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Chromatic binary search trees

A structure for concurrent rebalancing

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Abstract

We propose a new rebalancing method for binary search trees that allows rebalancing and updating to be uncoupled. In this way we obtain fast updates and, whenever the search tree is accessed by multiple users, a high degree of concurrency. The trees we use are obtained by relaxing the balance conditions ofred-black trees. The relaxed red-black trees, calledchromatic trees, contain information of possible imbalance such that the rebalancing can be done gradually as a shadow process, or it can be performed separately when no urgent operations are present.

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References

  1. Adel’son-Vels’kii, G.M., Landis, E.M.: An algorithm for the organization of information. Soviet Math. Dokl.3, 1259–1262 (1962)

    Google Scholar 

  2. Bayer, R.A.: Symmetric binary B-trees: Data structure and maintenance algorithms. Acta Inform.1, 290–306 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  3. Dijkstra, E.W., Lamport, L., Martin, A.J., Scholten, C.S., Steffens, E.F.M.: On-the-fly garbage collection: An exercise in cooperation. Comm. ACM21, 699–975 (1978)

    Article  Google Scholar 

  4. Ellis, C.S.: Concurrent search in AVL-trees. IEEE Trans. ComputersC-29, 811–817 (1980)

    Article  Google Scholar 

  5. Ellis, C.S.: Concurrent search and insertions in 2–3 trees. Acta Inform.14, 63–86 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  6. Guibas, L.J., Sedgewick, R.: A dichromatic framework for balanced trees. In: Proceedings of the 19th IEEE Symp. Foundations of Computer Science, 1978, 8–21.

  7. Kessels, J.L.W.: On-the-fly optimization of data structures. Comm. ACM26, 895–901 (1983)

    Article  MATH  Google Scholar 

  8. Kung, H.T., Lehman, P.L.: A concurrent database manipulation problem: Binary search trees. ACM Trans. Database Syst.5, 339–353 (1980)

    Article  Google Scholar 

  9. Manber, U., Ladner, R.E.: Concurrency control in a dynamic search structure. ACM Trans. Database Syst.9, 439–455 (1984)

    Article  MathSciNet  Google Scholar 

  10. McCreight, E.M.: Priority search trees. SIAM J. Comput.14, 257–276 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  11. Nurmi, O., Soisalon-Soininen, E., Wood, D.: Concurrency control in database structures with relaxed balance. In: Proceedings of the 6th ACM Conf. Principles of Database Systems, 1987, 1702-176.

  12. Sarnak, N., Tarjan, R.E.: Planar point location using persistent search trees. Comm. ACM29, 669–679 (1986)

    Article  MathSciNet  Google Scholar 

  13. Stout, Q.F., Warren, B.L.: Tree rebalancing in optimal time and space. Comm. ACM29, 902–908 (1986)

    Article  Google Scholar 

  14. Tarjan, R.E.: Updating a balanced search tree in O(1) rotations. Inf. Proc. Lett.16, 253–257 (1983).

    Article  MATH  MathSciNet  Google Scholar 

  15. Tarjan, R.E.: Data Structures and Network Algorithms. Society for Industrial and Applied Mathematics, Philadelphia, Pa, 1983.

    Google Scholar 

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The work is supported by the Academy of Finland. A version of this paper appeared at the 9th ACM Conference on Principles of Database Systems, Denver, Colorado, 1991.

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Nurmi, O., Soisalon-Soininen, E. Chromatic binary search trees. Acta Informatica 33, 547–557 (1996). https://doi.org/10.1007/BF03036462

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  • DOI: https://doi.org/10.1007/BF03036462

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