TY - JOUR

T1 - Distributed strong diameter network decomposition

AU - Elkin, Michael

AU - Neiman, Ofer

N1 - Funding Information:
This research was supported by the ISF grant 724/15.Supported in part by ISF grant No. (1817/18) and by BSF grant No. 2015813.
Publisher Copyright:
© 2022 Elsevier B.V.

PY - 2022/6/24

Y1 - 2022/6/24

N2 - 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(log2n) 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.

AB - 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(log2n) 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.

KW - Distributed model

KW - Network decompositions

UR - http://www.scopus.com/inward/record.url?scp=85129979529&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2022.04.019

DO - 10.1016/j.tcs.2022.04.019

M3 - Article

AN - SCOPUS:85129979529

SN - 0304-3975

VL - 922

SP - 150

EP - 157

JO - Theoretical Computer Science

JF - Theoretical Computer Science

ER -