Abstract
A static dictionary is a data structure for storing a subset S of a finite universe U so that membership queries can be answered efficiently. We explore space efficient structures to also find the rank of an element if found. We first give a representation of a static dictionary that takes n lg m + O(lg lg m) bits of space and supports membership and rank (of an element present in S) queries in constant time, where n = |S| and m = |U|. Using our structure we also give a representation of a m-ary cardinal tree with n nodes using n⌈lgm⌉ + 2n + o(n) bits of space that supports the tree navigational operations in O(1) time, when m is o(2lg n/ lg lg n). For arbitrary m, we give a structure that takes the same space and supports all the navigational operations, except finding the child labeled i (for any i), in O(1) time. Finding the child labeled i in this structure takes O(lg lg lg m) time.
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© 1999 Springer-Verlag Berlin Heidelberg
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Raman, V., Rao, S.S. (1999). Static Dictionaries Supporting Rank. In: Algorithms and Computation. ISAAC 1999. Lecture Notes in Computer Science, vol 1741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46632-0_3
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DOI: https://doi.org/10.1007/3-540-46632-0_3
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