Double digest revisited: complexity and approximability in the presence of noisy data

  • Authors:

  • Mark Cieliebak;Stephan Eidenbenz;Gerhard J. Woeginger

  • Affiliations:

  • Institute of Theoretical Computer Science, ETH Zurich;Basic and Applied Simulation Science, Los Alamos National Laboratory;Faculty of Mathematical Sciences, University of Twente and Department of Mathematics and Computer Science, TU Eindhoven

  • Venue:
  • COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
  • Year:
  • 2003

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Abstract

We revisit the DOUBLE DIGEST problem, which occurs in sequencing of large DNA strings and consists of reconstructing the relative positions of cut sites from two different enzymes: we first show that DOUBLE DIGEST is strongly NP-complete, improving upon previous results that only showed weak NP-completeness. Even the (experimentally more meaningful) variation in which we disallow coincident cut sites turns out to be strongly NP-complete. In a second part, we model errors in data as they occur in real-life experiments: we propose several optimization variations of DOUBLE DIGEST that model partial cleavage errors. We then show APX-completeness for most of these variations. In a third part, we investigate these variations with the additional restriction that conincident cut sites are disallowed, and we show that it is NP-hard to even find feasible solutions in this case, thus making it impossible to guarantee any approximation ratio at all.