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.

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