# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1706.05250