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Shape fitting is a fundamental optimization problem in computer
science. In this paper, we present a general and unified technique
for solving a certain family of such problems. Given a point
set P in R^{d}, this technique can be used
to µ-approximate:(i) the min-width annulus and shell
that contains P,(ii) minimum width cylindrical shell containing
P,(iii) diameter, width, minimum volume bounding box of
P, and(iv) all the previous measures for the case the
points are moving. The running time of the resulting algorithms
is O(n + 1/µ^{c}), where c is a constant
that depends on the problem at hand.

Our new general technique
enable us to solve those problems without resorting to a careful
and painful case by case analysis, as was previously done for
those problems. Furthermore, for several of those problems our
results are considerably simpler and faster than what was previously
known. In particular, for the minimum width cylindrical shell
problem, our solution is the first algorithm whose running time
is subquadratic in n.(In fact we get running time linear
in n.)