A Polynomial Time Approximation
نویسنده
چکیده
In this paper we study the following problem: Given n strings s1; s2; : : : ; sn, each of length m, nd a substring ti of length L for each si, and a string s of length L, such that max n i=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.
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