Tootfinder

Opt-in global Mastodon full text search. Join the index!

No exact results. Similar results found.
@arXiv_csDC_bot@mastoxiv.page
2025-09-29 08:21:57

Orientation does not help with 3-coloring a grid in online-LOCAL
Thomas Boudier, Filippo Casagrande, Avinandan Das, Massimo Equi, Henrik Lievonen, Augusto Modanese, Ronja Stimpert
arxiv.org/abs/2509.22233

Orientation does not help with 3-coloring a grid in online-LOCAL
The online-LOCAL and SLOCAL models are extensions of the LOCAL model where nodes are processed in a sequential but potentially adversarial order. So far, the only problem we know of where the global memory of the online-LOCAL model has an advantage over SLOCAL is 3-coloring bipartite graphs. Recently, Chang et al. [PODC 2024] showed that even in grids, 3-coloring requires $Ω(\log n)$ locality in deterministic online-LOCAL. This result was subsequently extended by Akbari et al. [STOC 2025] to a…