, Gene Probes for Bacteria, Academic Press, 1990.
R. Motwani and P. Raghavan, Randomized Algorithms, Cambridge University Press, 1995.
L. Wang, Personal Communication, 1999.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ma, B. (2000). A Polynomial Time Approximation Scheme for the Closest Substring Problem. In: Giancarlo, R., Sankoff, D. (eds) Combinatorial Pattern Matching. CPM 2000. Lecture Notes in Computer Science, vol 1848. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45123-4_10
Download citation
DOI: https://doi.org/10.1007/3-540-45123-4_10
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67633-1
Online ISBN: 978-3-540-45123-5
eBook Packages: Springer Book Archive