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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(n 11/6) 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(n c) with c < ⌈k/2⌉. Revisiting a known algorithm due to Meiser (1993), we show that there exist… (More)

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