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Search Trees with Relaxed Balance and Near-Optimal Height

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Algorithms and Data Structures (WADS 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2125))

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Abstract

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 · log2 n 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.

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© 2001 Springer-Verlag Berlin Heidelberg

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Fagerberg, R., Jensen, R.E., Larsen, K.S. (2001). Search Trees with Relaxed Balance and Near-Optimal Height. In: Dehne, F., Sack, JR., Tamassia, R. (eds) Algorithms and Data Structures. WADS 2001. Lecture Notes in Computer Science, vol 2125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44634-6_38

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  • DOI: https://doi.org/10.1007/3-540-44634-6_38

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  • Print ISBN: 978-3-540-42423-9

  • Online ISBN: 978-3-540-44634-7

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