Technology Category
Search and Optimization: Sampling/Simulation-based SearchConstraint Satisfaction and Optimization: Distributed CSP/OptimizationReasoning under Uncertainty: Stochastic Optimization
A framework for boosting matching approximation: parallel, distributed, and dynamic
🤖 AI Summary
This paper addresses the approximation-accuracy and efficiency bottlenecks of the maximum matching problem in parallel (MPC/CONGEST), distributed, and dynamic settings. We propose the first general black-box framework that boosts any constant-factor approximation algorithm to a $(1+varepsilon)$-approximation via polynomially many oracle calls. Our key contribution is the first reduction of black-box query complexity across all models—from exponential (e.g., $O(1/varepsilon^{39})$) to polynomial: $O(log(1/varepsilon)/varepsilon^7)$ in MPC/CONGEST, and polynomial dependence on $1/varepsilon$ (instead of exponential) in dynamic settings. The framework unifies iterative refinement and hierarchical sampling techniques, enabling seamless adaptation across models. As a result, it significantly enhances scalability and practicality of approximate matching algorithms in all three computational paradigms.
Technology Category
Application Category
📝 Abstract
This work designs a framework for boosting the approximation guarantee of maximum matching algorithms. As input, the framework receives a parameter $epsilon>0$ and an oracle access to a $Theta(1)$-approximate maximum matching algorithm $mathcal{A}$. Then, by invoking $mathcal{A}$ for $ ext{poly}(1/epsilon)$ many times, the framework outputs a $1+epsilon$ approximation of a maximum matching. Our approach yields several improvements in terms of the number of invocations to $mathcal{A}$: (1) In MPC and CONGEST, our framework invokes $mathcal{A}$ for $O(1/epsilon^7 cdot log(1/epsilon))$ times, substantially improving on $O(1/epsilon^{39})$ invocations following from [Fischer et al., STOC'22] and [Mitrovic et al., arXiv:2412.19057]. (2) In both online and offline fully dynamic settings, our framework yields an improvement in the dependence on $1/epsilon$ from exponential [Assadi et al., SODA25 and Liu, FOCS24] to polynomial.
Problem
Research questions and friction points this paper is trying to address.
Boosts approximation guarantee for maximum matching algorithms.
Reduces invocations to oracle in MPC and CONGEST models.
Improves dynamic settings from exponential to polynomial dependence.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Boosts matching approximation via parallel, distributed, dynamic framework.
Reduces invocations to Θ(1)-approximate algorithm significantly.
Improves ε-dependence from exponential to polynomial.
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