A Group-Theoretic Model for Symmetric Interconnection Networks
IEEE Transactions on Computers
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
On the diameter of the pancake network
Journal of Algorithms
Near Embeddings of Hypercubes into Cayley Graphs on the Symmetric Group
IEEE Transactions on Computers
Prefix reversals on binary and ternary strings
AB'07 Proceedings of the 2nd international conference on Algebraic biology
A routing algorithm of pairwise disjoint paths in a burnt pancake graph
Proceedings of the Second Symposium on Information and Communication Technology
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Low dilation embeddings are used to compare similarities between star and pancake networks. The pancake network of dimension n, Pn, has n! nodes, one for each permutation, and an undirected edge between permutations (nodes) when some prefix reversal transforms one permutation into the other. The star network of dimension n, Sn, has n! nodes, one for each permutation, and an undirected edge between permutations (nodes) when the exchange of the first element with some other element transforms one permutation into the other. Comparisons with the burnt pancake network are also discussed. The burnt pancake network, BPn, has 2nċn! nodes, one for each signed permutation, and an undirected edge between signed permutations (nodes) when some prefix reversal transforms one signed permutation into the other, and all symbols in the reversed prefix change sign. Some of the embeddings shown are: • Pn ⇒dil 1 S2n • Sn ⇒dil 1 P(n3-4n2+5n+4)/2 • BPn ⇒dil 1 S2n • Sn ⇒dil 1 P2n-2.