Kaifeng Lin | Searcharxiv

arXiv2026

Generalized Balls into Bins

Consider a set of bins and two-choice balls arriving by a Poisson process. We must allocate each incoming ball immediately to one of two incident bins. For a given function $f$ and every bin, we aim to bound the expectation of $f(L)$---where $L$ is the bin's final load---based on the arrival rate of balls incident to that bin. We call this problem Generalized Balls into Bins, capturing many problems as special cases including the original Balls into Bins by Azar et al. (1994) and Online Stochastic Matching by Feldman et al. (2009). We show that Greedy provides optimal amortized bounds for all convex and concave functions $f$. Further, we propose another algorithm that achieves non-trivial bounds without amortization. As an application, we design a competitive algorithm for a stochastic model of completion time minimization on unrelated machines.

cs.DS↗

arXiv2026

Deterministic Algorithm for Non-monotone Submodular Maximization under Matroid and Knapsack Constraints

Submodular maximization constitutes a prominent research topic in combinatorial optimization and theoretical computer science, with extensive applications across diverse domains. While substantial advancements have been achieved in approximation algorithms for submodular maximization, the majority of algorithms yielding high approximation guarantees are randomized. In this work, we investigate deterministic approximation algorithms for maximizing non-monotone submodular functions subject to matroid and knapsack constraints. For the two distinct constraint settings, we propose novel deterministic algorithms grounded in an extended multilinear extension framework. Under matroid constraints, our algorithm achieves an approximation ratio of $(0.385 - \epsilon)$, whereas for knapsack constraints, the proposed algorithm attains an approximation ratio of $(0.367 -\epsilon)$. Both algorithms run in $\mathrm{poly}(n)$ query complexity, where $n$ is the size of the ground set, and improve upon the state-of-the-art deterministic approximation ratios of $(0.367 - \epsilon)$ for matroid constraints and $0.25$ for knapsack constraints.

cs.DS↗