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arXiv · 2606.04946

A General Framework for Dynamic Consistent Submodular Maximization

Paul Dütting·Federico Fusco·Silvio Lattanzi·Ashkan Norouzi-Fard·Ola Svensson·Morteza Zadimoghaddam
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Abstract

Consistency is an important property in dynamic submodular maximization and entails maintaining a near-optimal solution at all times, making only a small number of adjustments to the solution in each step. Prior work has explored this question for the insertion-only case, where the algorithm faces a stream of $n$ insertions, and has established lower and upper bounds for the cardinality-constrained version of the problem. We consider this question in the fully dynamic setting, where the stream of operations may contain both insertions and deletions. We develop a general framework for designing algorithms for this setting, and instantiate it to obtain the first constant-factor approximations with sublinear consistency. For cardinality constraints, we propose a $\frac 12 - O(\varepsilon)$ approximation that is $O\left(\frac{1}{\varepsilon^2}\right)$ consistent. For rank-$k$ matroid constraints, we construct a $\frac 14 - O(\varepsilon)$ approximation to the dynamic optimum that is $O\left(\frac{\log k}{\varepsilon^2}\right)$ consistent.

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Paul Dütting, Federico Fusco, Silvio Lattanzi, Ashkan Norouzi-Fard, Ola Svensson, Morteza Zadimoghaddam. 2026-06-03. A General Framework for Dynamic Consistent Submodular Maximization. https://arxiv.org/abs/2606.04946

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