# pgRouting Manual (2.5)

## 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 – proposed - Get the aggregate cost of the shortest paths.
- pgr_aStarCostMatrix - proposed - Get the cost matrix of the shortest paths.

## The problem definition (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

## See Also

- pgr_aStar
- pgr_aStarCost – proposed
- pgr_aStarCostMatrix - proposed
- http://www.boost.org/libs/graph/doc/astar_search.html
- http://en.wikipedia.org/wiki/A*_search_algorithm

Indices and tables

- Index
- Search Page