标题： 子模最大化问题在均匀和划分拟阵约束下的理论与实际应用及分布式解决方案 显示英文标题

标题： Submodular Maximization Subject to Uniform and Partition Matroids: From Theory to Practical Applications and Distributed Solutions

摘要： 本文全面探讨了子模最大化问题，重点研究受统一和划分拟阵约束的问题。 在从计算机科学到系统工程的广泛领域中至关重要，子模最大化涉及从离散集合中选择元素，在某些约束下优化子模效用函数。 我们探讨了子模函数和拟阵的基础方面，概述了它们的核心属性，并通过各种优化场景说明了它们的应用。 我们论述的核心是算法策略，特别是顺序贪心算法及其在拟阵约束下的有效性。 此外，我们将分析扩展到分布式子模最大化，强调大规模分布式优化问题的挑战和解决方案。 本研究旨在简洁地弥合子模最大化理论见解与实际应用之间的差距，为研究人员在此复杂领域提供坚实的基础。 显示英文摘要

摘要： This article provides a comprehensive exploration of submodular maximization problems, focusing on those subject to uniform and partition matroids. Crucial for a wide array of applications in fields ranging from computer science to systems engineering, submodular maximization entails selecting elements from a discrete set to optimize a submodular utility function under certain constraints. We explore the foundational aspects of submodular functions and matroids, outlining their core properties and illustrating their application through various optimization scenarios. Central to our exposition is the discussion on algorithmic strategies, particularly the sequential greedy algorithm and its efficacy under matroid constraints. Additionally, we extend our analysis to distributed submodular maximization, highlighting the challenges and solutions for large-scale, distributed optimization problems. This work aims to succinctly bridge the gap between theoretical insights and practical applications in submodular maximization, providing a solid foundation for researchers navigating this intricate domain.