# Generalizing the Covering Path Problem on a Grid

## TL;DR

This paper extends the covering path problem on grids, providing bounds and approximation algorithms for both rectangular and convex grids, advancing the understanding of efficient coverage strategies.

## Contribution

It generalizes previous results to arbitrary grids and offers new approximation algorithms with proven bounds for convex and general grids.

## Key findings

- Covering path cost bounded by area and perimeter.
- (2+ε)-approximation for general grids.
- (1+ε)-approximation for convex grids.

## Abstract

We study the covering path problem on a grid of R^{2}. We generalize earlier results on a rectangular grid and prove that the covering path cost can be bounded by the area and perimeter of the grid. We provide (2+\epsilon) and (1+\epsilon)-approximations for the problem on a general grid and on a convex grid, respectively.