Using hashing techniques, this paper develops a family of space-efficient Las Vegas randomized algorithms for $k$-SUM problems. This family includes an algorithm that can solve 3-SUM in $O(n^2)$ time and $O(\sqrt{ n})$ space. It also establishes a new time-space upper bound for SUBSET-SUM, which can be solved by a Las Vegas algorithm in $O^*(2^{ (1-\sqrt{ \8/9\beta})n})$ time and $O^*(2^{ \beta n})$ space, for any $\beta \in [0, \9/32]$.
Categories: cs.DS