tc comments

tc.cc

@@ -12,11 +12,37 @@
 #include "pvector.h"
 
 
-using namespace std;
+/*
+GAP Benchmark Suite
+Kernel: Triangle Counting (TC)
+Author: Scott Beamer
+
+Will count the number of triangles (cliques of size 3)
+
+Requires input graph:
+  - to be undirected
+  - no duplicate edges (or else will be counted as multiple triangles)
+  - neighborhoods are sorted by vertex identifiers
+
+Other than symmetrizing, the rest of the requirements are done by SquishCSR
+during graph building.
 
+This implementation reduces the search space by counting each triangle only
+once. A naive implementation will count the same triangle six times because
+each of the three vertices (u, v, w) will count it in both ways. To count
+a triangle only once, this implementation only counts a triangle if u > v > w.
+Once the remaining unexamined neighbors identifiers get too big, it can break
+out of the loop, but this requires that the neighbors to be sorted.
+
+Another optimization this implementation has is to relabel the vertices by
+degree. This is beneficial if the average degree is high enough and if the
+degree distribution is sufficiently non-uniform. To decide whether or not
+to relabel the graph, we use the heuristic in WorthRelabelling.
+*/
+
+
+using namespace std;
 
-// assumes neighborhoods are sorted, no self loops, no duplicate edges
-// counts triangles only once by ordering u>v>w
 size_t OrderedCount(const Graph &g) {
   size_t total = 0;
   #pragma omp parallel for reduction(+ : total) schedule(dynamic)