Geometric hitting set problems, in which we seek a smallest set of points
that collectively hit a given set of ranges, are ubiquitous in computational
geometry. Most often, the set is discrete and is given explicitly. We propose
new variants of these problems, dealing with continuous families of convex
polyhedra, and show that they capture decision versions of the two-level finite
adaptability problem in robust optimization. We show that these problems can be
solved in strongly polynomial time when the size of the hitting/covering set
and the dimension of the polyhedra and the parameter space are constant. Nous
also show that the hitting set problem can be solved in strongly quadratic time
for one-parameter families of convex polyhedra in constant dimension. Ce
leads to new tractability results for finite adaptability that are the first
ones with so-called left-hand-side uncertainty, where the underlying problem is
non-linear.

Cet article explore les excursions dans le temps et leurs implications.

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