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Optimal bi-weighted binary trees and the complexity of maintaining partial sums

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2 Author(s)
Hampapuram, H. ; Rutgers Univ., NJ, USA ; Fredman, Michael L.

Let A be an array. The partial sum problem concerns the design of a data structure for implementing the following operations. The operation update(j,x) has the effect, A[j]←A[j]+x, and the query operation sum(j) returns the partial sum, Σi=1j A[i]. Our interest centers upon the optimal efficiency with which sequences of such operations can be performed, and we derive new upper and lower bounds in the semi-group model of computation. Our analysis relates the optimal complexity of the partial sum problem to optimal binary trees relative to a type of weighting scheme that defines the notion of bi-weighted binary tree

Published in:

Foundations of Computer Science, 1993. Proceedings., 34th Annual Symposium on

Date of Conference:

3-5 Nov 1993