Randomized algorithms
Finding similar regions in many strings
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Distinguishing string selection problems
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Efficient approximation algorithms for the Hamming center problem
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Banishing Bias from Consensus Sequences
CPM '97 Proceedings of the 8th Annual Symposium on Combinatorial Pattern Matching
A PTAS for Distinguishing (Sub)string Selection
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
On the Parameterized Intractability of CLOSEST SUBSTRINGsize and Related Problems
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
On the hardness of counting and sampling center strings
SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
More Efficient Algorithms for Closest String and Substring Problems
SIAM Journal on Computing
On the longest common rigid subsequence problem
CPM'05 Proceedings of the 16th annual conference on Combinatorial Pattern Matching
On approximating string selection problems with outliers
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
On the Hardness of Counting and Sampling Center Strings
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
On approximating string selection problems with outliers
Theoretical Computer Science
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In this paper we study the following problem: Given n strings s1, s2,..., sn, each of length m, find a substring ti of length L for each si, and a string s of length L, such that maxni=1 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.