### 9 unstable releases (4 breaking)

0.5.0 | Aug 8, 2021 |
---|---|

0.4.3 | Jun 13, 2021 |

0.4.2 | May 18, 2021 |

0.3.6 | Oct 12, 2020 |

0.1.0 | Mar 30, 2019 |

#**1051** in Algorithms

**MIT**license

145KB

2.5K
SLoC

# Hierarchical Pathfinding

A Rust crate to find Paths on a Grid using HPA* (Hierarchical Pathfinding A*) and Hierarchical Dijkstra.

## Description

Provides a fast algorithm for finding Paths on a Grid-like structure by caching segments of Paths to form a Node Graph. Finding a Path in that Graph is a lot faster than on the Grid itself, but results in Paths that are *slightly* worse than the optimal Path.

Implementation based on the Paper "Near Optimal Hierarchical Path-Finding".

### Advantages

- Finding a Path is a lot faster compared to regular algorithms (A*, Dijkstra)
- It is always correct: A Path is found
**if and only if**it exists- This means that Hierarchical Pathfinding can be used as Heuristic to check if a Path exists and how long it will roughly be (upper bound)

### Disadvantages

- Paths are slightly worse (negligible in most cases)
- Creating the cache takes time (only happens once at the start)
- Changes to the Grid require updating the cache
- Whenever a Tile within a Chunk changes, that entire Chunk needs to recalculate its Paths. Performance depends on Chunk size (configurable) and the number of Nodes in a Chunk

## Use Case

Finding Paths on a Grid is an expensive Operation. Consider the following Setup:

In order to calculate a Path from Start to End using regular A*, it is necessary to check a lot of Tiles:

(This is simply a small example, longer Paths require a quadratic increase in Tile checks,
and unreachable Goals require the check of * every single* Tile)

The Solution that Hierarchical Pathfinding provides is to divide the Grid into Chunks and cache the Paths between Chunk entrances as a Graph of Nodes:

This allows Paths to be generated by connecting the Start and End to the Nodes within the Chunk and using the Graph for the rest:

## Example

`use` `hierarchical_pathfinding``::``prelude``::``*``;`
`let` `mut` pathfinding `=` `PathCache``::`new`(`
`(`width`,` height`)``,` `//` the size of the Grid
`|``(`x`,` y`)``|` `walking_cost``(`x`,` y`)``,` `//` get the cost for walking over a Tile
`ManhattanNeighborhood``::`new`(`width`,` height`)``,` `//` the Neighborhood
`PathCacheConfig``::`with_chunk_size`(``3``)``,` `//` config
`)``;`
`let` start `=` `(``0``,` `0``)``;`
`let` goal `=` `(``4``,` `4``)``;`
`//` find_path returns Some(Path) on success
`let` path `=` pathfinding`.``find_path``(`
start`,`
goal`,`
`|``(``x``,` `y``)``|` `walking_cost``(`x`,` y`)``,`
`)``;`
`if` `let` `Some``(`path`)` `=` path `{`
`println!``(``"`Number of steps: `{}``"``,` path`.``length``(``)``)``;`
`println!``(``"`Total Cost: `{}``"``,` path`.``cost``(``)``)``;`
`for` `(`x`,` y`)` `in` path `{`
`println!``(``"`Go to `{}`, `{}``"``,` x`,` y`)``;`
`}`
`}`

#### Dependencies

~0.9–1.3MB

~21K SLoC