Abstract
The concept of compressions of trees encompasses many foundamental problems of computer science. We define a greedy strategy consisting in performing compressions from end-vertices of maximum distance to the root.
We use a lexicorgaphic coding to obtain a lower bound for maximum total length of greedy compression systems in form n. α(n), where α(n) is the functional inverse to the Ackermann function. This bound is optimal for balanced trees.
We also discuss other strategies with better bounds.
The author is supported by Sonderforschungsbetreich 303 (DFG), of the Institut für Diskrete Mathematik, Bonn, West Germany, and by the Alexander von Humboldt Stiftung.
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References
Aho, A.V., Hopcroft, J.E., Ullman, J.D. (1974): The design and analysis of computer algoritms. Addison-Wesley, Reading
Galler, B.A., Fischer, M.J.(1964): An improved equivalence algorithm. Commun. ACM 7, 301–303
Hart, S., Sharir, M. (1986): Non-linearity of Davenport-Schinzel sequences and of generalized path compression schemes. Combinatorica 6, 151–177 (see also Proc. 24th IEEE FOCS (1985), pp. 313–319)
Hopcroft, J.E., Ullman, J.D. (1973): Set merging algorithms. SIAM J. Comput. 2, 294–303
Loebl, M., Matoušek, J. (1987): Hercules versus Hidden Hydra Helper. KAM-series (submitted)
Loebl, M., Nešetřil, J. (1988): Linearity and unprovability of the Set Union Problem Strategies (an extended abstract). Proceedings STOC Conference
Loebl, M., Nešetřil, J. (1989): Unprovability of Set Union Problem Strategies. Report No. 88528-OR, Institut für Operations Research, Bonn
Loebl, M., Nešetřil, J. (1989(: Linearity and unprovability of set union problem strategies: I. Linearity of on-line postorder. Technical Report 89–04, University of Chicago (Submitted for publication)
Tarjan, R.E. (1975): Efficiently of a good but not linear set union algorithm. J. Assoc. Comput. Mach. 22, 215–225
Loebl, M. (1990): Partial Postorder, manuscript
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Loebl, M. (1990). Greedy compression systems. In: Dassow, J., Kelemen, J. (eds) Aspects and Prospects of Theoretical Computer Science. IMYCS 1990. Lecture Notes in Computer Science, vol 464. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53414-8_39
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DOI: https://doi.org/10.1007/3-540-53414-8_39
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