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xuanleilinxuanleilin
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[ALGOS-268] feat(algos): improve triangle count algorithm;
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‎GDBMS_ALGO/community/tri_count.gsql

Lines changed: 34 additions & 33 deletions
Original file line numberDiff line numberDiff line change
@@ -1,12 +1,14 @@
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CREATE TEMPLATE QUERY GDBMS_ALGO.community.tri_count(STRING v_type, STRING e_type) SYNTAX V1 {
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CREATE TEMPLATE QUERY GDBMS_ALGO.community.tri_count(
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SET<STRING> v_type_set,
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SET<STRING> e_type_set
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) SYNTAX V1 {
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/*
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First Author: <First Author Name>
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First Commit Date: <First Commit Date>
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Recent Author: <Recent Commit Author Name>
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Recent Commit Date: <Recent Commit Date>
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/*
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First Author: [email protected]
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First Commit Date: 2024-07-17
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Recent Author: [email protected]
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Recent Commit Date: 2024-07-17
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Repository:
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https://github.com/tigergraph/gsql-graph-algorithms/tree/master/algorithms/Community
@@ -15,7 +17,7 @@ CREATE TEMPLATE QUERY GDBMS_ALGO.community.tri_count(STRING v_type, STRING e_typ
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Production
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Description:
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This algorithm uses the classic edge-iterator method to count triangles. It is slower than the fast version, but uses less memory.
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This query computes the total number of triangles in the graph.
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Publications:
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NA
@@ -24,31 +26,30 @@ CREATE TEMPLATE QUERY GDBMS_ALGO.community.tri_count(STRING v_type, STRING e_typ
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https://docs.tigergraph.com/graph-ml/current/community-algorithms/triangle-counting
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Parameters:
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v_type:
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Vertex type to count
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e_type:
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Edge type to traverse
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v_type_set:
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The set of vertex types to traverse.
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e_type_set:
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The set of edge types to traverse.
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*/
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# Compute the total number of triangles in the GRAPH. No input parameters are needed.
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SumAccum<INT> @@sum_cnt;
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SetAccum<VERTEX> @self_set;
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all = {v_type};
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all = SELECT s
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FROM all:s
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ACCUM s.@self_set += s;
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# For each edge e, the number of triangles that contain e is equivalent
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# to the number of common neighbors between vertices s and t
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tmp = SELECT t
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FROM all:s -(e_type:e) -:t
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WHERE getvid(s) > getvid(t)
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ACCUM INT c1 = COUNT(s.neighbors(e_type) MINUS s.@self_set),
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INT c2 = COUNT((s.neighbors(e_type) MINUS s.@self_set) MINUS (t.neighbors(e_type) MINUS t.@self_set)),
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@@sum_cnt += c1-c2;
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# Each triangle is counted 3 times for each edge, so final result is divided by 3
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PRINT @@sum_cnt/3 AS num_triangles;
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SumAccum<INT> @@sum_tri_count;
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SetAccum<VERTEX> @set_neighbors;
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Nodes = {v_type_set};
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// Build neighbor sets manually, only for vertices with smaller IDs in the triangle.
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// This ensures that only two of the three vertices in a triangle will build neighbor sets.
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Tmp = SELECT t
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FROM Nodes:s-(e_type_set)- v_type_set:t
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WHERE getvid(s) > getvid(t)
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ACCUM t.@set_neighbors += s;
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// Compute the intersection of neighbor sets to count triangles.
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// This step ensures that each triangle is counted only once.
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Tmp = SELECT t
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FROM Nodes:s-(e_type_set)- :t
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WHERE getvid(s) > getvid(t)
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ACCUM @@sum_tri_count += COUNT(s.@set_neighbors INTERSECT t.@set_neighbors);
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// Output the results
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PRINT @@sum_tri_count AS num_triangles;
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}

‎GDBMS_ALGO/community/tri_count_fast.gsql

Lines changed: 0 additions & 56 deletions
This file was deleted.

