Sorting using non-binary comparisons
Richard A. B. Johnson, Gabor Meszaros

TL;DR
This paper explores a generalized sorting problem using a scale that compares multiple coins at once, providing optimal algorithms for both online and offline scenarios with non-binary comparisons.
Contribution
It introduces a novel multi-input comparison model for sorting and develops optimal algorithms for both online and offline settings.
Findings
Established lower bounds for query complexity.
Designed optimal algorithms matching these bounds.
Extended classical sorting to non-binary comparison models.
Abstract
In this paper we investigate the problem of sorting a set of 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 coins as input and returns the lightest, for a fixed and . 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.
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Taxonomy
TopicsLimits and Structures in Graph Theory
