
Locally Checkable Labelings with Small Messages
A rich line of work has been addressing the computational complexity of ...
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Locality of notsoweak coloring
Many graph problems are locally checkable: a solution is globally feasib...
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The Complexity Landscape of Distributed Locally Checkable Problems on Trees
Recent research revealed the existence of gaps in the complexity landsca...
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Hardness of minimal symmetry breaking in distributed computing
A graph is weakly 2colored if the nodes are labeled with colors black a...
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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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Seeing Far vs. Seeing Wide: Volume Complexity of Local Graph Problems
Consider a graph problem that is locally checkable but not locally solva...
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Distributed Computing in the Asynchronous LOCAL model
The LOCAL model is among the main models for studying locality in the fr...
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Local Mending
In this work we introduce the graphtheoretic notion of mendability: for each locally checkable graph problem we can define its mending radius, which captures the idea of how far one needs to modify a partial solution in order to "patch a hole." We explore how mendability is connected to the existence of efficient algorithms, especially in distributed, parallel, and faulttolerant settings. It is easy to see that O(1)mendable problems are also solvable in O(log^* n) rounds in the LOCAL model of distributed computing. One of the surprises is that in paths and cycles, a converse also holds in the following sense: if a problem Π can be solved in O(log^* n), there is always a restriction Π' ⊆Π that is still efficiently solvable but that is also O(1)mendable. We also explore the structure of the landscape of mendability. For example, we show that in trees, the mending radius of any locally checkable problem is O(1), Θ(log n), or Θ(n), while in general graphs the structure is much more diverse.
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