Average Case Analysis of Searching in Associative Processing

Panagiotis E. Nastou, Dimitrios N. Serpanos, Dimitrios G. Maritsas

Research output: Contribution to journalArticle

Abstract

We introduce an average case analysis of the search primitive operations (equality and thresholding) in associative memories. We provide a general framework for analysis, using as parameters the word space distribution and the CAM size parameters:m(number of memory words) andn(memory word length). Using this framework, we calculate the probability that the whole CAM memory responds to a search primitive operation after comparing up tokmost significant bits (1≤k≤n) in each word; furthermore, we provide a closed formula for the average value ofkand the probability that there exists at least one memory word that equals the centrally broadcast word. Additionally, we derive results for the cases of uniform and exponential distribution of word spaces. We prove that in both cases the average value ofkdepends strongly on lgm, whenn>lgm: for the case of uniform distribution, the average value is practically independent ofn, while in the exponential depends weakly on the difference between the sample space size 2nand the CAM sizem. Furthermore, in both cases, the averagekis approximatelynwhenn≤lgm. Verification of our theoretical results through massive simulations on a parallel machine is presented. One of the main results of this work, that the average value ofkcan be much smaller than n or even practically independent ofnin some cases, has an important practical effect: associative memories can be designed with fast execution times of threshold primitives and low implementation complexity, leading to high performance associative memories that can scale up to sizes larger than previous designs at a low cost.

Original languageEnglish
Pages (from-to)133-161
Number of pages29
JournalJournal of Parallel and Distributed Computing
Volume54
Issue number2
DOIs
Publication statusPublished - 1 Nov 1998
Externally publishedYes

Fingerprint

Associative processing
Average-case Analysis
Associative Memory
Data storage equipment
Uniform distribution
Computer aided manufacturing
Sample space
Scale-up
Parallel Machines
Thresholding
Exponential distribution
Broadcast
Execution Time
Equality
High Performance
Calculate
Closed
Simulation

ASJC Scopus subject areas

  • Computer Science Applications
  • Hardware and Architecture
  • Control and Systems Engineering

Cite this

Average Case Analysis of Searching in Associative Processing. / Nastou, Panagiotis E.; Serpanos, Dimitrios N.; Maritsas, Dimitrios G.

In: Journal of Parallel and Distributed Computing, Vol. 54, No. 2, 01.11.1998, p. 133-161.

Research output: Contribution to journalArticle

Nastou, Panagiotis E. ; Serpanos, Dimitrios N. ; Maritsas, Dimitrios G. / Average Case Analysis of Searching in Associative Processing. In: Journal of Parallel and Distributed Computing. 1998 ; Vol. 54, No. 2. pp. 133-161.
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