Improving I/O Complexity of Triangle Enumeration

In the age of big data, many graph algorithms are now required to operate in external memory and deliver performance that does not significantly degrade with the scale of the problem. One particular area that frequently deals with graphs larger than RAM is
triangle listing
, where the algorithms must carefully piece together edges from multiple partitions to detect cycles. In recent literature, two competing proposals (i.e., Pagh and PCF) have emerged; however, neither one is universally better than the other. Since little is known about the I/O cost of PCF or how these methods compare to each other, we undertake an investigation into the properties of these algorithms, model their I/O cost, understand their shortcomings, and shed light on the conditions under which each method defeats the other. This insight leads us to develop a novel framework we call Trigon that surpasses the I/O performance of both previous techniques in all graphs and under all RAM conditions.