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Computing on a free tree via complexity-preserving mappings

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Abstract

The relationship between linear lists and free trees is studied. We examine a number of well-known data structures for computing functions on linear lists and show that they can be canonically transformed into data structures for computing the same functions defined over free trees. This is used to establish new upper bounds on the complexity of several query-answering problems.

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References

  1. A. V. Aho, J. E. Hopcroft, and J. D. Ullman,The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, MA, 1974.

    MATH  Google Scholar 

  2. J. L. Bentley, Multidimensional divide and conquer,Comm. ACM,23 (1980), 214–229.

    Article  MATH  MathSciNet  Google Scholar 

  3. B. Chazelle, A functional approach to data structures and its use in multidimensional searching,SIAM J. Comput. (in press). Preliminary version inProceedings of the 26th Annual IEEE Symposium on Foundations of Computer Science, 1985, pp. 165–174.

  4. B. Chazelle and L. J. Guibas, Fractional cascading: I. A data structuring technique,Algorithmica,1 (1986), 133–162.

    Article  MATH  MathSciNet  Google Scholar 

  5. H. Edelsbrunner, A new approach to rectangle intersections, Part II,Internat. J. Comput. Math.,13 (1983) 221–229.

    Article  MATH  MathSciNet  Google Scholar 

  6. H. N. Gabow, J. L. Bentley, and R. E. Tarjan, Scaling and related techniques for geometry problems,Proceedings of the 16th Annual ACM Symposium on Theory of Computing, 1984, pp. 135–143.

  7. D. Harel and R. E. Tarjan, Fast algorithms for finding nearest common ancestors,SIAM J. Comput.,13 (1984), 338–355.

    Article  MATH  MathSciNet  Google Scholar 

  8. D. E. Knuth,The Art of Computer Programming, Vol. I, 2nd edn., Addison-Wesley, Reading, MA, 1973

    Google Scholar 

  9. J. Komlós, Linear verification for spanning trees,Proceedings of the 25th Annual IEEE Symposium on Foundations of Computer Science, 1984, pp. 201–206.

  10. E. M. McCreight, Efficient algorithms for enumerating intersecting intervals and rectangles, Technical Report CSL-80-9, Xerox Pare, 1980.

  11. E. M. McCreight, Priority search trees,SIAM J. Comput.,14 (1985), 256–276.

    Article  MathSciNet  Google Scholar 

  12. D. D. Sleator and R. E. Tarjan, A data structure for dynamic trees,J. Comput. System Sci.,26 (1983), 362–391.

    Article  MATH  MathSciNet  Google Scholar 

  13. D. D. Sleator and R. E. Tarjan, Self-adjusting binary search trees,J. Assoc. Comput. Mach.,32 (1985), 652–686.

    MATH  MathSciNet  Google Scholar 

  14. R. E. Tarjan, Efficiency of a good but not linear set union algorithm,J. Assoc. Comput. Mach.,22 (1975), 215–225.

    MATH  MathSciNet  Google Scholar 

  15. R. E. Tarjan, Applications of path compression on balanced trees,J. Assoc. Comput. Mach.,26 (1979), 690–715.

    MATH  MathSciNet  Google Scholar 

  16. J. Vuillemin, A unifying look at data structuŕes,Comm. ACM,23 (1980), 229–239.

    Article  MATH  MathSciNet  Google Scholar 

  17. D. E. Willard, New data structures for orthogonal range queries,SIAM J. Comput.,14 (1985), 232–253.

    Article  MATH  MathSciNet  Google Scholar 

  18. A. C. Yao, Space-time tradeoff for answering range queries,Proceedings of the 14th Annual ACM Symposium on Theory of Computing, 1982, pp. 128–136.

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Authors and Affiliations

  1. Department of Computer Science, Princeton University, 08544, Princeton, NJ, USA

    Bernard Chazelle

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  1. Bernard Chazelle
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Additional information

Communicated by D. T. Lee.

This work was started when the author was at Brown University, Providence, RI. It was partly supported by NSF Grant MCS 83-03925. A preliminary version of this work has appeared in theProceedings of the 25th Annual IEEE Symposium on Foundations of Computer Science, West Palm Beach, FL, October 1984, pp. 358–368.

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Chazelle, B. Computing on a free tree via complexity-preserving mappings. Algorithmica 2, 337–361 (1987). https://doi.org/10.1007/BF01840366

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  • DOI: https://doi.org/10.1007/BF01840366

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