‎GDBMS_ALGO/community/tri_count_small_world.gsql

Lines changed: 206 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,206 @@
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CREATE TEMPLATE QUERY GDBMS_ALGO.community.tri_count_small_world(
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SET<STRING> v_type_set,
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SET<STRING> e_type_set,
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UINT supernode_min_degree = 100000,
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UINT threshold = 100000
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) SYNTAX V1 {
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/*
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First Author: [email protected]
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First Commit Date: 2024-07-18
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Recent Author: [email protected]
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Recent Commit Date: 2024-07-18
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Repository:
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https://github.com/tigergraph/gsql-graph-algorithms/tree/master/algorithms/Community
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Maturity:
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Production
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Description:
22+
This query computes the total number of triangles in the graph.
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It is optimized for small-world graphs to save memory.
24+
25+
Publications:
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NA
27+
28+
TigerGraph Documentation:
29+
https://docs.tigergraph.com/graph-ml/current/community-algorithms/triangle-counting
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31+
Parameters:
32+
v_type_set:
33+
The set of vertex types to traverse.
34+
e_type_set:
35+
The set of edge types to traverse.
36+
supernode_min_degree:
37+
The minimum degree for a vertex to be considered a supernode.
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The default value is 100000.
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threshold:
40+
The threshold for choosing initial pivot vertices. Only vertices whose product of indegree
41+
and outdegree exceeds this threshold will be considered candidates for the pivot vertex.
42+
The default value is 100000.
43+
*/
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SumAccum<INT> @sum_outdegree; // Accumulator for the outdegree
46+
SumAccum<INT> @sum_indegree; // Accumulator for the indegree
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SumAccum<INT> @sum_degree_product; // Accumulator for the product of outdegree and indegree
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OrAccum @or_in_frontier; // Flag to check if the vertex is in the frontier
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OrAccum @or_tri_counted; // Flag to check if all triangles that contain the vertex have been counted
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OrAccum @or_is_neighbor; // Flag to check if the vertex is a neighbor of nodes in the frontier
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SetAccum<VERTEX> @set_nodes_in_frontier; // Set of nodes in the frontier
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SumAccum<INT> @@sum_tri_count; // The count of triangles
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// -------------------- 1. Initialization --------------------
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// Calculate the product of indegree and outdegree,
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// and filter vertices with a product no less than the threshold
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AllNodes = {v_type_set};
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PivotCandidates = SELECT s
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FROM AllNodes:s-(e_type_set)-v_type_set:t
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WHERE s != t
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ACCUM s.@sum_outdegree += 1,
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s.@sum_indegree += 1
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POST-ACCUM (s)
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s.@sum_degree_product = s.@sum_indegree * s.@sum_outdegree
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HAVING s.@sum_degree_product >= threshold;
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// -------------------- 2. Handle the supernodes --------------------
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// Count the number of triangles for supernodes
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SuperNodes = SELECT s
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FROM PivotCandidates:s
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WHERE s.@sum_outdegree >= supernode_min_degree;
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WHILE SuperNodes.size() > 0 DO
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// Select some supernodes and set them as frontier
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Nodes = SELECT s
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FROM SuperNodes:s
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LIMIT 10;
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Nodes = SELECT s
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FROM Nodes:s
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POST-ACCUM (s)
80+
s.@or_in_frontier += TRUE;
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// Find neighbors of nodes in the frontier
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Neighbors = SELECT t
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FROM Nodes:s-(e_type_set)-v_type_set:t
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WHERE s != t
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AND t.@or_tri_counted == FALSE // Don't visit nodes whose all triangles have been counted
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AND (t.@or_in_frontier == FALSE // Neighbor not in the frontier
88+
OR getvid(s) > getvid(t)) // If neighbor is in the frontier, only consider one direction
89+
ACCUM t.@set_nodes_in_frontier += s
90+
POST-ACCUM (t)
91+
t.@or_is_neighbor += TRUE;
92+
93+
// Calculate the number of triangles involving nodes in the frontier
94+
Tmp = SELECT s
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FROM Neighbors:s-(e_type_set)-v_type_set:t
96+
WHERE getvid(s) > getvid(t) // Traverse only one direction of the undirected edge
97+
AND t.@or_is_neighbor == TRUE
98+
ACCUM @@sum_tri_count += COUNT(s.@set_nodes_in_frontier INTERSECT t.@set_nodes_in_frontier);
99+
100+
