# Distributed graph problems through an automata-theoretic lens

@inproceedings{Chang2020DistributedGP, title={Distributed graph problems through an automata-theoretic lens}, author={Yi-Jun Chang and Jan Studen'y and Jukka Suomela}, booktitle={DISC}, year={2020} }

The locality of a graph problem is the smallest distance $T$ such that each node can choose its own part of the solution based on its radius-$T$ neighborhood. In many settings, a graph problem can be solved efficiently with a distributed or parallel algorithm if and only if it has a small locality.
In this work we seek to automate the study of solvability and locality: given the description of a graph problem $\Pi$, we would like to determine if $\Pi$ is solvable and what is the asymptotic…

## 13 Citations

Local Mending

- Computer ScienceSIROCCO
- 2022

This work introduces the graph-theoretic notion of mendability, which captures the idea of how far one needs to modify a partial solution in order to “patch a hole,” and explores how mendability is connected to the existence of efficient algorithms, especially in distributed, parallel, and fault-tolerance settings.

Locally Checkable Problems in Rooted Trees

- Computer Science, MathematicsPODC
- 2021

This work provides a freely available implementation of the classifier algorithm, and it is fast enough to classify many problems of interest, including vertex coloring, edge coloring, and maximal independent set.

What Can Be Certified Compactly? Compact local certification of MSO properties in tree-like graphs

- Computer Science, MathematicsPODC
- 2022

The logic used is MSO, the most classic fragment for logics on graphs, and it is proved that in bounded treedepth graphs, every MSO property has a compact certification.

Deterministic Distributed algorithms and Descriptive Combinatorics on Δ-regular trees

- Mathematics, Computer ScienceArXiv
- 2022

It is shown that a local problem admits a continuous solution if and only if it admits a local algorithm with local complexity O (log ∗ n ) , and a Baire measurable solution is admitted if andonly if it admitting a local algorithms with local simplicity O ( log n ) .

Deterministic Distributed algorithms and Descriptive Combinatorics on \Delta-regular trees

- Mathematics, Computer Science
- 2022

It is shown that a local problem admits a continuous solution if and only if it admits a local algorithm with local complexity O (log ∗ n ) , and a Baire measurable solution is admitted if andonly if it admitting a local algorithms with local simplicity O ( log n ) .

Efficient Classification of Local Problems in Regular Trees

- Computer Science, MathematicsArXiv
- 2022

We give practical, efficient algorithms that automatically determine the distributed round complexity of a given locally checkable graph problem, in two settings. We present one algorithm for…

What can be certified compactly?

- Computer Science, Mathematics
- 2022

The first meta-theorems for local certification is proved, using MSO, the most classic fragment for logics on graphs, to prove that in bounded treedepth graphs, every MSO property has a compact certification.

The Landscape of Distributed Complexities on Trees and Beyond

- Computer Science, MathematicsPODC
- 2022

The main contribution is to complete the classification of the complexity landscape of LCL problems on trees in the LOCAL model, by proving that every LCL problem with local complexity o (log* n) has actually complexityO(1), which improves upon the previous speedup result.

Local Problems on Trees from the Perspectives of Distributed Algorithms, Finitary Factors, and Descriptive Combinatorics

- MathematicsITCS
- 2022

This approach that borrows techniques from the fields (a), (b) and (c) implies a number of results about possible complexities of finitary factor solutions and helps to view all three perspectives as a part of a common theory of locality.

Online Algorithms with Lookaround

- Computer ScienceArXiv
- 2021

The OLOCAL model provides a new, more fine-grained perspective for studying the locality of graph problems, enabling us to separate the problems of 2-coloring in grids in terms of their localities, and proves an exponential separation in 2-dimensional grids.

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Locally Checkable Problems in Rooted Trees

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This work provides a freely available implementation of the classifier algorithm, and it is fast enough to classify many problems of interest, including vertex coloring, edge coloring, and maximal independent set.

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