. ALGORITHMIC APPROACH
In this section we describe an algorithmic approach for
generating a useful and diverse list of related businesses for
a source business x. We assume that we are given the relevance scores between every pair of categories, and how relevant a business y is to x given a desired recommendation
category. In the next section, we explain how we mine such
signals from data, and for the purpose of the discussion in
this section, we treat these two signals as given.
We first construct an optimization problem for generating
a useful and diverse list of related business recommendations
in the more general setting where each business can belong
to any number of categories, and we explain the reasoning
behind that construction. Since the problem under this setting is NP-hard, we relax the problem by associating each
business to a single category, which results in an optimization problem that can be solved in polynomial time using a
simple greedy algorithm.
Relevance Scores: We begin by explaining how the relevance between businesses is determined, and introducing
notation that we will use in this section and throughout the
rest of the pape