Optimal Fit of Arbitrary Sized Segments

A doubly optimal ellipse fit

We study the problem of fitting ellipses to observed points in the context of Errors-In-Variables regression analysis. The accuracy of fitting methods is characterized by their variances and biases. The variance has a theoretical lower bound (the KCR bound), and many practical fits attend it, so they are optimal in this sense. There is no lower bound on the bias, though, and in fact our higher ...

When are best fit and first fit optimal?

View-dependent Tetrahedral Meshing and Rendering using Arbitrary Segments

We present a meshing and rendering framework for tetrahedral meshes that constructs a multi-resolution representation and uses this representation to adapt the mesh to rendering parameters. The mesh is partitioned into several segments which are simplified independently. A multi-resolution representation is constructed by merging simplified segments and again simplifying the merged segments. We...

Optimal Analysis of Best Fit Bin Packing

In the bin packing problem we are given an instance consisting of a sequence of items with sizes between 0 and 1. The objective is to pack these items into the smallest possible number of bins of unit size. BestFit algorithm packs each item into the most full bin where it fits, possibly opening a new bin if the item cannot fit into any currently open bin. In early seventies it was shown that th...

Rate-Optimal Detection of Very Short Signal Segments

Motivated by a range of applications in genomics and engineering, we consider in this paper detection of very short signal segments in three settings: signals with known shape, arbitrary signals, and smooth signals. Optimal rates of detection are established for the three cases and rate-optimal detectors are constructed. The detectors are easily implementable and are based on scanning with line...