Deterministic massively parallel connectivity

Coy, Sam; Czumaj, Artur

doi:10.1145/3519935.3520055

Cited by 9 publications

(3 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In relation to our work, previous works have studied finding rooted spanning forests. In [BFU19, ASS + 18], O(log D • log log n) algorithms for rooting were given and the runtime was improved to O(log D + log log n) by [CC22].…”

Section: Further Related Workmentioning

confidence: 99%

“…If all of our guesses fail, it must be that D > n δ/8 . In this case, we can run the deterministic O(log n) time connected components algorithm of Coy and Czumaj [CC22] with the requirement that all nodes output the maximum ID of the component (their algorithm is component-stable for the same reasons the algorithm in this paper is). Hence, we can safely assume that D ≤ n δ/8 .…”

Section: Cc: Removing Knowledge Of the Diametermentioning

confidence: 99%

“…First, a randomized O(log D • log log m/n n) time algorithm was designed in [ASS + 18]. This was further improved to O(log D+ log log m/n n) in [BDE + 19] and derandomized with the same asymptotic runtime in [CC22]. All of the aforementioned algorithms require only O(n+m) words of global memory.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optimal Deterministic Massively Parallel Connectivity on Forests

Balliu¹,

Latypov²,

Maus³

et al. 2022

Preprint

View full text Add to dashboard Cite

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.

show abstract

Section: Further Related Workmentioning

confidence: 99%

Section: Cc: Removing Knowledge Of the Diametermentioning

confidence: 99%