
Locally Checkable Problems in Rooted Trees
Consider any locally checkable labeling problem Π in rooted regular tree...
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Faster Deterministic Distributed Coloring Through Recursive List Coloring
We provide novel deterministic distributed vertex coloring algorithms. A...
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Intersecting edge distinguishing colorings of hypergraphs
An edge labeling of a graph distinguishes neighbors by sets (multisets, ...
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Deterministic Distributed EdgeColoring with Fewer Colors
We present a deterministic distributed algorithm, in the LOCAL model, th...
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Distributed graph problems through an automatatheoretic lens
We study the following algorithm synthesis question: given the descripti...
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Predicting Switching Graph Labelings with Cluster Specialists
We address the problem of predicting the labeling of a graph in an onlin...
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A Nearoptimal Algorithm for Edge Connectivitybased Hierarchical Graph Decomposition
Driven by many applications in graph analytics, the problem of computing...
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Classification of distributed binary labeling problems
We present a complete classification of the deterministic distributed time complexity for a family of graph problems: binary labeling problems in trees. These are locally checkable problems that can be encoded with an alphabet of size two in the edge labeling formalism. Examples of binary labeling problems include sinkless orientation, sinkless and sourceless orientation, 2vertex coloring, perfect matching, and the task of coloring edges of red and blue such that all nodes are incident to at least one red and at least one blue edge. More generally, we can encode e.g. any cardinality constraints on indegrees and outdegrees. We study the deterministic time complexity of solving a given binary labeling problem in trees, in the usual LOCAL model of distributed computing. We show that the complexity of any such problem is in one of the following classes: O(1), Θ(log n), Θ(n), or unsolvable. In particular, a problem that can be represented in the binary labeling formalism cannot have time complexity Θ(log^* n), and hence we know that e.g. any encoding of maximal matchings has to use at least three labels (which is tight). Furthermore, given the description of any binary labeling problem, we can easily determine in which of the four classes it is and what is an asymptotically optimal algorithm for solving it. Hence the distributed time complexity of binary labeling problems is decidable, not only in principle, but also in practice: there is a simple and efficient algorithm that takes the description of a binary labeling problem and outputs its distributed time complexity.
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