On the Multiplexing Degree Required to Embed Permutations in a Class of Networks with Direct Interconnects

Authors:
Chunming Qiao;Yousong Mei
Affiliations:
-;-
Venue:
HPCA '96 Proceedings of the 2nd IEEE Symposium on High-Performance Computer Architecture
Year:
1996

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Abstract

There are two approaches for establishing a connection in a network whose links are multiplexed with virtual channels. One is called Path Multiplexing (PM), in which the same channel has to be used on each link along a path, and the other is called Link Multiplexing (LM), in which different channels may be used. We study the problem of embedding permutations in LM and PM, and in particular, determine the threshold (minimal) multiplexing degrees needed for a network to be rearrangeably nonblocking. We found that PM and LM are equally effective in linear arrays, and LM is only slightly more effective than PM in rings, meshes, tori and hypercubes. Our results suggest that PM may be more cost-effective in implementing networks with multiplexed optical interconnects.