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A Simpler and Faster Min-Cost Flow Solver via Min-Ratio Cycles from Distance Oracles — arXiv:2609.23852

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.23852
License (as archived): CC0-1.0
Archived: 2026-10-09T22:40:52.306Z
SHA-256 of the archived text: 97cc074fa1264357b8a83f5be6c54f552f875bf7bdd4eca00dc385b658a22796
Stable URL of this page: https://metraipolis.com/documento/dc_3442afcada4e

How to cite

A Simpler and Faster Min-Cost Flow Solver via Min-Ratio Cycles from Distance Oracles — arXiv:2609.23852 — arXiv (en), https://arxiv.org/abs/2609.23852 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_3442afcada4e (Metraipolis archive dc_3442afcada4e, sha256 97cc074fa1264357b8a83f5be6c54f552f875bf7bdd4eca00dc385b658a22796)

BibTeX

@misc{dc3442afcada4e,
  title = {A Simpler and Faster Min-Cost Flow Solver via Min-Ratio Cycles from Distance Oracles — arXiv:2609.23852},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.23852},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_3442afcada4e; sha256 97cc074fa1264357b8a83f5be6c54f552f875bf7bdd4eca00dc385b658a22796},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.23852. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The first almost-linear time maximum and minimum cost flow algorithm of Chen-Kyng-Liu-Peng-Probst Gutenberg-Sachdeva (FOCS 2022), reduced these flow objectives to a sequence of min-ratio cycle problems. Solving this core primitive requires approximately minimizing the ratio of a linear gradient term and an undirected length term. In Chen-Kyng-Liu-Peng-Probst Gutenberg-Sachdeva (FOCS 2022) and the subsequent work of Chen-Kyng-Liu-Meierhans-Probst Gutenberg (STOC 2024), intricate data structures were given to solve the min-ratio problem. We show that such a cycle can be extracted directly from the dynamic distance oracle of Kyng-Meierhans-Probst Gutenberg (STOC 2024) using linearity. This simplifies previous algorithms that relied on multiple additional steps to extract the cycle, and can be seen as evidence that solving the min-ratio cycle problem really is all about distances. As a result, we obtain a faster primal maxflow and min-cost flow solver that also extends to incremental graphs.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-22 in cs.DS).
Categorie arXiv: Data Structures and Algorithms (cs.DS).
Pagina del lavoro: https://arxiv.org/abs/2609.23852 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-09T22:24:05.636Z dalla pagina https://arxiv.org/catchup/cs.DS/2026-09-22?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).