Abstract
A cost function for trees is introduced; roughly speaking the cost of a tree is the time needed to traverse all of its branches. A tree of least cost for a given number of leaves is called optimal. Bounds for the cost of an optimal tree are proved, and these bounds are used to restrict the possible outdegrees in optimal trees. Finally, a method for proving regularity in optimal trees is presented.
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References
Peter Eades and John Staples, “On Optimal Trees”, Technical Report No. 19, Dept. of Computer Science, University of Queensland (1980). (To appear).
F. Göbel and C. Hoede, “On an optimality property of ternary trees”, Inf. and Control 42, 10–26 (1979).
Leslie M. Goldschlager and Peter Eades, “Cheapsort”, (to appear).
D. Knuth, The Art of Computer Programming, Vol. 3, “Sorting and Searching”, Addison-Wesley, Mass, 1973.
M. Schumberger and J. Vuillemin, Acta Informatica 3 (1973), 25–36.
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© 1981 Springer-Verlag
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Eades, P. (1981). Regularity and optimality for trees. In: McAvaney, K.L. (eds) Combinatorial Mathematics VIII. Lecture Notes in Mathematics, vol 884. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091816
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DOI: https://doi.org/10.1007/BFb0091816
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