An Analysis of a Memory Allocation Scheme - I * for Implementing Stacks Andrew

Consider the implementation of two stacks by letting them grow towards each other in a table of size m . Suppose a random sequence of insertions and deletions are executed, with each instruction having a fixed probability p (0 < p < l/2) to be a deletion. Let (m % ) denote the expected value of max{x,yj , where x and y are the stack heights when the table first becomes full. We shall. -prove that, as m4=, Ap(4 = (2x(1-2~)) + O((log m)/&) . This gives a solution to an open problem in Knuth [The Art of Computer Programming Vol. 1, Exercise 2.2.2-131. f* This research was supported in part by National Science Foundation under grant MCS77-05313. Part of this paper was prepared while the author was visiting Bell Laboratories, Murray Hill, N.J.