# Edge N-Level Sparse Visibility Graphs: Fast Optimal Any-Angle Pathfinding Using Hierarchical Taut Paths

## TL;DR

This paper introduces hierarchical sparse visibility graphs and a fast line-of-sight scanning method to significantly accelerate optimal any-angle pathfinding on large maps, outperforming existing algorithms.

## Contribution

The paper presents Edge N-Level Sparse Visibility Graphs and Line-of-Sight Scans, novel methods that improve the efficiency of optimal pathfinding algorithms on complex grid maps.

## Key findings

- ENLSVGs are significantly faster on large maps.
- SVGs reduce average vertex degree, improving speed.
- Hierarchical pruning enhances pathfinding efficiency.

## Abstract

In the Any-Angle Pathfinding problem, the goal is to find the shortest path between a pair of vertices on a uniform square grid, that is not constrained to any fixed number of possible directions over the grid. Visibility Graphs are a known optimal algorithm for solving the problem with the use of pre-processing. However, Visibility Graphs are known to perform poorly in terms of running time, especially on large, complex maps. In this paper, we introduce two improvements over the Visibility Graph Algorithm to compute optimal paths. Sparse Visibility Graphs (SVGs) are constructed by pruning unnecessary edges from the original Visibility Graph. Edge N-Level Sparse Visibility Graphs (ENLSVGs) is a hierarchical SVG built by iteratively pruning non-taut paths. We also introduce Line-of-Sight Scans, a faster algorithm for building Visibility Graphs over a grid. SVGs run much faster than Visibility Graphs by reducing the average vertex degree. ENLSVGs, a hierarchical algorithm, improves this further, especially on larger maps. On large maps, with the use of pre-processing, these algorithms are orders of magnitude faster than existing algorithms like Visibility Graphs and Theta*.