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pgr_binaryBreadthFirstSearch - Experimental

pgr_breadthFirstSearch — Returns the shortest path(s) in a binary graph. Any graph whose edge-weights belongs to the set {0,X}, where 'X' is any non-negative real integer, is termed as a 'binary graph'.

images/boost-inside.jpeg

Boost Graph Inside

Availability

  • To-be experimental on v3.0.0

Description

It is well-known that the shortest paths between a single source and all other vertices can be found using Breadth First Search in :math:` O(|E|)` in an unweighted graph, i.e. the distance is the minimal number of edges that you need to traverse from the source to another vertex. We can interpret such a graph also as a weighted graph, where every edge has the weight 1. If not all edges in graph have the same weight, that we need a more general algorithm, like Dijkstra's Algorithm which runs in O(|E|log|V|) time.

However if the weights are more constrained, we can use a faster algorithm. This algorithm, termed as 'Binary Breadth First Search' aswell as '0-1 BFS', is a variation of the standard Breadth First Search problem to solve the SSSP (single-source shortest path) problem in O(|E|), if the weights of each edge belongs to the set {0,X}, where 'X' is any non-negative real integer.

The main Characteristics are:

  • Process is done only on 'binary graphs'. ('Binary Graph': Any graph whose edge-weights belongs to the set {0,X}, where 'X' is any non-negative real integer.)
  • For optimization purposes, any duplicated value in the start_vids or end_vids are ignored.
  • The returned values are ordered:
    • start_vid ascending
    • end_vid ascending
  • Running time: O(| start\_vids | * |E|)

Signatures

pgr_binaryBreadthFirstSearch(edges_sql, start_vid,  end_vid  [, directed])
pgr_binaryBreadthFirstSearch(edges_sql, start_vid,  end_vids [, directed])
pgr_binaryBreadthFirstSearch(edges_sql, start_vids, end_vid  [, directed])
pgr_binaryBreadthFirstSearch(edges_sql, start_vids, end_vids [, directed])
RETURNS SET OF (seq, path_seq [, start_vid] [, end_vid], node, edge, cost, agg_cost)
OR EMPTY SET

pgr_binaryBreadthFirstSearch(TEXT edges_sql, BIGINT start_vid, BIGINT end_vid)
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost) or EMPTY SET
Example:From vertex 2 to vertex 3 on a directed binary graph 
.. literalinclude:: doc-pgr_binaryBreadthFirstSearch.queries
   :start-after: -- q1
   :end-before: -- q2


.. index::
    single: binaryBreadthFirstSearch(One to One)

One to One

pgr_binaryBreadthFirstSearch(TEXT edges_sql, BIGINT start_vid, BIGINT end_vid,
BOOLEAN directed:=true);
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET
Example:From vertex 2 to vertex 3 on an undirected binary graph 
.. literalinclude:: doc-pgr_binaryBreadthFirstSearch.queries
   :start-after: -- q2
   :end-before: -- q3


.. index::
    single: Binary Breadth First Search(One to Many)

One to many

pgr_binaryBreadthFirstSearch(TEXT edges_sql, BIGINT start_vid, ARRAY[ANY_INTEGER] end_vids,
BOOLEAN directed:=true);
RETURNS SET OF (seq, path_seq, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET
Example:From vertex 2 to vertices \{3, 5\} on an undirected binary graph 
.. literalinclude:: doc-pgr_binaryBreadthFirstSearch.queries
   :start-after: -- q3
   :end-before: -- q4


.. index::
    single: Binary Breadth First Search(Many to One)

Many to One

pgr_binaryBreadthFirstSearch(TEXT edges_sql, ARRAY[ANY_INTEGER] start_vids, BIGINT end_vid,
    BOOLEAN directed:=true);
RETURNS SET OF (seq, path_seq, start_vid, node, edge, cost, agg_cost)
OR EMPTY SET
Example:From vertices \{2, 11\} to vertex 5 on a directed binary graph 
.. literalinclude:: doc-pgr_binaryBreadthFirstSearch.queries
   :start-after: -- q4
   :end-before: -- q5


.. index::
    single: Binary Breadth First Search(Many to Many)

Many to Many

pgr_binaryBreadthFirstSearch(TEXT edges_sql, ARRAY[ANY_INTEGER] start_vids, ARRAY[ANY_INTEGER] end_vids,
    BOOLEAN directed:=true);
RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET
Example:From vertices \{2, 11\} to vertices \{3, 5\} on an undirected binary graph 
.. literalinclude:: doc-pgr_binaryBreadthFirstSearch.queries
   :start-after: -- q5
   :end-before: -- q6

Parameters

Parameter Type Default Description
edges_sql TEXT   Inner SQL query as described below.
start_vid BIGINT   Identifier of the starting vertex of the path.
start_vids ARRAY[BIGINT]   Array of identifiers of starting vertices.
end_vid BIGINT   Identifier of the ending vertex of the path.
end_vids ARRAY[BIGINT]   Array of identifiers of ending vertices.
directed BOOLEAN true
  • When true Graph is considered Directed
  • When false the graph is considered as Undirected.

Inner query

Return Columns

Example Application

This algorithm is best applied when trying to answer queries such as the following: “Find the path with the minimum number from Source to Destination” Here: * Source = Source Vertex, Destination = Any arbitrary destination vertex * X is an event/property * Each edge in the graph is either “X” or “Not X” .

Example: “Find the path with the minimum number of road works from Source to Destination”

Here, a road under work(aka road works) means that part of the road is occupied for construction work/maintenance.

Here: * Edge ( u , v ) has weight = 0 if no road work is ongoing on the road from u to v. * Edge ( u, v) has weight = 1 if road work is ongoing on the road from u to v.

Then, upon running the algorithm, we obtain the path with the minimum number of road works from the given source and destination.

Thus, the queries used in the previous section can be interpreted in this manner.

Table Data

The queries in the previous sections use the table 'roadworks'. The data of the table:

.. literalinclude:: doc-pgr_binaryBreadthFirstSearch.queries
   :start-after: --data
   :end-before: --q1

See Also

Indices and tables