2025/07/10 by Leung, Yui Hin Arvin
#Combinatorics (math.CO) #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Mathematics
paper · doi:10.48550/arxiv.2507.08139
The Erdős-Ginzburg-Ziv theorem states that for any sequence of 2n-1 integers, there exists a subsequence of n elements whose sum is divisible by n. In this article, we provide a simple, practical O(nloglog n) algorithm and a theoretical O(nlogloglog n) algorithm, both of which improve upon the best previously known O(nlog n) approach. This shows that a specific variant of boolean convolution can be implemented in time faster than the usual O(nlog n) expected from FFT-based methods.