Geometry-Dependent Approximation for Non-Monotone $k$-Submodular Maximization
We study nonnegative, non-monotone $k$-submodular maximization with $k\ge2$ labels under support constraints, and show how the certified approximation coefficient improves as the support region permits more uniform selection. For a compact convex down-closed support region $P\subseteq[0,1]^n$, the diagonal level $ζ(P)=\max\{t\in[0,1]:t {\bf 1} \in P\}$ ranges from $ζ=0$, which carries no geometric promise, to $ζ=1$, which is unrestricted support. Our main structural result is a comparator-uniform linearization of the multilinear extension, built from an objective-independent action and a comparator-independent update field. For $k\ge3$, its validity reduces, independently of the number of...
| Authors | Vaneet Aggarwal |
|---|---|
| Primary category | cs.DS |
| Published | 2 October 2026 |
| Last updated at source | 2 October 2026 |
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