Multirate rearrangeable clos networks and a generalized edge coloring problem on bipartite graphs
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
A new routing algorithm for multirate rearrangeable Clos networks
Theoretical Computer Science
An approximate König's theorem for edge-coloring weighted bipartite graphs
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
On rearrangeable multirate three-stage Clos networks
Theoretical Computer Science
Edge Coloring and Decompositions of Weighted Graphs
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Constructions of given-depth and optimal multirate rearrangeably nonblocking distributors
Journal of Combinatorial Optimization
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Chung and Ross [SIAM J. Comput., 20 (1991), pp. 726--736] conjectured that the multirate three-stage Clos network C(n,2n-1,r) is rearrangeable in the general discrete bandwidth case; i.e., each connection has a weight chosen from a given finite set {p1, p2,. . .,pk} where $1 \geq p_1 p_2 \cdots p_k 0$ and pi is an integer multiple of pi, denoted by $p_k \mid p_i$, for $1 \leq i \leq k-1$. In this paper, we prove that multirate three-stage Clos network C(n,2n-1,r) is rearrangeable when each connection has a weight chosen from a given finite set {p1, p2,. . .,pk} where $1 \geq p_1 p_2 \cdots p_{h} 1/2 \geq p_{h+1} \cdots p_k 0$ and ph+2 | ph+1,ph+3 |ph+2,. . . ,pk | ph+1. We also prove that C(n,2n-1,r) is two-rate rearrangeable and $C(n, \lceil \frac{7n}{3} \rceil, r)$ is three-rate rearrangeable.