The estimated cost of a search tree on binary words

Author

Fedotov, Alexey ; Ryabko, Boris

Author_Institution

Dept. of Inf. Technol., Inst. of Comput. Technol., Novosibirsk, Russia

Volume

47

Issue

1

fYear

2001

fDate

1/1/2001 12:00:00 AM

Firstpage

326

Lastpage

329

Abstract

The problem of constructing a binary search tree for a set of binary words has wide applications in computer science, biology, mineralogy, etc. Shannon considered a similar statement in his optimal coding theorem. It is NP-complete to construct a tree of minimum cost; therefore, the problem arises of finding simple algorithms for constructing nearly optimal trees. We show that there is a simple algorithm for constructing search trees sufficiently close to the optimal tree on average. By means of this algorithm we prove that for the optimal tree the average number of bits to be checked is near to its natural lower bound, i.e., the binary logarithm of the number of given words: their difference is less than 1.04

Keywords

binary codes; optimisation; tree searching; NP-complete problem; Shannon theorem; algorithms; binary logarithm; binary search tree; binary words; biology; computer science; estimated cost; lower bound; mineralogy; minimum cost tree; optimal coding theorem; optimal trees; Application software; Binary search trees; Binary trees; Biology; Codes; Computer science; Cost function; Information theory; Notice of Violation; Telecommunication computing;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.904530

Filename

904530