Conflict-Aware Weighted Bipartite B-Matching and Its Application to E-Commerce

The weighted bipartite b-matching problem (WBM) plays a significant role in many real-world applications, including resource allocation, scheduling, Internet advertising, and E-commerce. WBM has been widely studied and efficient matching algorithms are well known. In this work, we study a novel variant of WBM, called conflict-aware WBM (CA-WBM), where conflict constraints are present between vertices of the bipartite graph. In CA-WBM, if two vertices (on the same side) are in conflict, they may not be included in the matching result simultaneously. We present a generalized formulation of CA-WBM in the context of E-commerce, where diverse matching results are often desired (e.g., movies of different genres and merchants selling products of different categories). While WBM is efficiently solvable in polynomial-time, we show that CA-WBM is NP-hard. We propose approximate and randomized algorithms to solve CA-WBM and show that they achieve close to optimal solutions via comprehensive experiments using synthetic datasets. We derive a theoretical bound on the approximation ratio of a greedy algorithm for CA-WBM and show that it is scalable on a large-scale real-world dataset.