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Rearrangeability of bit permutation networks. (English) Zbl 1086.68010
Summary: We introduce the concept of routing grid as a tool for analyzing realizability of permutations on Bit Permutation Networks (BPNs). We extend a result by Linial and Tarsi which characterizes permutations realizable on shuffle-exchange networks to any BPNs. A necessary condition for a BPN to be rearrangeable is given, and the rearrangeability of two families of BPNs are explored. Finally, we present a method which may help to tackle one kind of balanced matrix problems whose solution implies an answer to Benes conjecture. Hopefully, our treatment brings some new insight into the problem of permutation routing.
68M10 Network design and communication in computer systems
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