The Complexity of Maintaining an Array and Computing Its Partial Sums

Abstract

Given an array A (k), I k N, it is desired to perform two tasks’ (a) A (i) i A (0 + x, and (b) compute A(I) + A(2) +.-. + A(j), where t, j, and x are arbitrary inputs These tasks are to be performed on-hne Two computational models are defined relative to which computational complexity is assessed’ an algebraic model, and an reformation-theoretic model The informatlon-theoreuc complexity measure counts the number of accesses and changes to a random access memory. Upper and lower bounds are derived, and a trade-off between the complexmes of (a) versus (b) is observed. © 1982, ACM. All rights reserved.