# Improved Distributed Lower Bounds for MIS and Bounded (Out-)Degree Dominating Sets in Trees

@article{Balliu2021ImprovedDL, title={Improved Distributed Lower Bounds for MIS and Bounded (Out-)Degree Dominating Sets in Trees}, author={Alkida Balliu and Sebastian Brandt and Fabian Kuhn and Dennis Olivetti}, journal={Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing}, year={2021} }

Recently, Balliu, Brandt, and Olivetti [FOCS '20] showed the first ω(log n) lower bound for the maximal independent set (MIS) problem in trees. In this work we prove lower bounds for a much more relaxed family of distributed symmetry breaking problems. As a by-product, we obtain improved lower bounds for the distributed MIS problem in trees. For a parameter k and an orientation of the edges of a graph G, we say that a subset S of the nodes of G is a k-outdegree dominating set if S is a…

## 7 Citations

Distributed $\Delta$-Coloring Plays Hide-and-Seek

- Computer Science, Mathematics
- 2021

Lower bounds as a function of ∆ are proved for a large class of distributed symmetry breaking problems, which can all be solved by a simple sequential greedy algorithm.

Distributed ∆-coloring plays hide-and-seek

- Computer Science, MathematicsSTOC
- 2022

Lower bounds as a function of Δ are proved for a large class of distributed symmetry breaking problems, which can all be solved by a simple sequential greedy algorithm, including the maximal independent set (MIS) in trees.

Locally Checkable Labelings with Small Messages

- Computer Science, MathematicsDISC
- 2021

The landscape of LCL complexities under bandwidth restrictions is studied, showing that on trees, the CONGEST complexity of an LCL problem is asymptotically equal to its complexity in the LOCAL model, and for general graphs this equivalence does not hold.

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.

Sleeping is Superefficient: MIS in Exponentially Better Awake Complexity

- Computer ScienceArXiv
- 2022

The results show that an MIS in an awake complexity that is exponentially better compared to the best known round complexity of O (log n ) in the traditional model and bypassing its Ω ( cid:16)q log n loglog n (cid:17) lower bound.

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 ) .

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