Distributed strong diameter network decomposition

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1 Scopus citations


For a pair of positive parameters D,χ, a partition P of the vertex set V of an n-vertex graph G=(V,E) into disjoint clusters of diameter at most D each is called a (D,χ) network decomposition, if the supergraph G(P), obtained by contracting each of the clusters of P, can be properly χ-colored. The decomposition P is said to be strong (resp., weak) if each of the clusters has strong (resp., weak) diameter at most D, i.e., if for every cluster C∈P and every two vertices u,v∈C, the distance between them in the induced graph G(C) of C (resp., in G) is at most D. Network decomposition is a powerful construct, very useful in distributed computing and beyond. In this paper we show that strong (O(log⁡n),O(log⁡n)) network decompositions can be computed in O(log2⁡n) time in the CONGEST model. We also present a tradeoff between parameters of our network decomposition. Our work is inspired by and relies on the “shifted shortest path approach”, due to Blelloch et al. [11], and Miller et al. [20]. These authors developed this approach for PRAM algorithms for padded partitions. We adapt their approach to network decompositions in the distributed model of computation.

Original languageEnglish
Pages (from-to)150-157
Number of pages8
JournalTheoretical Computer Science
StatePublished - 24 Jun 2022


  • Distributed model
  • Network decompositions

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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