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# A deterministic algorithm for fitting a step function to a weighted point-set

09/2011;
Source: arXiv

ABSTRACT Given a set of n points in the plane, each point having a positive weight,
and an integer k>0, we present an optimal O(n \log n)-time deterministic
algorithm to compute a step function with k steps that minimizes the maximum
weighted vertical distance to the input points. It matches the expected time
bound of the best known randomized algorithm for this problem. Our approach
relies on Cole's improved parametric searching technique.

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### Keywords

input points

integer k>0

known randomized algorithm

n points

positive weight

step function