Advertisement

An application of maximum-minimum distance circuits on hypercubes

  • Gustavus J. Simmons
Contributed Papers
Part of the Lecture Notes in Mathematics book series (LNM, volume 686)

Abstract

The related questions of finding Hamilton circuits in the n-dimensional cube with d points on an edge which maximize the minimum "taxicab" distance between successive vertices and/or which maximize the sum of such distances over the entire circuit is investigated. A "good" bound for the first quantity and an achievable limit for the second are developed and several optimal constructions found. Both of these circuits are central to designing pseudo-color graphics displays in which minimal grey scale differences become maximal color differences.

Keywords

Hamilton Cycle Complete Bipartite Graph Gray Code Adjacent Pair Vertex Pair 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. (1).
    E. N. Gilbert, "Gray Codes and Paths on the n-Cube," Bell System Tech. Jour. (37) 3 (1958), 815–825.MathSciNetCrossRefGoogle Scholar
  2. (2).
    David L. MacAdam, "Specification of Small Chromaticity Differences," Jour. of the Optical Soc. of Amer. (33) 1 (1943), 18–26.CrossRefGoogle Scholar
  3. (3).
    Parry Moon, "A Metric Based on the Composite Color Stimulus," Jour. of the Optical Soc. of Amer. (33) 5 (1943), 270–277.CrossRefGoogle Scholar
  4. (4).
    D. H. Smith, "Hamiltonian Circuits on the n-Cube," Canadian Math. Bulletin (17) 5 (1975), 759–761.MathSciNetCrossRefzbMATHGoogle Scholar
  5. (5).
    W. D. Wright, "The Graphical Representation of Small Color Differences," Jour. of the Optical Soc. of Amer. (33) 11 (1943), 632–636.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Gustavus J. Simmons
    • 1
  1. 1.Department of Applied MathematicsSandia LaboratoriesAlbuquerqueUSA

Personalised recommendations