Improved Routing and Sorting on Multibutterflies.
Abstract
This paper shows that an N-node AKS network can be embedded in a (3N/2)-node degree-8 multibutterfly network with load 1, congestion 1, and dilation 2. The result has several implications, including the first deterministic algorithms for sorting and finding the median of n log n keys on an n-input multibutterfly in O(log n) time, a work-efficient algorithm for finding the median of n log2 n log log n keys on an n-input multibutterfly in O(log n log log n) time, and a three-dimensional VLSI layout for the n-input AKS network with volume O(n3/2). While these algorithms are not practical, they provide further evidence of the robustness of multibutterfly networks. We also present a separate, and more practical, deterministic algorithm for routing h relations on an n-input multibutterfly in O(h + log n) time. Previously, only algorithms for solving h one-to-one routing problems were known. Finally, we show that a 2-folded butterfly, whose individual splitters do not exhibit expansion, can emulate a bounded-degree multibutterfly with an (a,b) expansion property, for any a.b < 1/4.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1996
- Accession Number
- ADA319255
Entities
People
- Berthold Voecking
- Bruce M. Maggs
Organizations
- Carnegie Mellon University