Lipschitz Unimodal and Isotonic Regression on Paths and Trees

  • Pankaj K. Agarwal
  • Jeff M. Phillips
  • Bardia Sadri
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6034)


We describe algorithms for finding the regression of t, a sequence of values, to the closest sequence s by mean squared error, so that s is always increasing (isotonicity) and so the values of two consecutive points do not increase by too much (Lipschitz). The isotonicity constraint can be replaced with a unimodular constraint, for exactly one local maximum in s. These algorithm are generalized from sequences of values to trees of values. For each we describe near-linear time algorithms.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Pankaj K. Agarwal
    • 1
  • Jeff M. Phillips
    • 2
  • Bardia Sadri
    • 3
  1. 1.Duke University 
  2. 2.University of Utah 
  3. 3.University of Toronto 

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