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Locally Checkable Labelings with Small Messages

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arxiv 2105.05574 v2 pith:PRIOLL2R submitted 2021-05-12 cs.DS cs.DC

Alkida Balliu , Keren Censor-Hillel , Yannic Maus , Dennis Olivetti , Jukka Suomela This is my paper · ORCID
classification cs.DScs.DC
keywords complexitymodelcheckablecomplexitiescongestgenerallabelingslandscape
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abstract

A rich line of work has been addressing the computational complexity of locally checkable labelings (LCLs), illustrating the landscape of possible complexities. In this paper, we study the landscape of LCL complexities under bandwidth restrictions. Our main results are twofold. First, we show that on trees, the CONGEST complexity of an LCL problem is asymptotically equal to its complexity in the LOCAL model. An analog statement for general (non-LCL) problems is known to be false. Second, we show that for general graphs this equivalence does not hold, by providing an LCL problem for which we show that it can be solved in $O(\log n)$ rounds in the LOCAL model, but requires $\tilde{\Omega}(n^{1/2})$ rounds in the CONGEST model.

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  1. New Complexity Classes in Locally Checkable Labeling for Local Computation Algorithms

    cs.DC 2026-07 accept novelty 7.0 of 10

    Stacking of Rosenbaum–Suomela base LCLs yields LCLs of randomized VOLUME/LCA probe complexity Θ(log^k n) and ˜Θ(n^{p/q}) on bounded-degree graphs and trees.

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