Faster Exact Algorithms for Equal-Subset-Sum

Abstract

We study exact algorithms for Equal-Subset-Sum in the worst-case setting: given a set $S$ of $n$ integers, find two distinct subsets $A,B\subseteq S$ whose sums are equal. We establish a new state-of-the-art bound for this problem by improving the fastest known algorithm, due to Randolph and Węgrzycki (STOC 2026), from $O^{\ast }(1.7067^n)$ time and space to an algorithm that runs in $O^{\ast }(1.6994^n)$ time and uses $O^{\ast }(1.5664^n)$ space. We also improve the best known polynomial-space running time, due to Mucha, Nederlof, Pawlewicz, and Węgrzycki (ESA 2019), from $O^{\ast }(2.6817^n)$ to $O^{\ast }(2.5430^n)$. Finally, we investigate time-space tradeoffs for this problem and improve the running times achievable under a broad range of exponential-space bounds.