Accelerated Relax-and-Round for Concave Coverage Problems

• URL: http://arxiv.org/abs/2605.06900v1
• Date: Thu, 07 May 2026 20:00:40 GMT
• Title: Accelerated Relax-and-Round for Concave Coverage Problems
• Abstract summary: We present an accelerated relax-and-round algorithm for concave coverage problems.<n>Our algorithm outperforms approaches that use state-of-the-art LP solvers.
• Score: 7.984421247931201
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present an accelerated relax-and-round algorithm for concave coverage problems, which generalize the classic maximum coverage problem. Building on the relax-and-round framework of Barman et al. [STACS 2021], we propose two significant improvements. First, we replace the linear programming (LP) relaxation step with a projected accelerated gradient method applied to a smooth surrogate objective to achieve a $\widetilde{O}(mn \varepsilon^{-1})$ running time. Second, we use a specialized rounding scheme for the hypersimplex that combines the Carathéodory decomposition algorithm in Karalias et al. [NeurIPS 2025] with randomized swap rounding of Chekuri et al. [FOCS 2010]. We prove tight approximation ratios for new reward functions, including a $0.827$-approximation for the logarithmic reward $\varphi(x) = \log(1 + x)$. Finally, we conduct maximum multi-coverage experiments on synthetic and real-world graphs, demonstrating that our algorithm outperforms approaches that use state-of-the-art LP solvers.

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