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Binary trees, fringe thickness and minimum path length. (English) Zbl 0833.68092

Summary: We solve the following problem: Characterize the minimum-path-length binary trees with respect to size and fringe thickness, where the fringe thickness of a tree is the difference between the lengths of shortest and longest root-to-frontier paths. This result demonstrates that minimum path length is, in this setting, more amenable to analysis than maximum path length.

MSC:

68R10 Graph theory (including graph drawing) in computer science
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References:

[1] . H. CAMERON, Extremal Cost Binary Trees, PhD thesis, University of Waterloo, 1991.
[2] . H. CAMERON and D. WOOD, Maximal path length of binary trees, Discrete Applied Mathematics, 1994, 55 (1), pp. 15-35. Zbl0821.68094 MR1298512 · Zbl 0821.68094
[3] . R. DE PRISCO, G. PARLATI and G. PERSIANO, On the path length of trees with known fringe, Unpublished manuscript, 1994. · Zbl 0875.68705
[4] . A. DE SANTIS and G. PERSIANO, Tight upper and lower bounds on the path length of binary trees, SIAM Journal on Computing, 1994, 23 (1), pp. 12-23. Zbl0802.68034 MR1258991 · Zbl 0802.68034
[5] . D. E. KNUTH, The Art of Computer Programming, Vol. 3: Sorting and Searching, Addison-Wesley, Reading, MA, 1973. MR445948 · Zbl 0191.17903
[6] . R. KLEIN and D. WOOD, On the path length of binary trees, Journal of the ACM, 1989, 36 (2), pp. 280-289. Zbl0674.68012 MR1072422 · Zbl 0674.68012
[7] . J. NIEVERGELT and CHAK-KUEN WONG, Upper bounds for the total path length of binary trees, Journal of the ACM, January 1973, 20 (1), pp. 1-6. Zbl0263.68022 MR495300 · Zbl 0263.68022
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