## Abstract

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(logn),O(logn)) network decompositions can be computed in O(log^{2}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 language | English |
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Pages (from-to) | 150-157 |

Number of pages | 8 |

Journal | Theoretical Computer Science |

Volume | 922 |

DOIs | |

State | Published - 24 Jun 2022 |

## Keywords

- Distributed model
- Network decompositions

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science