Given a graph and a source vertex, the single source shortest path (SSSP) algorithm finds a path from the source vertex to every other vertex in the graph, such that the sum of the weights of the path edges is minimized.
graph_sssp( vertex_table, vertex_id, edge_table, edge_args, source_vertex, out_table )
Arguments
TEXT. Name of the table containing the vertex data for the graph. Must contain the column specified in the 'vertex_id' parameter below.
TEXT, default = 'id'. Name of the column in 'vertex_table' containing vertex ids. The vertex ids are of type INTEGER with no duplicates. They do not need to be contiguous.
TEXT. Name of the table containing the edge data. The edge table must contain columns for source vertex, destination vertex and edge weight. Column naming convention is described below in the 'edge_args' parameter.
TEXT. A comma-delimited string containing multiple named arguments of the form "name=value". The following parameters are supported for this string argument:
INTEGER. The source vertex id for the algorithm to start. This vertex id must exist in the 'vertex_id' column of 'vertex_table'.
The path retrieval function returns the shortest path from the source vertex to a specified desination vertex.
graph_sssp( sssp_table, dest_vertex )
Arguments
TEXT. Name of the table that contains the SSSP output.
The Bellman-Ford algorithm [1] is used to implement SSSP. This algorithm allows negative edges but not negative cycles. In the case of graphs with negative cycles, an error will be given and no output table will be generated.
Also see the Grail project [2] for more background on graph analytics processing in relational databases.
DROP TABLE IF EXISTS vertex, edge; CREATE TABLE vertex( id INTEGER ); CREATE TABLE edge( src INTEGER, dest INTEGER, weight FLOAT8 ); INSERT INTO vertex VALUES (0), (1), (2), (3), (4), (5), (6), (7); INSERT INTO edge VALUES (0, 1, 1.0), (0, 2, 1.0), (0, 4, 10.0), (1, 2, 2.0), (1, 3, 10.0), (2, 3, 1.0), (2, 5, 1.0), (2, 6, 3.0), (3, 0, 1.0), (4, 0, -2.0), (5, 6, 1.0), (6, 7, 1.0);
DROP TABLE IF EXISTS out; SELECT madlib.graph_sssp( 'vertex', -- Vertex table NULL, -- Vertix id column (NULL means use default naming) 'edge', -- Edge table NULL, -- Edge arguments (NULL means use default naming) 0, -- Source vertex for path calculation 'out'); -- Output table of shortest paths SELECT * FROM out ORDER BY id;
id | weight | parent ----+--------+-------- 0 | 0 | 0 1 | 1 | 0 2 | 1 | 0 3 | 2 | 2 4 | 10 | 0 5 | 2 | 2 6 | 3 | 5 7 | 4 | 6 (8 rows)
SELECT madlib.graph_sssp_get_path('out',6) AS spath;
spath ----------- {0,2,5,6}
DROP TABLE IF EXISTS vertex_alt, edge_alt; CREATE TABLE vertex_alt AS SELECT id AS v_id FROM vertex; CREATE TABLE edge_alt AS SELECT src AS e_src, dest, weight AS e_weight FROM edge;
DROP TABLE IF EXISTS out_alt; SELECT madlib.graph_sssp( 'vertex_alt', -- Vertex table 'v_id', -- Vertix id column (NULL means use default naming) 'edge_alt', -- Edge table 'src=e_src, weight=e_weight', -- Edge arguments (NULL means use default naming) 1, -- Source vertex for path calculation 'out_alt'); -- Output table of shortest paths SELECT * FROM out_alt ORDER BY v_id;
v_id | e_weight | parent ------+----------+-------- 0 | 4 | 3 1 | 0 | 1 2 | 2 | 1 3 | 3 | 2 4 | 14 | 0 5 | 3 | 2 6 | 4 | 5 7 | 5 | 6 (8 rows)
[1] Bellman–Ford algorithm. https://en.wikipedia.org/wiki/Bellman%E2%80%93Ford_algorithm
[2] The case against specialized graph analytics engines, J. Fan, G. Soosai Raj, and J. M. Patel. CIDR 2015. http://cidrdb.org/cidr2015/Papers/CIDR15_Paper20.pdf