### 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 2^{n}and 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 language | English |
---|---|

Pages (from-to) | 133-161 |

Number of pages | 29 |

Journal | Journal of Parallel and Distributed Computing |

Volume | 54 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Nov 1998 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of Parallel and Distributed Computing*,

*54*(2), 133-161. https://doi.org/10.1006/jpdc.1998.1461

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

Research output: Contribution to journal › Article

*Journal of Parallel and Distributed Computing*, vol. 54, no. 2, pp. 133-161. https://doi.org/10.1006/jpdc.1998.1461

}

TY - JOUR

T1 - Average Case Analysis of Searching in Associative Processing

AU - Nastou, Panagiotis E.

AU - Serpanos, Dimitrios N.

AU - Maritsas, Dimitrios G.

PY - 1998/11/1

Y1 - 1998/11/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0040041772&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040041772&partnerID=8YFLogxK

U2 - 10.1006/jpdc.1998.1461

DO - 10.1006/jpdc.1998.1461

M3 - Article

AN - SCOPUS:0040041772

VL - 54

SP - 133

EP - 161

JO - Journal of Parallel and Distributed Computing

JF - Journal of Parallel and Distributed Computing

SN - 0743-7315

IS - 2

ER -