NDLI: A Binary Search with a Parallel Recovery of the Bits

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Arazi, Benjamin
Copyright Year	1986
Abstract	In this paper we consider the problem of assigning a numerical value of each of N elements which are arranged in a linear array, for the purpose of being able to recover the location of any specified element (with respect to the first element), with this aim being achieved using a small number of possible different assigned values. An obvious solution is using a binary search approach, characterized by the features: (a) At least $[\log _2 N] + 2$ different values are needed for implementing the process. (b) The bits forming the binary representation of the specified location are recovered sequentially (starting with the least significant bit).A new approach in assigning values to elements, for the purpose of recovering efficiently their location, is presented in this paper, for the case where N is of the form $2^n - 1$. Its main features are (a) less than $[\log _2 N] + 2$ different values are sufficient for achieving this task (even 2 are enough!). (b) The bits forming the binary representation of the specified location are recovered in parallel. This is achieved by very simple means, where the value of each bit in the binary representation is recovered by considering the numerical values assigned to 4 elements having fixed location with respect to the element whose location is to be found.
Starting Page	851
Ending Page	855
Page Count	5
File Format	PDF
ISSN	00975397
DOI	10.1137/0215060
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	3
Volume Number	15
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-31
Access Restriction	Subscribed
Subject Keyword	binary search finite fields Ordered fields modular arthmetic Galois theory location recovery in ordered sets
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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