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Articles 121 - 123 of 123
Full-Text Articles in Discrete Mathematics and Combinatorics
A New Lower Bound For The Number Of Switches In Rearrangeable Networks, Nicholas Pippenger
A New Lower Bound For The Number Of Switches In Rearrangeable Networks, Nicholas Pippenger
All HMC Faculty Publications and Research
For the commonest model of rearrangeable networks with $n$ inputs and $n$ outputs, it is shown that such a network must contain at least $6n \log _6 n + O( n )$ switches. Similar lower bounds for other models are also presented.
Optimal 2,3-Trees, Nicholas J. Pippenger, Raymond E. Miller, Arnold L. Rosenberg, Lawrence Snyder
Optimal 2,3-Trees, Nicholas J. Pippenger, Raymond E. Miller, Arnold L. Rosenberg, Lawrence Snyder
All HMC Faculty Publications and Research
The 2,3-trees that are optimal in the sense of having minimal expected number of nodes visited per access are characterized in terms of their “profiles”. The characterization leads directly to a linear-time algorithm for constructing a K-key optimal 2,3-tree for a sorted list of K keys. A number of results are derived that demonstrate how different in structure these optimal 2,3-trees are from their “average” cousins.
The Eigenvalue Set Of A Class Of Equimodular Matrices, Gerald L. Bradley
The Eigenvalue Set Of A Class Of Equimodular Matrices, Gerald L. Bradley
CMC Faculty Publications and Research
The paper is divided into four sections, the first of which is basically introductory and contains definitions, notational conventions, and well-known results. The second section contains a fundamental theorem on multilinear polynomials which forms the crux of all our mail results, and the final two sections are devoted to discussions of the combinatorial and boundary properties of Y(A), respectively.