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In this paper, we consider the online vertex-weighted bipartite matchingproblem in the random arrival model. We consider the generalization of theRANKING algorithm for this problem introduced by Huang, Tang, Wu, and Zhang(TALG 2019), who show that their algorithm has a competitive ratio of 0.6534.We show that assumptions in their analysis can be weakened, allowing us toreplace their derivation of a crucial function $g$ on the unit square with alinear program that computes the values of a best possible $g$ under theseassumptions on a discretized unit square. We show that the discretization doesnot incur much error, and show computationally that we can obtain a competitiveratio of 0.6629. To compute the bound over our discretized unit square we useparallelization, and still needed two days of computing on a 64-core machine.Furthermore, by modifying our linear program somewhat, we can showcomputationally an upper bound on our approach of 0.6688; any further progressbeyond this bound will require either further weakening in the assumptions of$g$ or a stronger analysis than that of Huang et al.

Improved Analysis of RANKING for Online Vertex-Weighted Bipartite Matching in the Random Order Model