Work

The Computational Complexity of Positive Non-Clashing Teaching in Graphs

Year: 2025

Type: conference-paper

Abstract: We study the classical and parameterized complexity of computing the positive non-clashing teaching dimension of a set of concepts, that is, the smallest number of examples per concept required to successfully teach an intelligent learner under the considered, previously established model. For any class of concepts, it is known that this problem can be effortlessly transferred to the setting of balls in a graph G. We establish (1) the NP-hardness of the problem even when restricted to instances with positive non-clashing teaching dimension k = 2 and where all balls in the graph are present, (2) near-tight running time upper and lower bounds for the problem on general graphs, (3) fixed-parameter tractability when parameterized by the vertex integrity of G, and (4) a lower bound excluding fixed-parameter tractability when parameterized by the feedback vertex number and pathwidth of G, even when combined with k. Our results provide a nearly complete understanding of the complexity landscape of computing the positive non-clashing teaching dimension and answer open questions from the literature.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.15222286

Authors: Ganian, Robert, Khazaliya, Liana, Mc Inerney, Fionn, Rocton, Mathis

Institutions: TU Wien, Telefónica (Spain)

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

SDG: Quality education

Open Access status: green

Funder: European Commission