  Online bipartite matching is a fundamental problem in online algorithms. The
goal is to match two sets of vertices to maximize the sum of the edge weights,
where for one set of vertices, each vertex and its corresponding edge weights
appear in a sequence. Currently, in the practical recommendation system or
search engine, the weights are decided by the inner product between the deep
representation of a user and the deep representation of an item. The standard
online matching needs to pay $nd$ time to linear scan all the $n$ items,
computing weight (assuming each representation vector has length $d$), and then
deciding the matching based on the weights. However, in reality, the $n$ could
be very large, e.g. in online e-commerce platforms. Thus, improving the time of
computing weights is a problem of practical significance. In this work, we
provide the theoretical foundation for computing the weights approximately. We
show that, with our proposed randomized data structures, the weights can be
computed in sublinear time while still preserving the competitive ratio of the
matching algorithm.
