Recommendation Subgraphs for Web Discovery

Recommendations are central to the utility of many popular e-commerce websites. Such sites typically contain a set of recommendations on every product page that enables visitors and crawlers to easily navigate the website. These recommendations are essentially universally present on all e-commerce websites. Choosing an appropriate set of recommendations at each page is a critical task performed by dedicated backend software systems. We formalize the concept of recommendations used for discovery as a natural graph optimization problem on a bipartite graph and propose three methods for solving the problem in increasing order of sophistication: a local random sampling algorithm, a greedy algorithm and a more involved partitioning based algorithm. We first theoretically analyze the performance of these three methods on random graph models and characterize when each method will yield a solution of sufficient quality and the parameter ranges when more sophistication is needed. We complement this by roviding an empirical analysis of these algorithms on simulated and real-world production data from a retail website. Our results confirm that it is not always necessary to implement complicated algorithms in the real-world, and demonstrate that very good practical results can be obtained by using simple heuristics that are backed by the confidence of concrete theoretical guarantees.