We introduce the relaxed k-tree, a search tree with relaxed balance and a height bound, when in balance, of (1 + ε)log2n + 1, for any g > 0. The rebalancing work is amortized O(1/ε) per update. This is the first binary search tree with relaxed balance having a height bound better than c · log2n for a fixed constant c. In all previous proposals, the constant is at least 1/log2 φ τ; 1.44, where φ is the golden ratio.
As a consequence, we can also define a standard (non-relaxed) k-tree with amortized constant rebalancing per update, which is an improvement over the original definition.
Search engines based on main-memory databases with strongly fluctuating workloads are possible applications for this line of work.
Neighboring Node Search Tree Binary Search Tree Black Node External Node
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G. M. Adel’son-Vel’skii and E. M. Landis. An Algorithm for the Organisation of Information. Doklady Akadamii Nauk SSSR, 146:263–266, 1962. In Russian. English translation in Soviet Math. Doklady, 3:1259–1263, 1962.MathSciNetGoogle Scholar
Joan Boyar, Rolf Fagerberg, and Kim S. Larsen. Amortization Results for Chromatic Search Trees, with an Application to Priority Queues. Journal of Computer and System Sciences, 55(3):504–521, 1997.zbMATHCrossRefMathSciNetGoogle Scholar
H. A. Maurer, Th. Ottmann, and H.-W. Six. Implementing Dictionaries using Binary Trees of Very Small Height. Information Processing Letters, 5(1):11–14, 1976.zbMATHCrossRefMathSciNetGoogle Scholar
Otto Nurmi and Eljas Soisalon-Soininen. Uncoupling Updating and Rebalancing in Chromatic Binary Search Trees. In Proceedings of the Tenth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pages 192–198, 1991.Google Scholar
Otto Nurmi and Eljas Soisalon-Soininen. Chromatic Binary Search Trees—A Structure for Concurrent Rebalancing. Acta Informatica, 33(6):547–557, 1996.CrossRefMathSciNetGoogle Scholar
Otto Nurmi, Eljas Soisalon-Soininen, and Derick Wood. Relaxed AVL Trees, Main-Memory Databases and Concurrency. International Journal of Computer Mathematics, 62:23–44, 1996.zbMATHCrossRefMathSciNetGoogle Scholar
Neil Sarnak and Robert E. Tarjan. Planar Point Location Using Persistent Search Trees. Communications of the ACM, 29:669–679, 1986.CrossRefMathSciNetGoogle Scholar