Abstract

We investigate the problem of computing of the least significant set bit in a word. We describe a constant time algorithm for the problem assuming a cell probe model of computation. 1 Introduction and Definitions The problem of computing an index of the least significant set bit in a word arises in different issues of data organization such as bit representation of ordered sets etc. In this paper we describe a novel algorithm to compute the index. Our algorithm runs on a cell probe model of computation (c.f. [2, 4, 5]), which is a generalization of a random access machine model. We assume that the memory registers are of bounded size. The bits in the word (register) are enumerated from 0, which is the least significant bit, to m \Gamma 1, which is the most significant bit -- the word is m bits wide. Using the terminology of Fredman and Saks [2] we are dealing with CPROB(m) model. Furthermore, we assume that we can perform in one unit of time arithmetic operations of multiplication, add...

Citations

120	Should tables be sorted - Yao - 1981
119	The cell probe complexity of dynamic data structures - Fredman, Saks - 1989
12	Blasting through the information theoretic barrier with fusion trees - Fredman, Willard - 1990
11	When can we sort in o(n log n) time - Ben-Amram, Galil - 1993