TY - JOUR

T1 - Multiple Addition and Prefix Sum on a Linear Array with a Reconfigurable Pipelined Bus System

AU - Datta, Amitava

PY - 2004

Y1 - 2004

N2 - We present several fast algorithms for multiple addition and prefix sum on the Linear Array with a Reconfigurable Pipelined Bus System (LARPBS), a recently proposed architecture based on optical buses. Our algorithm for adding N integers runs on an N log M-processor LARPBS in O(log* N) time, where log* N is the number of times logarithm has to be taken to reduce N below 1 and M is the largest integer in the input. Our addition algorithm improves the time complexity of several matrix multiplication algorithms proposed by Li, Pan and Zheng (IEEE Trans. Parallel and Distributed Systems, 9(8):705–720, 1998). We also present several fast algorithms for computing prefix sums of N integers on the LARPBS. For integers with bounded magnitude, our first algorithm for prefix sum computation runs in O(log log N) time using N processors and in O(1) time using N1+ℇ processors, for \frac{1}{3} ≤ ℇ <1. For integers with unbounded magnitude, the first algorithm for multiple addition runs in O(log log N log* N) time using N log M processors, when M is the largest integer in the input. Our second algorithm for multiple addition runs in O(log* N) time using N1+ℇ log M processors, for \frac {1}{3} ≤ ℇ <1. We also show suitable extensions of our algorithm for real numbers. [ABSTRACT FROM AUTHOR]Copyright of Journal of Supercomputing is the property of Springer Science & Business Media B.V. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

AB - We present several fast algorithms for multiple addition and prefix sum on the Linear Array with a Reconfigurable Pipelined Bus System (LARPBS), a recently proposed architecture based on optical buses. Our algorithm for adding N integers runs on an N log M-processor LARPBS in O(log* N) time, where log* N is the number of times logarithm has to be taken to reduce N below 1 and M is the largest integer in the input. Our addition algorithm improves the time complexity of several matrix multiplication algorithms proposed by Li, Pan and Zheng (IEEE Trans. Parallel and Distributed Systems, 9(8):705–720, 1998). We also present several fast algorithms for computing prefix sums of N integers on the LARPBS. For integers with bounded magnitude, our first algorithm for prefix sum computation runs in O(log log N) time using N processors and in O(1) time using N1+ℇ processors, for \frac{1}{3} ≤ ℇ <1. For integers with unbounded magnitude, the first algorithm for multiple addition runs in O(log log N log* N) time using N log M processors, when M is the largest integer in the input. Our second algorithm for multiple addition runs in O(log* N) time using N1+ℇ log M processors, for \frac {1}{3} ≤ ℇ <1. We also show suitable extensions of our algorithm for real numbers. [ABSTRACT FROM AUTHOR]Copyright of Journal of Supercomputing is the property of Springer Science & Business Media B.V. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

U2 - 10.1023/B:SUPE.0000032783.66123.63

DO - 10.1023/B:SUPE.0000032783.66123.63

M3 - Article

SN - 0920-8542

VL - 29

SP - 303

EP - 317

JO - The Journal of Supercomputing

JF - The Journal of Supercomputing

IS - 3

ER -