The Labeled Coupon Collector Problem with Random Sample Sizes and Partial Recovery

TL;DR

This paper introduces a generalized coupon collector problem model that considers bipartite graph recovery with perfect matchings, including heterogeneous sample sizes and partial recovery scenarios, advancing theoretical understanding.

Contribution

It extends the classical CCP to a bipartite graph setting with new variants for heterogeneous samples and partial recovery, providing a broader framework.

Findings

Developed the k-LCCP model for bipartite graph recovery.

Extended the model to heterogeneous sample sizes (K-LCCP).

Analyzed partial recovery scenarios within the generalized model.

Abstract

We extend the Coupon Collector's Problem (CCP) and present a novel generalized model, referred as the k-LCCP problem, where one is interested in recovering a bipartite graph with a perfect matching, which represents the coupons and their matching labels. We show two extra-extensions to this variation: the heterogeneous sample size case (K-LCCP) and the partly recovering case.