Conflict - Aware Weighted Bipartite b - Matching and Its Application to E - Commerce ( Extended

Weighted bipartite b-matching (WBM) is one of the fundamental and widely studied problems in combinatorial optimization. Given a weighted bipartite graph G = (U, V,E) with weights W : E → R, where U , V and E represent left vertices, right vertices and edges, respectively, the weighted bipartite b-matching problem (WBM) is to find a subgraph H ⊆ G with maximum total weight w(H) = ∑ e∈H w(e), such that every vertex i in H is incident to at most b(i) edges. An implicit assumption of WBM is that any two nodes on the same side do not conflict with each other, even if they share similar features in practice. For example, a recommender system running WBM can recommend several books of the same subject to a reader, as long as the subject is his/her favorite and the availability constraints of the books are not violated. This, however, does not generate desired results in some real-world scenarios. For book recommendation, a reader may not want all recommended books from the same subject but instead may prefer books of diverse subjects so that more interesting topics can be discovered. However, considering conflicts would inevitably lead to new challenges for WBM when generating the matching result. This conflict challenge has not been fully studied and thus is the focus of this work. In this article, we introduce a new generalization of WBM, Conflict-Aware Weighted Bipartite b-Matching (CA-WBM), that can address the conflict challenges mentioned above.