Distributed strong diameter network decomposition

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