Improved Space-Time Tradeoffs for kSUM.

In the kSUM problem we are given an array of numbers $a_1,a_2,...,a_n$ and we are required to determine if there are $k$ different elements in this array such that their sum is 0. This problem is a parameterized version of the well-studied SUBSET-SUM problem, and a special case is the 3SUM problem that is extensively used for proving conditional hardness. Several works investigated the interplay between time and space in the context of SUBSET-SUM. Recently, improved time-space tradeoffs were proven for kSUM using both randomized and deterministic algorithms. In this paper we obtain an improvement over the best known results for the time-space tradeoff for kSUM. A major ingredient in achieving these results is a general self-reduction from kSUM to mSUM where $m 1$. (iv) An algorithm for 6SUM running in $O(n^4)$ time using just $O(n^{2/3})$ space. (v) A solution to 3SUM on random input using $O(n^2)$ time and $O(n^{1/3})$ space, under the assumption of a random read-only access to random bits.