arXiv subjects
Publications and source records attributed to Christian Berthet.
Based upon inequalities on Subset Probabilities, proofs of several conjectures on the Generalized Coupon Collector Problem (i.e. CCP with unequal popularity) are presented. Then we derive a very simple asymptotic relation between the expectation of the waiting time for a partial collection in the CCP, and the Miss rate of a LRU cache.
Building on the 1977 pioneering work of R. Fagin, we give a closed-form expression for the approximated Miss Rate (MR) of LRU Caches assuming a power-law popularity. Asymptotic behavior of this expression is an already known result when power-law parameter is above 1. It is extended to any value of the parameter. In addition, we bring a new analysis of the conditions (cache relative size, popularity parameter) under which the ratio of LRU MR to Static MR is worst-case.
This paper gives an algebraic proof of the correctness of Von Schelling formula for the probability of the coupon collector problem waiting time for non-uniform distributions and partial collections. It introduces a theorem on sums of powers of subset probabilities which to our knowledge is new. A set of binomial coefficients is used as a basis for decomposition of these sums of powers.
This short paper gives a detailed proof of identity between two classic formulas for the computation of the exact Miss Rate of LRU caches. An extension to the identity of two formulas of the expected time of a partial collection in the coupon collector problem is also presented.