On the k-Closest Substring and k-Consensus Pattern Problems

Given a set S ={s 1,s 2,...,s n } of strings each of length m, and an integer L, we study the following two problems.

[1]  Rafail Ostrovsky,et al.  Polynomial-time approximation schemes for geometric min-sum median clustering , 2002, JACM.

[2]  Russ Bubley,et al.  Randomized algorithms , 1995, CSUR.

[3]  Piotr Indyk,et al.  Approximate nearest neighbors: towards removing the curse of dimensionality , 1998, STOC '98.

[4]  Jesper Jansson,et al.  Consensus Algorithms for Trees and Strings , 2003 .

[5]  Andrzej Lingas,et al.  Efficient approximation algorithms for the Hamming center problem , 1999, SODA '99.

[6]  Jeremy Buhler,et al.  Efficient large-scale sequence comparison by locality-sensitive hashing , 2001, Bioinform..

[7]  Bin Ma,et al.  Finding similar regions in many strings , 1999, STOC '99.

[8]  Bin Ma,et al.  A Polynominal Time Approximation Scheme for the Closest Substring Problem , 2000, CPM.

[9]  David S. Johnson,et al.  The Rectilinear Steiner Tree Problem is NP Complete , 1977, SIAM Journal of Applied Mathematics.

[10]  Tomás Feder,et al.  Optimal algorithms for approximate clustering , 1988, STOC '88.

[11]  Teofilo F. GONZALEZ,et al.  Clustering to Minimize the Maximum Intercluster Distance , 1985, Theor. Comput. Sci..

[12]  Tao Jiang,et al.  Linear approximation of shortest superstrings , 1994, JACM.

[13]  Robert J. Fowler,et al.  Optimal Packing and Covering in the Plane are NP-Complete , 1981, Inf. Process. Lett..

[14]  Bin Ma,et al.  Distinguishing string selection problems , 2003, SODA '99.

[15]  Andrzej Lingas,et al.  Approximation Algorithms for Hamming Clustering Problems , 2000, CPM.

[16]  Bin Ma,et al.  On the closest string and substring problems , 2002, JACM.