Some Vignettes on Subgraph Counting Using Graph Orientations (Invited Talk)

Abstract

Subgraph counting is a fundamental problem that spans many areas in computer science: database theory, logic, network science, data mining, and complexity theory. Given a large input graph G and a small pattern graph H , we wish to count the number of occurrences of H in G . In recent times, there has been a resurgence on using an old (maybe overlooked?) technique of orienting the edges of G and H , and then using a combination of brute-force enumeration and indexing. These orientation techniques appear to give the best of both worlds. There is a rigorous theoretical explanation behind these techniques, and they also have excellent empirical behavior (on large real-world graphs). Time and again, graph orientations help solve subgraph counting problems in various computational models, be it sampling, streaming, distributed, etc. In this paper, we give some short vignettes on how the orientation technique solves a variety of algorithmic problems.