NDLI: Multirate rearrangeable clos networks and a generalized edge coloring problem on bipartite graphs

Content Provider	ACM Digital Library
Author	Ngo, Hung Q. Vu, Van H.
Abstract	Chung and Ross (SIAM J. Comput., 20, 1991) conjectured that the minimum number m(n, r) of middle-state switches for the symmetric 3-stage Clos network C(n, m(n, r), r) to be rearrangeable in the multirate enviroment is at most 2n -- 1. This problem is equivalent to a generalized version of the biparite graph edge coloring problem. The best bounds known so far on the function m(n, r) is 11n/9 ≤ m(n, r) ≤ 41n/16 + O(1), for n, r ≥ 2, derived by Du-Gao-Hwang-Kim (SIAM J. Comput., 28, 1999). In this paper, we make several contributions. Firstly, we give evidence to show that even a stronger result might hold. In particular, we give a coloring algorithm to show that m(n, r) ≤ [(r + 1)n/2], which implies m(n, 2) ≤ [3n/2] - stronger than the conjectured value of 2n -- 1. Secondly, we derive that m(2, r) = 3 by an elegant argument. Lastly, we improve both the best upper and lower bounds given above: [5n/4] ≤ m(n, r) ≤ 2n -- 1 + [(r -- 1)/2], where the upper bound is an improvement over 41n/16 when r is relatively small compared to n. We also conjecture that m(n, r) ≤ [2n (1 -- $1/2(^{r})].$
Starting Page	834
Ending Page	840
Page Count	7
File Format	PDF
ISBN	0898715385
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2003-01-12
Access Restriction	Subscribed
Content Type	Text
Resource Type	Article

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Multirate rearrangeable clos networks and a generalized edge coloring problem on bipartite graphs