The.Algorithm.Design.Manual.Springer-Verlag.1998

Dictionaries
Implementation-oriented treatments of a variety of dictionary data structures appear in [BR95], including
hashing, splay trees, red-black trees, and what looks like a thorough implementation of B-trees. Code in
C for these data structures is included in the text and is available on disk for a modest fee.
Notes: Mehlhorn and Tsakalidis [MT90b] give a thorough survey of the state of the art in modern data
structures. Knuth [Knu73a] provides a detailed analysis and exposition on fundamental dictionary data
structures but misses such modern data structures as red-black and splay trees. Gonnet and Baeza-Yates
[GBY91] provide implementations (in C and Pascal), detailed references, and experimental results for a
wide variety of dictionary data structures. We defer to these sources to avoid giving original references
for each of the data structures described above.
Good expositions on red-black trees [GS78] include [BR95, CLR90, Woo93]. Good expositions on splay
trees [ST85] include [Tar83, Woo93]. Good expositions on B-trees [BM72] include [BR95, CLR90].
Good expositions on hashing includes [Meh84, Woo93].
Several modern data structures, such as splay trees, have been studied via amortized analysis, where we
bound the total amount of time used by any sequence of operations. In an amortized analysis, we show
that if a single operation is very expensive, this is because we have already benefited from enough cheap
operations before it to pay off the higher cost. A data structure realizing an amortized complexity of
O(f(n)) is less desirable than one whose worst-case complexity is O(f(n)) (since a very bad operation
might still occur) but better than one with an average-case complexity O(f(n)), since the amortized bound
will achieve this average on any input.
Newer dictionary data structures that explicitly incorporate randomization into the construction include
randomized search trees [AS89] and skip lists [Pug90].
Related Problems: Sorting (see page ), Searching (see page ).
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