Measurement Errors Make the Partial Digest Problem NP-Hard

  • Mark Cieliebak
  • Stephan Eidenbenz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2976)


The Partial Digest problem asks for the coordinates of m points on a line such that the pairwise distances of the points form a given multiset of \(\left({m \atop 2}\right)\) distances. Partial Digest is a well-studied problem with important applications in physical mapping of DNA molecules. Its computational complexity status is open. Input data for Partial Digest from real-life experiments are always prone to error, which suggests to study variations of Partial Digest that take this fact into account. In this paper, we study the computational complexity of the variation of Partial Digest in which each distance is known only up to some error, due to experimental inaccuracies. The error can be specified either by some additive offset or by a multiplicative factor. We show that both types of error make the Partial Digest problem strongly NP-complete, by giving reductions from 3-Partition. In the case of relative errors, we show that the problem is hard to solve even for constant relative error.


Pairwise Distance Additive Error Adjacent Point Partial Digestion Multiplicative Error 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Mark Cieliebak
    • 1
  • Stephan Eidenbenz
    • 2
  1. 1.Institute of Theoretical Computer ScienceETH Zurich 
  2. 2.Los Alamos National Laboratory 

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