Randomized routing on fat trees. Interim research report
Fat trees are a class of routing networks for hardware-efficient parallel computation. This paper presents a randomized algorithm for routing messages on a fat tree. The quality of the algorithm is measured in terms of the load factor of a set of messages to be routed, which is a lower bound on the time required to deliver the messages. This document shows that if a set of messages has load factor lambda on a fat tree with n processors, the number of delivery cycles (routing attempts) that the algorithm requires is O(lambda + lg n lg lg n) with probability 1-O(1/n). The best previous bound was O(lambda lg n) for the off-line problem where switch settings can be determined in advance. In a VLSI-like model where hardware cost is equated with physical volume, the routing algorithm demonstrates that fat trees are universal routing networks in the sense that any routing network can be efficiently simulated by a fat tree of comparable hardware cost.
- Research Organization:
- Massachusetts Inst. of Tech., Cambridge (USA). Lab. for Computer Science
- OSTI ID:
- 6978668
- Report Number(s):
- AD-A-171546/5/XAB; MIT/LCS/TM-307
- Country of Publication:
- United States
- Language:
- English
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