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arXiv · 2610.20140

An Analytic 0.48-Approximation for Non-Monotone k-Submodular Maximization under a Matroid Constraint

Zizong Wang·Yibo Wang
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Abstract

We give a randomized polynomial-time $0.48$-approximation for maximizing a nonnegative non-monotone $k$-submodular function under a matroid constraint, for every $k\ge2$. The algorithm combines a top-two label rule with a nested-chain potential and maximum-weight matroid bases. Its analysis reduces the approximation guarantee to a one-dimensional time allocation: a uniform local lower bound leads to a linear differential equation, concavity closes the remaining interval, and two elementary budgets complete the proof. A strict saving in the time budget absorbs sampling and discretization errors, yielding the exact $0.48$ guarantee in the value-oracle model.

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Zizong Wang, Yibo Wang. 2026-10-14. An Analytic 0.48-Approximation for Non-Monotone k-Submodular Maximization under a Matroid Constraint. https://arxiv.org/abs/2610.20140

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