Contributions to the Generalized Coupon Collector and LRU Problems

TL;DR

This paper proves several conjectures related to the Generalized Coupon Collector Problem with unequal probabilities and establishes a simple asymptotic relation between the expected waiting time and LRU cache miss rate.

Contribution

It provides new proofs for conjectures in the generalized coupon collector problem and links the expected waiting time to LRU cache performance.

Findings

Proved multiple conjectures on the generalized coupon collector problem.

Derived a simple asymptotic relation between waiting time and cache miss rate.

Enhanced understanding of the connection between probabilistic collection problems and caching algorithms.

Abstract

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.