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This paper introduces a unified framework for the analysis of a class of random allocation processes thdt include: (i) the birthday paradox; (ii) the coupon collector problem* (iii) least-tecently-used (LRU) caching in memory management systems under the independent reference model; (iv) the move-to-front heuristic of self-organizing search. All analyses(More)
Given a set ξ = {H 1 , H 2 , · · ·} of connected non acyclic graphs, a ξ-free graph is one which does not contain any member of ξ as copy. Define the excess of a graph as the difference between its number of edges and its number of vertices. Let W k,ξ be theexponential generating function (EGF for brief) of connected ξ-free graphs of excess equal to k (k ≥(More)
Denote by an l-component a connected graph with l edges more than vertices. We prove that the expected number of creations of (l + 1)-component, by means of adding a new edge to an l-component in a randomly growing graph with n vertices, tends to 1 as l, n tends to ∞ but with l = o(n 1/4). We also show, under the same conditions on l and n, that the(More)