Matches in SemOpenAlex for { <https://semopenalex.org/work/W4316652356> ?p ?o ?g. }
Showing items 1 to 83 of
83
with 100 items per page.
- W4316652356 endingPage "2631" @default.
- W4316652356 startingPage "2589" @default.
- W4316652356 abstract "We show fast deterministic algorithms for fundamental problems on forests in the challenging low-space regime of the well-known Massive Parallel Computation (MPC) model. A recent breakthrough result by Coy and Czumaj [STOC'22] shows that, in this setting, it is possible to deterministically identify connected components on graphs in O (log D + log log n) rounds, where D is the diameter of the graph and n the number of nodes. The authors left open a major question: is it possible to get rid of the additive log log n factor and deterministically identify connected components in a runtime that is completely independent of n?We answer the above question in the affirmative in the case of forests. We give an algorithm that identifies connected components in O(log D) deterministic rounds. The total memory required is O(n + m) words, where m is the number of edges in the input graph, which is optimal as it is only enough to store the input graph. We complement our upper bound results by showing that Ω(log D) time is necessary even for component-unstable algorithms, conditioned on the widely believed 1 vs. 2 cycles conjecture. Our techniques also yield a deterministic forest-rooting algorithm with the same runtime and memory bounds.Furthermore, we consider Locally Checkable Labeling problems (LCLs), whose solution can be verified by checking the O(1)-radius neighborhood of each node. We show that any LCL problem on forests can be solved in O (log D) rounds with a canonical deterministic algorithm, improving over the O (log n) runtime of Brandt, Latypov and Uitto [DISC'21]. We also show that there is no algorithm that solves all LCL problems on trees asymptotically faster.* The full version of the paper can be accessed at https://arxiv.org/abs/2211.03530" @default.
- W4316652356 created "2023-01-17" @default.
- W4316652356 creator A5004571359 @default.
- W4316652356 creator A5035798037 @default.
- W4316652356 creator A5042405670 @default.
- W4316652356 creator A5064067007 @default.
- W4316652356 creator A5083037622 @default.
- W4316652356 date "2023-01-01" @default.
- W4316652356 modified "2023-09-26" @default.
- W4316652356 title "Optimal Deterministic Massively Parallel Connectivity on Forests" @default.
- W4316652356 doi "https://doi.org/10.1137/1.9781611977554.ch99" @default.
- W4316652356 hasPublicationYear "2023" @default.
- W4316652356 type Work @default.
- W4316652356 citedByCount "1" @default.
- W4316652356 countsByYear W43166523562023 @default.
- W4316652356 crossrefType "book-chapter" @default.
- W4316652356 hasAuthorship W4316652356A5004571359 @default.
- W4316652356 hasAuthorship W4316652356A5035798037 @default.
- W4316652356 hasAuthorship W4316652356A5042405670 @default.
- W4316652356 hasAuthorship W4316652356A5064067007 @default.
- W4316652356 hasAuthorship W4316652356A5083037622 @default.
- W4316652356 hasBestOaLocation W43166523562 @default.
- W4316652356 hasConcept C104317684 @default.
- W4316652356 hasConcept C112313634 @default.
- W4316652356 hasConcept C11413529 @default.
- W4316652356 hasConcept C114614502 @default.
- W4316652356 hasConcept C118615104 @default.
- W4316652356 hasConcept C127716648 @default.
- W4316652356 hasConcept C132525143 @default.
- W4316652356 hasConcept C134306372 @default.
- W4316652356 hasConcept C13533509 @default.
- W4316652356 hasConcept C185592680 @default.
- W4316652356 hasConcept C188082640 @default.
- W4316652356 hasConcept C193435613 @default.
- W4316652356 hasConcept C195292467 @default.
- W4316652356 hasConcept C2780990831 @default.
- W4316652356 hasConcept C311688 @default.
- W4316652356 hasConcept C33923547 @default.
- W4316652356 hasConcept C41008148 @default.
- W4316652356 hasConcept C45374587 @default.
- W4316652356 hasConcept C55493867 @default.
- W4316652356 hasConcept C63553672 @default.
- W4316652356 hasConcept C77553402 @default.
- W4316652356 hasConceptScore W4316652356C104317684 @default.
- W4316652356 hasConceptScore W4316652356C112313634 @default.
- W4316652356 hasConceptScore W4316652356C11413529 @default.
- W4316652356 hasConceptScore W4316652356C114614502 @default.
- W4316652356 hasConceptScore W4316652356C118615104 @default.
- W4316652356 hasConceptScore W4316652356C127716648 @default.
- W4316652356 hasConceptScore W4316652356C132525143 @default.
- W4316652356 hasConceptScore W4316652356C134306372 @default.
- W4316652356 hasConceptScore W4316652356C13533509 @default.
- W4316652356 hasConceptScore W4316652356C185592680 @default.
- W4316652356 hasConceptScore W4316652356C188082640 @default.
- W4316652356 hasConceptScore W4316652356C193435613 @default.
- W4316652356 hasConceptScore W4316652356C195292467 @default.
- W4316652356 hasConceptScore W4316652356C2780990831 @default.
- W4316652356 hasConceptScore W4316652356C311688 @default.
- W4316652356 hasConceptScore W4316652356C33923547 @default.
- W4316652356 hasConceptScore W4316652356C41008148 @default.
- W4316652356 hasConceptScore W4316652356C45374587 @default.
- W4316652356 hasConceptScore W4316652356C55493867 @default.
- W4316652356 hasConceptScore W4316652356C63553672 @default.
- W4316652356 hasConceptScore W4316652356C77553402 @default.
- W4316652356 hasLocation W43166523561 @default.
- W4316652356 hasLocation W43166523562 @default.
- W4316652356 hasOpenAccess W4316652356 @default.
- W4316652356 hasPrimaryLocation W43166523561 @default.
- W4316652356 hasRelatedWork W2005304136 @default.
- W4316652356 hasRelatedWork W2007715402 @default.
- W4316652356 hasRelatedWork W2043076786 @default.
- W4316652356 hasRelatedWork W2055932080 @default.
- W4316652356 hasRelatedWork W2066015450 @default.
- W4316652356 hasRelatedWork W2073908095 @default.
- W4316652356 hasRelatedWork W2131917572 @default.
- W4316652356 hasRelatedWork W2963181990 @default.
- W4316652356 hasRelatedWork W3087231590 @default.
- W4316652356 hasRelatedWork W3097369619 @default.
- W4316652356 isParatext "false" @default.
- W4316652356 isRetracted "false" @default.
- W4316652356 workType "book-chapter" @default.