Group-Aware Weighted Bipartite B-Matching

The weighted bipartite B-matching (WBM) problem models a host of data management applications, ranging from recommender systems to Internet advertising and e-commerce. Many of these applications, however, demand versatile assignment constraints, which WBM is weak at modelling. In this paper, we investigate powerful generalisations of WBM. We first show that a recent proposal for conflict-aware WBM by Chen et al. is hard to approximate by reducing their problem from Maximum Weight Independent Set. We then propose two related problems, collectively called group-aware WBM. For the first problem, which constrains the degree of groups of vertices, we show that a linear programming formulation produces a Totally Unimodular (TU) matrix and is thus polynomial-time solvable. Nonetheless, we also give a simple greedy algorithm subject to a 2-extendible system that scales to higher workloads. For the second problem, which instead limits the budget of groups of vertices, we prove its NP-hardness but again give a greedy algorithm with an approximation guarantee. Our experimental evaluation reveals that the greedy algorithms vastly outperform their theoretical guarantees and scale to bipartite graphs with more than eleven million edges.