Module minmax

A* search algorithm.

A set of heuristics is available under graph.algorithms.heuristics. User-created heuristics are allowed too.

Parameters:

• graph (graph, digraph) - Graph
• start (node) - Start node
• goal (node) - Goal node
• heuristic (function) - Heuristic function

Returns: list

Optimized path from start to goal node

Minimal spanning tree.

Parameters:

• graph (graph) - Graph.
• root (node) - Optional root node (will explore only root's connected component)

Returns: dictionary

Generated spanning tree.

Return the shortest path distance between source and all other nodes using Dijkstra's algorithm.

Parameters:

• graph (graph, digraph) - Graph.
• source (node) - Node from which to start the search.

Returns: tuple

A tuple containing two dictionaries, each keyed by target nodes.

1. Shortest path spanning tree
2. Shortest distance from given source to each target node

Inaccessible target nodes do not appear in either dictionary.

Return the shortest path distance between the source node and all other nodes in the graph using Bellman-Ford's algorithm.

This algorithm is useful when you have a weighted (and obviously a directed) graph with negative weights.

Parameters:

• graph (digraph) - Digraph
• source (node) - Source node of the graph

Returns: tuple

A tuple containing two dictionaries, each keyed by target nodes. (same as shortest_path function that implements Dijkstra's algorithm)

1. Shortest path spanning tree
2. Shortest distance from given source to each target node

Raises:

• NegativeWeightCycleError - raises if it finds a negative weight cycle. If this condition is met d(v) > d(u) + W(u, v) then raise the error.

Find a maximum flow and minimum cut of a directed graph by the Edmonds-Karp algorithm.

Parameters:

• graph (digraph) - Graph
• source (node) - Source of the flow
• sink (node) - Sink of the flow
• caps (dictionary) - Dictionary specifying a maximum capacity for each edge. If not given, the weight of the edge will be used as its capacity. Otherwise, for each edge (a,b), caps[(a,b)] should be given.

Returns: tuple

A tuple containing two dictionaries

1. contains the flow through each edge for a maximal flow through the graph
2. contains to which component of a minimum cut each node belongs

Calculate the value of a cut.

Parameters:

• graph (digraph) - Graph
• flow (dictionary) - Dictionary containing a flow for each edge.
• cut (dictionary) - Dictionary mapping each node to a subset index. The function only considers the flow between nodes with 0 and 1.

Returns: float

The value of the flow between the subsets 0 and 1

Construct a Gomory-Hu cut tree by applying the algorithm of Gusfield.

Parameters:

• igraph (graph) - Graph
• caps (dictionary) - Dictionary specifying a maximum capacity for each edge. If not given, the weight of the edge will be used as its capacity. Otherwise, for each edge (a,b), caps[(a,b)] should be given.

Returns: dictionary

Gomory-Hu cut tree as a dictionary, where each edge is associated with its weight