hqm / dijkstar

Graphs, Dijkstra, A*, shortest paths, HTTP graph server

Dijkstar

Dijkstar is an implementation of Dijkstra's single-source shortest-paths algorithm. If a destination node is given, the algorithm halts when that node is reached; otherwise it continues until paths from the source node to all other nodes are found.

Accepts an optional cost (or "weight") function that will be called on every iteration.

Also accepts an optional heuristic function that is used to push the algorithm toward a destination instead of fanning out in every direction. Using such a heuristic function converts Dijkstra to A* (and this is where the name "Dijkstar" comes from).

Example:

>>> from dijkstar import Graph, find_path
>>> graph = Graph()
>>> graph.add_edge(1, 2, 110)
>>> graph.add_edge(2, 3, 125)
>>> graph.add_edge(3, 4, 108)
>>> find_path(graph, 1, 4)
PathInfo(
    nodes=[1, 2, 3, 4],
    edges=[110, 125, 108],
    costs=[110, 125, 108],
    total_cost=343)

In this example, the edges are just simple numeric values--110, 125, 108--that could represent lengths, such as the length of a street segment between two intersections. find_path will use these values directly as costs.

Example with cost function:

>>> from dijkstar import Graph, find_path
>>> graph = Graph()
>>> graph.add_edge(1, 2, (110, 'Main Street'))
>>> graph.add_edge(2, 3, (125, 'Main Street'))
>>> graph.add_edge(3, 4, (108, '1st Street'))
>>> def cost_func(u, v, edge, prev_edge):
...     length, name = edge
...     if prev_edge:
...         prev_name = prev_edge[1]
...     else:
...         prev_name = None
...     cost = length
...     if name != prev_name:
...         cost += 10
...     return cost
...
>>> find_path(graph, 1, 4, cost_func=cost_func)
PathInfo(
    nodes=[1, 2, 3, 4],
    edges=[(110, 'Main Street'), (125, 'Main Street'), (108, '1st Street')],
    costs=[120, 125, 118],
    total_cost=363)

The cost function is passed the current node (u), a neighbor (v) of the current node, the edge that connects u to v, and the edge that was traversed previously to get to the current node.

A cost function is most useful when computing costs dynamically. If costs in your graph are fixed, a cost function will only add unnecessary overhead. In the example above, a penalty is added when the street name changes.

When using a cost function, one recommendation is to compute a base cost when possible. For example, for a graph that represents a street network, the base cost for each street segment (edge) could be the length of the segment multiplied by the speed limit. There are two advantages to this: the size of the graph will be smaller and the cost function will be doing less work, which may improve performance.

Graph Export & Import

The graph can be saved to disk (pickled) like so:

>>> graph.dump(path)

And read back like this (load is a classmethod that returns a populated Graph instance):

>>> Graph.load(path)