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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.
Network decompositions, as introduced by Awerbuch, Luby, Goldberg, and Plotkin [FOCS89], are one of the key algorithmic tools in distributed graph algorithms. We present an improved deterministic distributed algorithm for constructing network decompo
Consider any locally checkable labeling problem $Pi$ in rooted regular trees: there is a finite set of labels $Sigma$, and for each label $x in Sigma$ we specify what are permitted label combinations of the children for an internal node of label $x$
Locally checkable labeling problems (LCLs) are distributed graph problems in which a solution is globally feasible if it is locally feasible in all constant-radius neighborhoods. Vertex colorings, maximal independent sets, and maximal matchings are e
In the context of distance oracles, a labeling algorithm computes vertex labels during preprocessing. An $s,t$ query computes the corresponding distance from the labels of $s$ and $t$ only, without looking at the input graph. Hub labels is a class of
Subgraph counting is a fundamental problem in analyzing massive graphs, often studied in the context of social and complex networks. There is a rich literature on designing efficient, accurate, and scalable algorithms for this problem. In this work,