Set-to-Set Disjoint Path Routing in Bijective Connection Graphs

The bijective connection graph encompasses a family of cube-based topologies, and $n$ -dimensional graphs include the hypercube almost all its variants with order notation="LaTeX">$2^{n}$ degree . Hence, it is important to design implement algorithms that work in graphs. set-to-set disjoint paths problem as follows: given set source nodes notation="LaTeX">$S=\{ \boldsymbol s _{1}, _{2},\ldots, _{p}\}$ destination notation="LaTeX">$D=\{ d notation="LaTeX">$k$ -connected notation="LaTeX">$G=(V,E)$ notation="LaTeX">$p\le k$ , construct notation="LaTeX">$p$ notation="LaTeX">$P_{i}$ : notation="LaTeX">$\boldsymbol _{i}\leadsto _{j_{i}}$ ( notation="LaTeX">$1\le i\le p$ ) such notation="LaTeX">$\{j_{1},j_{2},\ldots,j_{p}\}=\{1,2,\ldots,p\}$ are node-disjoint. Finding solution this an issue parallel distributed computation well node-to-node node-to-set problem. In paper we propose algorithm constructs notation="LaTeX">$p~(\le n)$ between any pair node sets polynomial-order time We give proof correctness estimates complexity notation="LaTeX">$O(n^{3}p^{4})$ maximum path length notation="LaTeX">$n+p-1$ According computer experiment locally twisted cube example paths, average notation="LaTeX">$O(n^{2})$ notation="LaTeX">$0.6333n-0.266$