(2022) Efficient Classification of Locally Checkable Problems in Regular Trees.
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Abstract
We give practical, efficient algorithms that automatically determine the asymptotic distributed round complexity of a given locally checkable graph problem in the [Θ(log n), Θ(n)] region, in two settings. We present one algorithm for unrooted regular trees and another algorithm for rooted regular trees. The algorithms take the description of a locally checkable labeling problem as input, and the running time is polynomial in the size of the problem description. The algorithms decide if the problem is solvable in O(log n) rounds. If not, it is known that the complexity has to be Θ(n^{1/k}) for some k = 1, 2, ..., and in this case the algorithms also output the right value of the exponent k. In rooted trees in the O(log n) case we can then further determine the exact complexity class by using algorithms from prior work; for unrooted trees the more fine-grained classification in the O(log n) region remains an open question.
| Item Type: | Conference or Workshop Item (A Paper) (Paper) |
|---|---|
| Divisions: | Sebastian Brandt (SB) |
| Conference: | DISC International Symposium on Distributed Computing (was WDAG) |
| Depositing User: | Sebastian Brandt |
| Date Deposited: | 09 Sep 2022 09:45 |
| Last Modified: | 09 Sep 2022 09:45 |
| Primary Research Area: | NRA1: Trustworthy Information Processing |
| URI: | https://publications.cispa.saarland/id/eprint/3762 |
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