使用非二进制比较进行排序
Sorting using non-binary comparisons
摘要：
在本文中，我们研究的问题排序一组$n$硬币，每个不同的，但未知的重量，使用一个不寻常的规模。这个问题的经典版本，这已经得到了很好的研究，给用户一个二进制的规模，使他们能够确定这是轻/重的任何两个对象。我们对此进行概括，考虑接受$k$硬币作为输入并返回最轻的$t^{\text{th}}$的规模，对于固定的$k$和$t$。我们认为这是在一个在线和离线设置，并展示算法在这两种设置中，是最好的可能在所需的查询数量的顺序。
英文摘要：
In this paper we investigate the problem of sorting a set of $n$ coins, each with distinct but unknown weights, using an unusual scale. The classical version of this problem, which has been well-studied, gives the user a binary scale, enabling them to determine which is the lighter/heavier of any two objects. We generalise this, considering a scale that accepts $k$ coins as input and returns the $t^{\text{th}}$ lightest, for a fixed $k$ and $t$. We consider this in both an on-line and off-line setting, and exhibit algorithms in both settings that are best-possible in terms of the order of the number of queries required.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
