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 -