Abstract
We analyse a simple storage allocation scheme in which two stacks grow and shrink inside a shared memory area. To that purpose, we provide analytic expressions for the number of 2-dimensional random walks in a triangle with two reflecting barriers and one absorbing barrier.
We obtain probability distributions and expectations of characteristic parameters of that shared memory scheme, namely the sizes of the stacks and the time until the system runs out of memory.
This provides a complete solution to an open problem posed by Knuth in "The Art of Computer Programming", Vol. 1, 1968 [Ex. 2.2.2.13].
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© 1986 Springer-Verlag Berlin Heidelberg
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Flajolet, P. (1986). The evolution of two stacks in bounded space and random walks in a triangle. In: Gruska, J., Rovan, B., Wiedermann, J. (eds) Mathematical Foundations of Computer Science 1986. MFCS 1986. Lecture Notes in Computer Science, vol 233. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0016257
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DOI: https://doi.org/10.1007/BFb0016257
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