Hervé Brönnimann

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We investigate the complexity of <italic>halfspace range searching</italic>: Given <italic>n</italic> points in <italic>d</italic>-space, build a data structure that allows us to determine efficiently how many points lie in a query halfspace. We establish a tradeoff between the storage <italic>m</italic> and the worst-case query time <italic>t</italic> in(More)
We introduce the concept of a sensitive E-approximation, and use it to derive a more efficient algorithm for computing &-nets. We define and investigate product range spaces, for which we establish sampling theorems analogous to the standard finite VC-dimensional case. This generalizes and simplifies results from previous works. We derive a simpler optimal(More)
Motivated by visibility problems in three dimensions, we investigate the complexity and construction of the set of tangent lines in a scene of three-dimensional polyhedra. We prove that the set of lines tangent to four possibly intersecting convex polyhedra in R3 with a total of n edges consists of Θ(n2) connected components in the worst case. In the(More)
An important problem in mobile ad-hoc wireless sensor networks is the localization of individual nodes, i.e., each node's awareness of its position relative to the network. In this paper, we introduce a variant of this problem (directional localization) where each node must be aware of both its position and orientation relative to the network. This variant(More)
Payload attribution is an important problem often encountered in network forensics. Given an excerpt of a payload, finding its source and destination is useful for many security applications such as identifying sources and victims of a worm or virus. Although IP traceback techniques have been proposed in the literature, these techniques cannot help when we(More)
We consider a class of geometric facility location problems in which the goal is to determine a set <i>X</i> of disks given by their centers <i>(t<sub>j</sub>)</i> and radii <i>(r<sub>j</sub>)</i> that cover a given set of demand points <i>Y&#8712;R</i><sup>2</sup> at the smallest possible cost. We consider cost functions of the form(More)
A variety of mining and analysis problems --- ranging from association-rule discovery to contingency table analysis to materialization of certain approximate datacubes --- involve the extraction of knowledge from a set of categorical count data. Such data can be viewed as a collection of "transactions," where a transaction is a fixed-length vector of(More)
For many geometric problems, there are efficient algorithms that surprisingly use very little extra space other than the given array holding the input. For many geometric query problems, there are efficient data structures that need no extra space at all other than an array holding a permutation of the input. In this paper, we obtain the first such(More)