# Modular Subset Sum, Dynamic Strings, and Zero-Sum Sets

@inproceedings{Cardinal2021ModularSS, title={Modular Subset Sum, Dynamic Strings, and Zero-Sum Sets}, author={Jean Cardinal and John Iacono}, booktitle={SOSA}, year={2021} }

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 $t \pmod{m}$, 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 $\tilde{O}(m)$ w.h.p. algorithm from Axiotis, Backurs, Jin, Tzamos, and Wu (SODA 19…

## 5 Citations

Faster Deterministic Modular Subset Sum

- Computer Science, MathematicsArXiv
- 2020

A simple data structure, designed specifically to handle the text problem that arises in the algorithms for Modular Subset Sum, is developed, which provides both a hashing-based and a deterministic variant of the shift-trees.

Faster Deterministic Modular Subset Sum

- Computer Science, Mathematics
- 2020

A simple data structure, designed specifically to handle the text problem that arises in the algorithms for Modular Subset Sum, is developed, which is a simple variant of a segment tree and provides both a hashing-based and a deterministic variant of the shift-trees.

Classical and quantum dynamic programming for Subset-Sum and variants

- Mathematics, Computer ScienceArXiv
- 2021

A novel dynamic programming data structure is introduced with applications to Subset-Sum and a number of variants, including Equal-Sums, where one seeks two disjoint subsets with the same sum, and an O(2) quantum algorithm for Shifted-Sum, an improvement on the best known O( 2) classical running time.

Fast n-fold Boolean Convolution via Additive Combinatorics

- Computer Science, MathematicsICALP
- 2021

A deterministic or randomized o(nk) algorithm running in almost linear time with respect to the input plus output size k is presented, and a new deterministic almost linear output-sensitive algorithm for non-negative sparse convolution is presented.

Knapsack and Subset Sum with Small Items

- Computer ScienceICALP
- 2021

These algorithms work for the more general problem variants with multiplicities, where each input item comes with a (binary encoded) multiplicity, which succinctly describes how many times the item appears in the instance.

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