Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.16785

A Deterministic $0.401$-Approximation for Non-monotone Submodular Maximization under Matroid Constraints

Shengminjie Chen·Kaifeng Lin·Xiaoming Sun·Jialin Zhang
View original source ↗Read source document ↗Export metadata ↓

Abstract

Submodular maximization arises in a wide range of combinatorial optimization problems and has been extensively studied from the perspective of approximation algorithms. For maximizing nonnegative, non-monotone submodular functions subject to a matroid constraint, randomized algorithms achieve a $0.401$-approximation, whereas obtaining comparable deterministic guarantees remains challenging. In this paper, we present a deterministic $0.401$-approximation algorithm in the exact value and independence oracle model, improving upon the previous deterministic guarantee of $(0.385-\varepsilon)$ \cite{ChenGLSZ2026}. Our algorithm builds on the extended multilinear extension and provides a deterministic implementation of the recursive guided framework underlying the randomized $0.401$-approximation algorithm. The main technical ingredient is a direction oracle supported on at most two partitioned matroid bases. This oracle simultaneously satisfies the growth condition required by the extended-multilinear update and an approximate stationarity condition needed to construct the recursive guides. The resulting finite-support representation enables exact evaluation of the relevant expectations and marginal values without random sampling. The algorithm uses polynomially many value- and independence-oracle queries.

Explore related subjects

cs.DSmath.OC

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Shengminjie Chen, Kaifeng Lin, Xiaoming Sun, Jialin Zhang. 2026-10-12. A Deterministic $0.401$-Approximation for Non-monotone Submodular Maximization under Matroid Constraints. https://arxiv.org/abs/2610.16785

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Adding an Edge in a $P_4$-sparse Graph

For a graph family~${\cal F}$, the minimum ${\cal F}$-completion problem asks for the minimum number of non-edges to be added to a given graph~$G$ so that the resulting graph belongs to the family~${\cal F}$. This problem is NP-complete for many subclasses of perfect graphs, while polynomial solutions are available for minimal completion sets or restricted input. We study the minimum $P_4$-sparse completion problem that arises after adding a prescribed non-edge to a \(P_4\)-sparse graph \(G\), with the resulting graph required to remain \(P_4\)-sparse. For the case in which $G$ consists of two connected components, each containing one endpoint of the added non-edge, we characterize the possible forms of an optimal solution. Combining this characterization with the solution of the other cases identified by the structural decomposition of \(P_4\)-sparse graphs, we obtain an algorithm for the general problem that runs in $O(n^2)$ time and $O(n)$ space.

cs.DS↗
arXiv2026

Optimal Extrapolation Bounds for Sparse Fourier Sums

We prove a sharp extrapolation bound for $k$-sparse Fourier sums with arbitrary real frequencies and no separation assumption. For every $g(t)=\sum_{j=1}^k v_je^{iλ_jt}$ with $λ_j\in\mathbb{R}$ and every $x\geq 1$, \begin{align*} |g(x)|\le k\exp(O(k\operatorname{arcosh} x))\|g\|_{L^2[-1,1]}. \end{align*} Near the endpoint at $x=1+δ$, this gives an exponential factor of $\exp(O(k\sqrtδ))$, improving on the $\exp(O(k^2\log k\cdotδ))$ estimate of Chen and Price (ICALP 2019), and the exponent is optimal up to a constant factor. Our theorem has algorithmic applications to recovering gapless Fourier-sparse signals: it improves the resolution of cluster-location algorithms and the sample complexity of Fourier interpolation algorithms. In addition, it gives sharp bounds on the error transfer of sparse Fourier models just outside the training interval.

cs.DS↗
arXiv2026

Stochastic Network Speed Scaling with Competitive Ratios Independent of the Network

In network speed scaling, jobs arrive over time at a network of servers whose speeds can be tuned, every job must be processed by the servers along one of its allowed routes, and the goal is to minimize the total flow time plus the total energy. For stochastic arrivals, the competitive ratio of Vaze and Nair depends on the network, through the lengths of the routes it uses. We show that this dependence can be removed: we give an algorithm, which routes the jobs by solving a convex program and runs every server at a fixed speed, whose competitive ratio depends only on the power functions; for $P(s)=s^2$, it is at most the golden ratio $φ\approx1.618$. The key idea is a lower bound on the optimal cost which, like the cost of our algorithm, is a sum over the servers of a function of each server's load, so the analysis reduces to a single server. We also show that the routing rule of Vaze and Nair can be a factor $Ω(L)$ away from optimal, where $L$ is the length of the longest route.

cs.DS↗