The paper presents a deterministic Congested Clique algorithm that solves the (degree+1)-list coloring problem in a constant number of rounds.
The key highlights and insights are:
The (degree+1)-list coloring problem is a natural generalization of the classical (Δ+1)-coloring and (Δ+1)-list coloring problems, which are benchmark problems extensively studied in distributed and parallel computing.
While randomized algorithms for (degree+1)-list coloring have been developed for the LOCAL and CONGEST models, matching the state-of-the-art complexity for the simpler (Δ+1)-coloring problem, the deterministic complexity in the Congested Clique model was previously unknown.
The paper resolves this challenge by presenting a deterministic Congested Clique algorithm that finds a (degree+1)-list coloring in a constant number of rounds.
The algorithm uses a novel bucketing approach that partitions nodes and colors into a tree-structured hierarchy of buckets. This allows nodes to be bucketed correctly according to their own degree, despite the varying palette sizes.
The algorithm also employs derandomization techniques using the method of conditional expectations and bounded-independence hash functions to make the randomized steps deterministic.
The analysis shows that the algorithm terminates in a constant number of rounds and produces a valid (degree+1)-list coloring.
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by Sam Coy,Artu... at arxiv.org 04-25-2024
https://arxiv.org/pdf/2306.12071.pdfDeeper Inquiries