# Bidirectional A* - Family of functions¶

## 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 query¶

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

ANY-NUMERICAL

SMALLINT, INTEGER, BIGINT, REAL, FLOAT

### Combinations query¶

Column

Type

Default

Description

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.

Where:

ANY-INTEGER

SMALLINT, INTEGER, BIGINT

## Parameters¶

Parameter

Type

Description

Edges SQL

TEXT

Edges query as described above.

Combinations SQL

TEXT

Combinations 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.