Nonlinear Bipartite Matching

Generalized Stable Matching in Bipartite Networks

In this paper we study the generalized version of weighted matching in bipartite networks. Consider a weighted matching in a bipartite network in which the nodes derive value from the split of the matching edge assigned to them if they are matched. The value a node derives from the split depends both on the split as well as the partner the node is matched to. We assume that the value of a split to the node is continuous and strictly increasing in the part of the split assigned to the node. A stable weighted matching is a matching and splits on the edges in the matching such that no two adjacen…

Almost sure convergence of the minimum bipartite matching functional in Euclidean space

Let $L_N = L_{MBM}(X_1,..., X_N; Y_1,..., Y_N)$ be the minimum length of a bipartite matching between two sets of points in $\mathbf{R}^d$, where $X_1,..., X_N,...$ and $Y_1,..., Y_N,...$ are random points independently and uniformly distributed in $[0,1]^d$. We prove that for $d \ge 3$, $L_N/N^{1-1/d}$ converges with probability one to a constant $β_{MBM}(d)>0$ as $N\to \infty $.

随机二分匹配市场中的灵活性分配：精确匹配率与支配机制

Flexibility allocation in random bipartite matching markets: exact matching rates and dominance regimes

研究在平衡二分匹配市场中，如何分配固定灵活性预算以最大化渐近匹配率，通过局部弱收敛框架导出精确变分公式，并分析单侧分配与双侧分配的支配条件。

Semi-Streaming Bipartite Matching in Fewer Passes and Optimal Space

We provide $\widetilde{O}(ε^{-1})$-pass semi-streaming algorithms for computing $(1-ε)$-approximate maximum cardinality matchings in bipartite graphs. Our most efficient methods are deterministic and use optimal, $O(n)$, space, improving upon the space complexity of the previous state-of-the-art $\widetilde{O}(ε^{-1})$-pass algorithm of Ahn and Guha. To obtain our results we provide semi-streaming adaptations of more general continuous optimization tools. Further, we leverage these techniques to obtain improvements for streaming variants of approximate linear programming, optimal transport, ex…

Restricted Boltzmann Machine Assignment Algorithm: Application to solve many-to-one matching problems on weighted bipartite graph

In this work an iterative algorithm based on unsupervised learning is presented, specifically on a Restricted Boltzmann Machine (RBM) to solve a perfect matching problem on a bipartite weighted graph. Iteratively is calculated the weights $w_{ij}$ and the bias parameters $θ= ( a_i, b_j) $ that maximize the energy function and assignment element $i$ to element $j$. An application of real problem is presented to show the potentiality of this algorithm.

时空异质性下的动态随机二分匹配：通用模型及其在出行服务中的应用

Dynamic Random Bipartite Matching under Spatiotemporal Heterogeneity: General Models and Application to Mobility Services

本文提出时空随机二分匹配问题（ST-RBMP）建模框架，推导异质性场景下匹配距离闭式公式，将其建模为最优控制问题，可优化出行服务动态匹配策略、降低系统成本。