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- W4287687130 abstract "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 ErdH{o}s-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)." @default.
- W4287687130 created "2022-07-26" @default.
- W4287687130 creator A5011369568 @default.
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- W4287687130 date "2020-08-19" @default.
- W4287687130 modified "2023-10-16" @default.
- W4287687130 title "Modular Subset Sum, Dynamic Strings, and Zero-Sum Sets" @default.
- W4287687130 doi "https://doi.org/10.48550/arxiv.2008.08417" @default.
- W4287687130 hasPublicationYear "2020" @default.
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