Supported versions: latest (3.8) 3.7 3.6 3.5 3.4 3.3 3.2 3.1 3.0 main dev
Unsupported versions:2.6 2.5 2.4

aStar - Family of functions¶

The A* (pronounced “A Star”) algorithm is based on Dijkstra’s algorithm with a heuristic that allow it to solve most shortest path problems by evaluation only a sub-set of the overall graph.

pgr_aStar - A* algorithm for the shortest path.
pgr_aStarCost - Get the aggregate cost of the shortest paths.
pgr_aStarCostMatrix - Get the cost matrix of the shortest paths.

General Information¶

The main Characteristics are:

Default kind of graph is directed when
- directed flag is missing.
- directed flag is set to true
Unless specified otherwise, ordering is:
- first by start_vid (if exists)
- then by end_vid
Values are returned when there is a path
Let $v$ and $u$ be nodes on the graph:
- If there is no path from $v$ to $u$ :
  - no corresponding row is returned
  - agg_cost from $v$ to $u$ is $\infty$
- There is no path when $v = u$ therefore
  - no corresponding row is returned
  - agg_cost from v to u is $0$
Edges with negative costs are not included in the graph.
When (x,y) coordinates for the same vertex identifier differ:
- A random selection of the vertex’s (x,y) coordinates is used.
Running time: $O((E + V) * \log V)$

Advanced documentation¶

The A* (pronounced “A Star”) algorithm is based on Dijkstra’s algorithm with a heuristic, that is an estimation of the remaining cost from the vertex to the goal, that allows to solve most shortest path problems by evaluation only a sub-set of the overall graph. Running time: $O((E + V) * \log V)$

Heuristic¶

Currently the heuristic functions available are:

0: $h(v) = 0$ (Use this value to compare with pgr_dijkstra)
1: $h(v) = abs(max(\Delta x, \Delta y))$
2: $h(v) = abs(min(\Delta x, \Delta y))$
3: $h(v) = \Delta x * \Delta x + \Delta y * \Delta y$
4: $h(v) = sqrt(\Delta x * \Delta x + \Delta y * \Delta y)$
5: $h(v) = abs(\Delta x) + abs(\Delta y)$

where $\Delta x = x_1 - x_0$ and $\Delta y = y_1 - y_0$

Factor¶

Analysis 1

Working with cost/reverse_cost as length in degrees, x/y in lat/lon: Factor = 1 (no need to change units)

Analysis 2

Working with cost/reverse_cost as length in meters, x/y in lat/lon: Factor = would depend on the location of the points:

Latitude	Conversion	Factor
45	1 longitude degree is 78846.81 m	78846
0	1 longitude degree is 111319.46 m	111319

Analysis 3

Working with cost/reverse_cost as time in seconds, x/y in lat/lon: Factor: would depend on the location of the points and on the average speed say 25m/s is the speed.

Latitude	Conversion	Factor
45	1 longitude degree is (78846.81m)/(25m/s)	3153 s
0	1 longitude degree is (111319.46 m)/(25m/s)	4452 s

aStar - Family of functions¶

General Information¶

Advanced documentation¶

Heuristic¶

Factor¶

See Also¶