A*  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 subset 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.
Description¶
The main Characteristics are:
Process works for directed and undirected graphs.
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 \(0\)
When \((x,y)\) coordinates for the same vertex identifier differ:
A random selection of the vertex’s \((x,y)\) coordinates is used.
Running time: \(O((E + V) * \log V)\)
aStar optional parameters¶
Parameter 
Type 
Default 
Description 



5 
Heuristic number. Current valid values 0~5.




For units manipulation. \(factor > 0\). 



For less restricted results. \(epsilon >= 1\). 
See heuristics available and factor handling.
Advanced documentation¶
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 
See Also¶
Indices and tables