Abstract
Let P be a d-dimensional n-point set. A partition \(\mathcal{T}\) of P is called a Tverberg partition if the convex hulls of all sets in \(\mathcal{T}\) intersect in at least one point. We say \(\mathcal{T}\) is t-tolerated if it remains a Tverberg partition after deleting any t points from P. Soberon and Strausz proved that there is always a t-tolerated Tverberg partition with ⌈n / (d + 1)(t + 1) ⌉ sets. However, so far no nontrivial algorithms for computing or approximating such partitions have been presented.
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