Finding Points in General Position

TL;DR

This paper investigates the computational complexity of selecting the largest subset of points in general position from a given set, establishing NP-hardness, APX-hardness, and fixed-parameter tractability results.

Contribution

It proves the NP-hardness and APX-hardness of the problem and provides fixed-parameter tractability results along with a subexponential time lower bound.

Findings

Proves NP-hardness of the problem

Establishes APX-hardness of the problem

Provides fixed-parameter tractability results

Abstract

We study computational aspects of the General Position Subset Selection problem defined as follows: Given a set of points in the plane, find a maximum-cardinality subset of points in general position. We prove that General Position Subset Selection is NP-hard, APX-hard, and give several fixed-parameter tractability results as well as a subexponential running time lower bound based on the Exponential Time Hypothesis.