Abstract
A new form of optimality for comparison-based static dictionaries is introduced. This type of optimality, key-independent optimality, is motivated by applications that assign key values randomly. It is shown that any data structure that is key-independently optimal is expected to execute any access sequence where the key values are assigned arbitrarily to unordered data as fast as any offline binary search tree algorithm, within a multiplicative constant. Asymptotically tight upper and lower bounds are presented for key-independent optimality. Splay trees are shown to be key-independently optimal.
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Iacono, J. Key-Independent Optimality. Algorithmica 42, 3–10 (2005). https://doi.org/10.1007/s00453-004-1136-8
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DOI: https://doi.org/10.1007/s00453-004-1136-8