// Reset variables for nodes in the frontier
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Nodes = SELECT s
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FROM Nodes:s
103+
POST-ACCUM (s)
104+
s.@or_in_frontier = FALSE,
105+
s.@or_tri_counted = TRUE;
106+
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// Reset variables for the next iteration
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Neighbors = SELECT s
109+
FROM Neighbors:s
110+
POST-ACCUM (s)
111+
s.@or_is_neighbor = FALSE,
112+
s.@set_nodes_in_frontier.clear();
113+
114+
// Remove visited vertices from the SuperNodes set
115+
SuperNodes = SuperNodes MINUS Nodes;
116+
PivotCandidates = PivotCandidates MINUS Nodes;
117+
END;
118+
119+
// -------------------- 3. Handle nodes in large WCCs --------------------
120+
// Count the number of triangles for nodes in large WCCs
121+
WHILE PivotCandidates.size() > 0 DO
122+
// Select the initial pivot vertex with the largest product of indegree and outdegree
123+
Nodes = SELECT s
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FROM PivotCandidates:s
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ORDER BY s.@sum_degree_product DESC
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LIMIT 1;
127+
Nodes = SELECT s
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FROM Nodes:s
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POST-ACCUM (s)
130+
s.@or_in_frontier += TRUE;
131+
132+
// Use BFS to find all elements in its connected component
133+
WHILE Nodes.size() > 0 DO
134+
// Find neighbors of nodes in the frontier
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Neighbors = SELECT t
136+
FROM Nodes:s-(e_type_set)-v_type_set:t
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WHERE s != t
138+
AND t.@or_tri_counted == FALSE // Don't visit nodes whose all triangles have been counted
139+
AND (t.@or_in_frontier == FALSE // Neighbor not in the frontier
140+
OR getvid(s) > getvid(t)) // If neighbor is in the frontier, only consider one direction
141+
ACCUM t.@set_nodes_in_frontier += s
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POST-ACCUM (t)
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t.@or_is_neighbor += TRUE;
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// Calculate the number of triangles involving nodes in the frontier
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Tmp = SELECT s
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FROM Neighbors:s-(e_type_set)-v_type_set:t
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WHERE getvid(s) > getvid(t) // Traverse only one direction of the undirected edge
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AND t.@or_is_neighbor == TRUE
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ACCUM @@sum_tri_count += COUNT(s.@set_nodes_in_frontier INTERSECT t.@set_nodes_in_frontier);
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// Reset variables for nodes in the frontier
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Nodes = SELECT s
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FROM Nodes:s
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POST-ACCUM (s)
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s.@or_in_frontier = FALSE,
157+
s.@or_tri_counted = TRUE;
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// Reset variables for the next iteration
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Neighbors = SELECT s
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FROM Neighbors:s
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POST-ACCUM (s)
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s.@or_is_neighbor = FALSE,
164+
s.@set_nodes_in_frontier.clear();
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// Use BFS to visit the next frontier
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Nodes = SELECT t
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FROM Nodes:s-(e_type_set:e)-v_type_set:t
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WHERE t.@or_tri_counted == FALSE
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POST-ACCUM t.@or_in_frontier += TRUE;
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END;
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// Remove visited vertices from the PivotCandidates set
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PivotCandidates = SELECT s
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FROM PivotCandidates:s
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WHERE s.@or_tri_counted == FALSE;
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END;
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// -------------------- 4. Handle nodes in small WCCs --------------------
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// For remaining vertices in small WCCs
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Nodes = SELECT s
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FROM AllNodes:s
183+
WHERE s.@or_tri_counted == FALSE;
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// Build neighbor sets manually, only for vertices with smaller IDs in the triangle.
186+
// This ensures that only two of the three vertices in a triangle will build neighbor sets.
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Tmp = SELECT t
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FROM Nodes:s-(e_type_set)-v_type_set:t
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WHERE t.@or_tri_counted == FALSE
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AND getvid(s) > getvid(t)
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ACCUM t.@set_nodes_in_frontier += s
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POST-ACCUM
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t.@or_is_neighbor = TRUE;
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// Compute the intersection of neighbor sets to count triangles.
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// This step ensures that each triangle is counted only once.
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Tmp = SELECT t
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FROM Nodes:s-(e_type_set)-:t
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WHERE getvid(s) > getvid(t)
200+
AND t.@or_is_neighbor == TRUE
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ACCUM @@sum_tri_count += COUNT(s.@set_nodes_in_frontier INTERSECT t.@set_nodes_in_frontier);
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// -------------------- 5. Output --------------------
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// Output the results
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PRINT @@sum_tri_count AS num_triangles;
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}

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