Space-Efficient Las Vegas Algorithms for K-SUM

TL;DR

This paper introduces space-efficient Las Vegas algorithms for k-SUM problems using hashing, achieving improved time-space bounds for 3-SUM and SUBSET-SUM, advancing the efficiency of randomized algorithms in this domain.

Contribution

It develops a family of space-efficient Las Vegas algorithms for k-SUM, including a 3-SUM algorithm with optimal time and space, and establishes new bounds for SUBSET-SUM.

Findings

3-SUM solved in O(n^2) time and O(√n) space

New time-space bounds for SUBSET-SUM with Las Vegas algorithms

Improved efficiency in randomized algorithms for k-SUM problems

Abstract

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 $\beta \in [0, \9/32]$.