# Bidirectional A* - Family of functions¶

• Supported versions: current(3.1) 3.0 2.6
• Unsupported versions: 2.5

## Description¶

Based on A* algorithm, the bidirectional search finds a shortest path from a starting vertex (start_vid) to an ending vertex (end_vid). It runs two simultaneous searches: one forward from the start_vid, and one backward from the end_vid, stopping when the two meet in the middle. This implementation can be used with a directed graph and an undirected graph.

The main Characteristics are:

• Process is done only on edges with positive costs.
• Values are returned when there is a path.
• When the starting vertex and ending vertex are the same, there is no path.
• The agg_cost the non included values (v, v) is 0
• When the starting vertex and ending vertex are the different and there is no path:
• The agg_cost the non included values (u, v) is $$\infty$$
• Running time (worse case scenario): $$O((E + V) * \log V)$$
• For large graphs where there is a path bewtween the starting vertex and ending vertex:
• It is expected to terminate faster than pgr_astar

## Signatures¶

edges_sql: an SQL query, which should return a set of rows with the following columns:
Column Type Default Description
id ANY-INTEGER   Identifier of the edge.
source ANY-INTEGER   Identifier of the first end point vertex of the edge.
target ANY-INTEGER   Identifier of the second end point vertex of the edge.
cost ANY-NUMERICAL

Weight of the edge (source, target)

• When negative: edge (source, target) does not exist, therefore it’s not part of the graph.
reverse_cost ANY-NUMERICAL -1

Weight of the edge (target, source),

• When negative: edge (target, source) does not exist, therefore it’s not part of the graph.
x1 ANY-NUMERICAL   X coordinate of source vertex.
y1 ANY-NUMERICAL   Y coordinate of source vertex.
x2 ANY-NUMERICAL   X coordinate of target vertex.
y2 ANY-NUMERICAL   Y coordinate of target vertex.

Where:

ANY-INTEGER: SMALLINT, INTEGER, BIGINT SMALLINT, INTEGER, BIGINT, REAL, FLOAT

## Parameters¶

Parameter Type Description
edges_sql TEXT Edges SQL query as described above.
start_vid ANY-INTEGER Starting vertex identifier.
start_vids ARRAY[ANY-INTEGER] Starting vertices identifierers.
end_vid ANY-INTEGER Ending vertex identifier.
end_vids ARRAY[ANY-INTEGER] Ending vertices identifiers.
directed BOOLEAN
• Optional.
• When false the graph is considered as Undirected.
• Default is true which considers the graph as Directed.
heuristic INTEGER

(optional). Heuristic number. Current valid values 0~5. Default 5

• 0: h(v) = 0 (Use this value to compare with pgr_dijkstra)
• 1: h(v) abs(max(dx, dy))
• 2: h(v) abs(min(dx, dy))
• 3: h(v) = dx * dx + dy * dy
• 4: h(v) = sqrt(dx * dx + dy * dy)
• 5: h(v) = abs(dx) + abs(dy)
factor FLOAT (optional). For units manipulation. $$factor > 0$$. Default 1. see Factor
epsilon FLOAT (optional). For less restricted results. $$epsilon >= 1$$. Default 1.