Algorithmica

, Volume 58, Issue 2, pp 282–303 | Cite as

Fingerprint Clustering with Bounded Number of Missing Values

  • Paola Bonizzoni
  • Gianluca Della Vedova
  • Riccardo Dondi
  • Giancarlo Mauri
Article

Abstract

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.

Keywords

Clustering Approximation algorithm Fingerprint vectors 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Paola Bonizzoni
    • 1
  • Gianluca Della Vedova
    • 2
  • Riccardo Dondi
    • 3
  • Giancarlo Mauri
    • 1
  1. 1.DISCoUniversità degli Studi di Milano-BicoccaMilanoItaly
  2. 2.Dip. StatisticaUniversità degli Studi di Milano-BicoccaMilanoItaly
  3. 3.Dipartimento di Scienze dei Linguaggi, della Comunicazione e degli Studi CulturaliUniversità degli Studi di BergamoBergamoItaly

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