Aurélien Ooms

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The 3SUM problem asks if an input n-set of real numbers contains a triple whose sum is zero. We consider the 3POL problem, a natural generalization of 3SUM where we replace the sum function by a constant-degree polynomial in three variables. The motivations are threefold. Raz, Sharir, and de Zeeuw gave an O(n11/6) upper bound on the number of solutions of(More)
In the k-SUM problem, we are given n real numbers as input, and we are asked whether there exists a zero-sum k-subset. The problem is of tremendous importance in complexity theory, and it is in particular open whether it admits an algorithm of complexity O(nc) with c < ⌈k/2⌉. Revisiting a known algorithm due to Meiser (1993), we show that there exist linear(More)
We study the following family of problems: Given a set of n points in convex position, what is the maximum number triangles one can create having these points as vertices while avoiding certain sets of forbidden configurations. As forbidden configurations we consider all 8 ways in which a pair of triangles in such a point set can interact. This leads to 256(More)
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