Closest Substring Problems with Small Distances
نویسندگان
چکیده
منابع مشابه
Closest Substring Problems with Small Distances
We study two pattern matching problems that are motivated by applications in computational biology. In the Closest Substring problem k strings s1, . . ., sk are given, and the task is to find a string s of length L such that each string si has a consecutive substring of length L whose distance is at most d from s. We present two algorithms that aim to be efficient for small fixed values of d an...
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The closest substring problem, where a short string is sought that minimizes the number of mismatches between it and each of a given set of strings, is a minimization problem with a polynomial time approximation scheme [6]. In this paper, both this problem and its maximization complement, where instead the number of matches is maximized, are examined and bounds on their hardness of approximatio...
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We propose a new cryptographic notion called generalized closest substring encryption. In this notion, a ciphertext encrypted with a string S can be decrypted with a private key of another string S′, if there exist a substring of S, i.e. Ŝ, and a substring of S′, i.e. Ŝ′, that are “close” to each other measured by their “overlap distance”. The overlap distance between Ŝ and Ŝ′ is the number of ...
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Given a set S = {s1, s2, . . . , sn} of strings each of length m, and an integer L, we study the following two problems. k-Closest Substring problem: find k center strings c1, c2, . . . , ck of length L minimizing d such that for each sj ∈ S, there is a length-L substring tj (closest substring) of sj with min1≤i≤k d(ci, tj) ≤ d. We give a PTAS for this problem, for k = O(1). k-Consensus Pattern...
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The closest string and substring problems find applications in PCR primer design, genetic probe design, motif finding, and antisense drug design. For their importance, the two problems have been extensively studied recently in computational biology. Unfortunately both problems are NP-complete. Researchers have developed both fixed-parameter algorithms and approximation algorithms for the two pr...
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2008
ISSN: 0097-5397,1095-7111
DOI: 10.1137/060673898