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Learning with Simulators: No Regret in a Computationally Bounded World Temporal Conductance and Bounds on the Voter Model for Dynamic Networks Diffusion-Network Alignment: An Efficient Algorithm and Explicit Probability Bounds A unified complexity bound for logconcave sampling Nearly Instance Optimal Sparse Matrix Approximation from Matrix-Vector Products Near-Optimal Distributed 2-Ruling Sets on Graphs with Low Arboricity On finding exact solutions of linear programs in the oracle model A Fast Gaussian Mechanism under Continual Observation, with Applications Beyond Frequency Marching: Orbit Recovery in Dihedral and Projected Multireference Alignment Density estimation for Hellinger via minimum-distance estimators: mixtures of Gaussians, log-concave, and more A Unified Lower Bound on the Noisy Query Complexity of Boolean Functions The Power of Test-Time Training for Approximate Sampling Fixed-Parameter Tractability of Private Synthetic Data Generation Express Language Modeling The 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Perfect Fractional Matchings in Bipartite Graphs Via Proportional Allocations
Daniel Hathcock, R. Ravi · 2025-10-02 · via cs.DS updates on arXiv.org

Given a bipartite graph that has a perfect matching, a prefect proportional allocation is an assignment of positive weights to the nodes of the right partition so that every left node is fractionally assigned to its neighbors in proportion to their weights, and these assignments define a fractional perfect matching. We prove that a bipartite graph has a perfect proportional allocation if and only if it is matching covered, by using a classical result on matrix scaling. We also present an extension of this result to provide a simple allocation strategy in non-matching covered bipartite graphs.

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