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A three-string approach to the closest string problem
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The bounded search tree algorithm for the closest string problem has quadratic smoothed complexity
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
A three-string approach to the closest string problem
Journal of Computer and System Sciences
Slightly superexponential parameterized problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
On approximating string selection problems with outliers
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
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CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
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IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
On approximating string selection problems with outliers
Theoretical Computer Science
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In the paper, we study three related problems, the closest string problem, the farthest string problem and the distinguishing string selection problem. These problems have applications in motif detection, binding sites locating, genetic drug target identification, genetic probes design, universal PCR primer design, etc. They have been extensively studied in recent years. The problems are defined as follows: The closest string problem: given a group of strings ${\cal B}=\{s_1, s_2, \ldots,$ s n }, each of length L , and an integer d , the problem is to compute a center string s of length L such that the Hamming distance d (s , s i ) ≤ d for all $s_y\in {\cal B}$. The farthest string problem: given a group of strings ${\cal G}=\{g_1,g_2,...,$ $g_{n_2}\}$, with all strings of the same length L , and an integer d b , the farthest string problem is to compute a center string s of length L such that the Hamming distance d (s ,g j ) *** L *** d b for all $ g_j\in {\cal G}$. The distinguishing string selection problem: given two groups of strings ${\cal B}$ (bad genes) and ${\cal G}$ (good genes), ${\cal B}=\{s_1,s_2,...,s_{n_1}\}$ and ${\cal G}=\{g_{n_1+1},g_{n_1+2},...,g_{n_2}\}$, with all strings of the same length L , and two integers d b and d g with d g *** L *** d b , the Distinguishing String Selection problem is to compute a center string s of length L such that the Hamming distance $d(s,s_i)\leq d_b, \forall s_i\in{\cal B}$ and the Hamming distance d (s ,g j ) *** d g for all $g_j\in {\cal G}$. Our results: We design an O (Ln + nd (|Σ *** 1|) d 23.25d ) time fixed parameter algorithm for the closest string problem which improves upon the best known O (Ln + nd 24d ×(|Σ | *** 1) d ) algorithm in [14], where |Σ | is the size of the alphabet. We also design fixed parameter algorithms for both the farthest string problem and the distinguishing string selection problem. Both algorithms run in time $O(Ln+nd2^{3.25d_b})$ when the input strings are binary strings over Σ = {0, 1}.