# An Improved Lower Bound for General Position Subset Selection

## TL;DR

This paper introduces an improved algorithm for the General Position Subset Selection problem, enhancing the lower bounds of the solution size by leveraging the number of collinear pairs, with experimental validation indicating potential for even tighter bounds.

## Contribution

It presents a new algorithm that improves the lower bound for GPSS based on collinear pairs, advancing previous guarantees.

## Key findings

- The new algorithm outperforms existing methods in certain cases.
- Experimental results suggest further improvements are possible.
- Tighter lower bounds can be achieved using collinear pair information.

## Abstract

In the General Position Subset Selection (GPSS) problem, the goal is to find the largest possible subset of a set of points such that no three of its members are collinear. If $s_{\mathrm{GPSS}}$ is the size of the optimal solution, $\sqrt{s_{\mathrm{GPSS}}}$ is the current best guarantee for the size of the solution obtained using a polynomial time algorithm. In this paper we present an algorithm for GPSS to improve this bound based on the number of collinear pairs of points. We experimentally evaluate this and few other GPSS algorithms; the result of these experiments suggests further opportunities for obtaining tighter lower bounds for GPSS.