Tournaments, Johnson Graphs, and NC-Teaching
Hans U. Simon

TL;DR
This paper explores the properties of NC-Teaching, a provably optimal collusion-free teaching model, characterizes classes with NC-teaching dimension 1 using tournaments, and demonstrates a significant separation from recursive teaching dimension through probabilistic methods.
Contribution
It characterizes maximum concept classes of NC-teaching dimension 1 via tournaments and shows a family of classes where NC-teaching dimension is minimal while recursive teaching dimension grows logarithmically, highlighting their differences.
Findings
Characterization of classes with NC-teaching dimension 1 using tournaments.
Existence of concept classes with minimal NC-teaching dimension but large recursive teaching dimension.
Improved upper bound on the number of concepts using Johnson graphs and maximum subgraphs.
Abstract
Quite recently a teaching model, called "No-Clash Teaching" or simply "NC-Teaching", had been suggested that is provably optimal in the following strong sense. First, it satisfies Goldman and Matthias' collusion-freeness condition. Second, the NC-teaching dimension (= NCTD) is smaller than or equal to the teaching dimension with respect to any other collusion-free teaching model. It has also been shown that any concept class which has NC-teaching dimension and is defined over a domain of size can have at most concepts. The main results in this paper are as follows. First, we characterize the maximum concept classes of NC-teaching dimension as classes which are induced by tournaments (= complete oriented graphs) in a very natural way. Second, we show that there exists a family of concept classes such that the well known recursive teaching…
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Taxonomy
TopicsMachine Learning and Algorithms · Rough Sets and Fuzzy Logic · Advanced Algebra and Logic
