The modular subset sum problem consists of deciding, given a modulus m, a multiset S of n integers in 0.. m , and a target integer t, whether there exists a subset of S with elements summing to t \mod  , and to report such a set if it exists. We give a simple O(m \log m)-time with high probability (w.h.p.) algorithm for the modular subset sum problem. This builds on and improves on a previous (m ) w.h.p. algorithm from Axiotis, Backurs, Jin, Tzamos, and Wu (SODA 19). Our method utilizes the ADT of the dynamic strings structure of Gawrychowski et . al(SODA 18). However, as this structure is rather complicated we present a much simpler alternative which we call the Data Dependent Tree. As an application, we consider the computational version of a fundamental theorem in zero-sum Ramsey theory. The Erdos-Ginzburg-Ziv Theorem states that a multiset of 2n - 1 integers always contains a subset of cardinality exactly n whose values sum to a multiple of n. We give an algorithm for finding such a subset in time O(n \log n) w.h.p. which improves on an O(n^2) algorithm due to Del Lungo, Marini, and Mori (Disc. Math. 09).
The modular subset sum problem consists of deciding, given a modulus m, a multiset S of n integers in 0.. m-1 , and a target integer t, whether there exists a subset of S with elements summing to t \mod m , and to report such a set if it exists. We give a simple O(m \log m)-time with high probability (w.h.p.) algorithm for the modular subset sum problem. This builds on and improves on a previous O(m \log^7 m ) w.h.p. algorithm from Axiotis, Backurs, Jin, Tzamos, and Wu (SODA 19). Our method utilizes the ADT of the dynamic strings structure of Gawrychowski et al. (SODA~ 18). However, as this structure is rather complicated we present a much simpler alternative which we call the Data Dependent Tree. As an application, we consider the computational version of a fundamental theorem in zero-sum Ramsey theory. The Erdos-Ginzburg-Ziv Theorem states that a multiset of 2n - 1 integers always contains a subset of cardinality exactly n whose values sum to a multiple of n. We give an algorithm for finding such a subset in time O(n \log n) w.h.p. which improves on an O(n^2) algorithm due to Del Lungo, Marini, and Mori (Disc. Math. 09).
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