Approximating Points by a Piecewise Linear Function: I

Authors:
Danny Z. Chen;Haitao Wang
Affiliations:
Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, USA 46556;Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, USA 46556
Venue:
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Year:
2009

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Abstract

We study the problem of approximating a set of weighted planar points by a step function, and the problems of approximating non-weighted and weighted planar points by a (more general) piecewise linear function. We either improve the previously best-known results or give the first-known results for these problems. Our algorithms are based on interesting and nontrivial geometric techniques and data structures, which may find other applications. Further, we present the first-known results for the 3-D versions of the step function approximation problem.