3 research outputs found
Local computation algorithms for hypergraph coloring – following Beck’s approach
We investigate local computation algorithms (LCA) for two-coloring of k-uniform hypergraphs. We
focus on hypergraph instances that satisfy strengthened assumption of the Lovász Local Lemma
of the form , where ∆ is the bound on the maximum edge degree. The main
question which arises here is for how large α there exists an LCA that is able to properly color such
hypergraphs in polylogarithmic time per query. We describe briefly how upgrading the classical
sequential procedure of Beck from 1991 with Moser and Tardos’ Resample yields polylogarithmic
LCA that works for α up to 1/4. Then, we present an improved procedure that solves wider range
of instances by allowing α up to 1/3
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum