Abstract:We consider a basic balls-and-bins question in which you have to distribute $n$ balls into $k$ bins. Then, round by round, a ball is removed from a non-empty bin chosen uniformly at random. The process ends when a single non-empty bin remains. The goal is to minimize the expected number of remaining balls. An open problem posed by Will Ma asks whether the initial assignment that minimizes the expected number of remaining balls is one that is as balanced as possible. Using a coupling argument, we answer this conjecture positively, and we discuss the case of non-uniform choice among the non-empty bins.
From: Marcos Kiwi [view email]
[v1]
Fri, 13 Feb 2026 02:02:05 UTC (11 KB)
[v2]
Mon, 17 Aug 2026 21:04:34 UTC (12 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。