Fingerprint Clustering with Bounded Number of Missing Values

The problem of clustering fingerprint vectors with missing values is an interesting problem in Computational Biology that has been proposed in Figueroa et al. (J. Comput. Biol. 11(5):887–901, 2004). In this paper we show some improvements in closing the gaps between the known lower bounds and upper bounds on the approximability of variants of the biological problem. Moreover, we have studied two additional variants of the original problem proposed in Figueroa et al. (Proc. 11th Computing: The Australasian Theory Symposium (CATS), CRPIT, vol. 41, pp. 57–60, 2005). We prove that all such problems are APX-hard even when each fingerprint contains only two unknown positions and we present a greedy algorithm that has constant approximation factors for these variants. Despite the hardness of these restricted versions of the problem, we show that the general clustering problem on an unbounded number of missing values such that they occur for every fixed position of an input vector in at most one fingerprint is polynomial time solvable.

[1]  R. Drmanac,et al.  Processing of cDNA and genomic kilobase-size clones for massive screening, mapping and sequencing by hybridization. , 1994, BioTechniques.

[2]  R. Drmanac,et al.  Gene-representing cDNA clusters defined by hybridization of 57,419 clones from infant brain libraries with short oligonucleotide probes. , 1996, Genomics.

[3]  Tao Jiang,et al.  Clustering Binary Fingerprint Vectors with Missing Values for DNA Array Data Analysis , 2004, J. Comput. Biol..

[4]  R. Drmanac,et al.  cDNA screening by array hybridization. , 1999, Methods in enzymology.

[5]  Max Planck,et al.  Complexity of approximating bounded variants of optimization problems , 2008 .

[6]  Christos H. Papadimitriou,et al.  Computational complexity , 1993 .

[7]  Viggo Kann,et al.  Some APX-completeness results for cubic graphs , 2000, Theor. Comput. Sci..

[8]  James Borneman,et al.  Oligonucleotide Fingerprinting of rRNA Genes for Analysis of Fungal Community Composition , 2002, Applied and Environmental Microbiology.

[9]  Tao Jiang,et al.  Approximate Clustering of Fingerprint Vectors with Missing Values , 2005, CATS.

[10]  Giorgio Gambosi,et al.  Complexity and Approximation , 1999, Springer Berlin Heidelberg.

[11]  Giorgio Gambosi,et al.  Complexity and approximation: combinatorial optimization problems and their approximability properties , 1999 .

[12]  M. Chrobak,et al.  Analysis of Bacterial Community Composition by Oligonucleotide Fingerprinting of rRNA Genes , 2002, Applied and Environmental Microbiology.