Improved Bounds for Finger Search on a RAM

• Published in: Algorithmica Vol. 66; no. 2; pp. 249 - 286
• Main Authors: Kaporis, Alexis, Makris, Christos, Sioutas, Spyros, Tsakalidis, Athanasios, Tsichlas, Kostas, Zaroliagis, Christos
• Format: Journal Article
• Language: English
• Published: New York Springer-Verlag 01.06.2013; Springer
• Subjects: Algorithm Analysis and Problem Complexity; Algorithmics. Computability. Computer arithmetics; Algorithms; Applied sciences; Computer Science; Computer science; control theory; systems; Computer Systems Organization and Communication Networks; Data Structures and Information Theory; Exact sciences and technology; Game theory; Information retrieval. Graph; Mathematics of Computing; Operational research and scientific management; Operational research. Management science; Theoretical computing; Theory of Computation; Balls and bins problem; Dictionary problem; Data structures; Interpolation search; Expected analysis; Dictionaries; Probabilistic approach; Insertion; Search time; Updating; Pointer; Combinatorial optimization; Modeling; Game theory; Random Access Machine; Interpolation; Dependence; Search tree; Log file; Data structure; Time complexity
• ISSN: 0178-4617; 1432-0541
• DOI: 10.1007/s00453-012-9636-4

We present a new finger search tree with O (loglog d ) expected search time in the Random Access Machine (RAM) model of computation for a large class of input distributions. The parameter d represents the number of elements (distance) between the search element and an element pointed to by a finger, in a finger search tree that stores n elements. Our data structure improves upon a previous result by Andersson and Mattsson that exhibits expected O (loglog n ) search time by incorporating the distance d into the search time complexity, and thus removing the dependence on n . We are also able to show that the search time is O (loglog d + ϕ ( n )) with high probability, where ϕ ( n ) is any slowly growing function of n . For the need of the analysis we model the updates by a “balls and bins” combinatorial game that is interesting in its own right as it involves insertions and deletions of balls according to an unknown distribution.