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Fully Dynamic All-Pairs Min Cuts on Planar Graphs via Planar Pattern Emulators — arXiv:2610.38730

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.38730
License (as archived): CC0-1.0
Archived: 2026-11-01T02:46:27.649Z
SHA-256 of the archived text: dde10a0f23ac51a807929f5461dab176c0c7065c44e6ae10b63bd22f6a454471
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How to cite

Fully Dynamic All-Pairs Min Cuts on Planar Graphs via Planar Pattern Emulators — arXiv:2610.38730 — arXiv (en), https://arxiv.org/abs/2610.38730 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ae710ae10dc2 (Metraipolis archive dc_ae710ae10dc2, sha256 dde10a0f23ac51a807929f5461dab176c0c7065c44e6ae10b63bd22f6a454471)

BibTeX

@misc{dcae710ae10dc2,
  title = {Fully Dynamic All-Pairs Min Cuts on Planar Graphs via Planar Pattern Emulators — arXiv:2610.38730},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.38730},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ae710ae10dc2; sha256 dde10a0f23ac51a807929f5461dab176c0c7065c44e6ae10b63bd22f6a454471},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.38730. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study the fully-dynamic all-pairs minimum cut problem on planar graphs. Given an $n$-vertex undirected planar graph $G=(V,E)$ undergoing edge insertions and deletions, the goal is to efficiently process these updates while supporting $s$-$t$ minimum cut queries for any pair of vertices $s$ and $t$. We give a $(1+\varepsilon)$-approximate dynamic algorithm that supports edge updates and minimum cut queries in $n^{o(1)}$ time, for any $1/\text{poly}(\log n) < \varepsilon < 1$. For general graphs, previous results either are limited to partially dynamic settings or achieve only logarithmic-factor approximations. The main conceptual and technical contribution is to show that a suitable adaptation of the planar emulator of Chang, Krauthgamer, and Tan~[STOC'22] satisfies the stronger pattern emulator introduced by Chen and Tan~[ICALP'25]. This leads almost immediately to a nearly linear-time construction of pattern emulators, which, when combined with the recent fully dynamic $(1+\varepsilon)$-approximate all-pairs shortest paths algorithm of Filtser, Goranci, Patel, and Probst Gutenberg~[FOCS'24], yields our result.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv cs.DS, nuovi lavori del giorno).
Categorie arXiv: Data Structures and Algorithms (cs.DS).
Pagina del lavoro: https://arxiv.org/abs/2610.38730 — 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 2026-11-01T02:17:58.592Z dalla pagina https://arxiv.org/list/cs.DS/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).