# Preprint claims faster algorithms for 3SUM and all-pairs shortest paths

_Published Tuesday, October 6, 2026 at 6:18 PM EDT · Science · Latest · Tier 2 — Notable_

An arXiv preprint claims the first polynomial improvements over textbook algorithms for 3SUM, which searches for three numbers summing to zero, and all-pairs shortest paths, which finds routes between every pair of graph vertices.

The authors give deterministic running times of O(n^1.9992) for 3SUM on polynomial-size integers and O(n^2.9995) for directed graphs with polynomially bounded integer weights. They say the results refute the corresponding computational hypotheses.

The method computes selected entries of thin matrix products by modifying a rectangular matrix multiplication algorithm. The results establish theoretical running-time improvements under the stated input restrictions.

## Sources

- [arxiv.org](https://arxiv.org/abs/2610.06783)

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Canonical: https://techandbusiness.org/newswire/jzuZRzgMKF7mowOpdlwFoc
Published: 2026-10-06T22:18:57.602Z
Story chronology: 2026-10-06T12:31:17.000Z
Retrieved: 2026-10-07T00:07:23.785Z
Publisher: Tech & Business (techandbusiness.org)