A unified framework for off-line permutation routing in parallel networks

Packet Routing in Fixed-Connection Networks: A Survey

“…is the time required for off-line permutation routing on graph G (respectively, on graph H ) [10,20]. Theorem 2.6 also holds if each ith copy of G in G_H, 1 i N G is permuted, where N G is the number of nodes in graph G. A similar theorem applies when, each copy of G in G_H contains a number f of faulty nodes [20].…”

“…Theorem 2.6 also holds if each ith copy of G in G_H, 1 i N G is permuted, where N G is the number of nodes in graph G. A similar theorem applies when, each copy of G in G_H contains a number f of faulty nodes [20]. Recently Youssef proved:…”

“…Using Theorem 2.6 we obtain: Corollary 3.1. Any permutation can be off-line routed on a uniaxial mesh in 3n&3 steps using queues of size one [20].…”

Separator-based graph embedding into higher-dimensional grids with small congestion

“…The following lemma can easily be obtained from a well-known permutation routing algorithm presented in [10], and hence, we omit the proof.…”

“…A quite general embedding based on the multicommodity flow problem was presented in [9], which showed that an N -node bounded degree graph G can be embedded into an N -node bounded degree graph H with both dilation and edge-congestion of O( Any permutation routing on a host graph can be applied to graph embedding. Based on the permutation routing given in [10], we can easily derive that an N -node, degree-Δ graph can be embedded into a d-dimensional grid with a dilation of O(dN In this paper, we present a separator-based embedding into optimally-sized grids. This is a generalization of the embedding into 2-dimensional grids presented in [11].…”