An Analytic 0.48-Approximation for Non-Monotone k-Submodular Maximization under a Matroid Constraint
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Wang, Zizong, Wang, Yibo, Yang, Wenguo
Institution: University of Chinese Academy of Sciences
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222234715