# Lipschitz Isotonic and Unimodal Regressions on Paths and Trees

Filed in: Topological Simplification | Data Structures

Pankaj K. Agarwal, Jeff Phillips, and Bardia Sadri

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, where there is exactly one local maximum in s. These algorithm are generalized from sequences of values to trees of values. For each scenario we describe near-linear time algorithms.

9th Latin American Theoretical Informatics Symposium (LATIN) 2010 [PDF]

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, where there is exactly one local maximum in s. These algorithm are generalized from sequences of values to trees of values. For each scenario we describe near-linear time algorithms.

9th Latin American Theoretical Informatics Symposium (LATIN) 2010 [PDF]