Finger Search Trees:Finger Searching

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Finger Searching

One of the most studied problems in computer science is the problem of maintaining a sorted sequence of elements to facilitate efficient searches. The prominent solution to the problem is to organize the sorted sequence as a balanced search tree, enabling insertions, deletions and searches in logarithmic time. Many different search trees have been developed and studied intensively in the literature. A discussion of balanced binary search trees can be found in Chapter 10.

This chapter is devoted to finger search trees, which are search trees supporting fingers, i.e., pointers to elements in the search trees and supporting efficient updates and searches in the vicinity of the fingers.

If the sorted sequence is a static set of n elements then a simple and space efficient representation is a sorted array. Searches can be performed by binary search using 1+llog nJ comparisons (we throughout this chapter let log x to denote log2 max{2, x}). A finger search starting at a particular element of the array can be performed by an exponential search by inspecting elements at distance 2i − 1 from the finger for increasing i followed by a binary search in a range of 2Llog dJ − 1 elements, where d is the rank difference in the sequence between the finger and the search element. In Figure 11.1 is shown an exponential search for the element 42 starting at 5. In the example d = 20. An exponential search requires

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