arXiv subjects

Zhaozi Wang

Publications and source records attributed to Zhaozi Wang.

4 recordsLinked to original sources

arXiv2026

Distributed Load Balancing on Unrelated Machines

We study the well-known load balancing problem in the distributed CONGEST model of computation. We consider the unrelated machines setting, where each job $j$ specifies a size $s_{ij}$ for every machine $i$. We want to find an assignment $φ: J \to M$ minimizing the maximum machine load, where the load of a machine $i$ is the total size of the jobs assigned to it. In the CONGEST model, the state-of-the-art is an algorithm that runs in polylog rounds and returns a $(1+\varepsilon)$-approximate fractional solution from Ahmadian, Liu, Peng, and Zadimoghaddam (2021). However, this algorithm, as well as all previous CONGEST algorithms only solve a special case of load balancing, where each job has the same size on each machine. Our main contribution is an algorithm for general sizes $s_{ij}$. The algorithm computes a $(1+\varepsilon)$-approximate fractional solution or a $(2+\varepsilon)$-approximate integral solution in polylog rounds. The problem structure changes significantly once we allow arbitrary edge-sizes, so our techniques are very different from those used in previous algorithms for distributed load balancing. One ingredient of our result is a black-box tool of independent interest: a $(1+\varepsilon)$-approximation algorithm to arbitrary mixed packing-covering linear programs in the CONGEST model in polylog rounds. such algorithms were known in the more powerful parallel model, but previous polylog-round algorithms in the distributed CONGEST model only solved pure packing or pure covering problems. We improve upon a recent $O(D\,\mathrm{polylog})$-round CONGEST algorithm for mixed packing-covering, where $D$ is the diameter of the communication graph.

cs.DS↗

arXiv2025

FrontierCS: Evolving Challenges for Evolving Intelligence

We introduce FrontierCS, a benchmark of 156 open-ended problems across diverse areas of computer science, designed and reviewed by experts, including CS PhDs and top-tier competitive programming participants and problem setters. Unlike existing benchmarks that focus on tasks with known optimal solutions, FrontierCS targets problems where the optimal solution is unknown, but the quality of a solution can be objectively evaluated. Models solve these tasks by implementing executable programs rather than outputting a direct answer. FrontierCS includes algorithmic problems, which are often NP-hard variants of competitive programming problems with objective partial scoring, and research problems with the same property. For each problem we provide an expert reference solution and an automatic evaluator. Combining open-ended design, measurable progress, and expert curation, FrontierCS provides a benchmark at the frontier of computer-science difficulty. Empirically, we find that frontier reasoning models still lag far behind human experts on both the algorithmic and research tracks, that increasing reasoning budgets alone does not close this gap, and that models often over-optimize for generating merely workable code instead of discovering high-quality algorithms and system designs.

cs.LG↗

arXiv2025

Online Makespan Minimization: Beat LPT by Dynamic Locking

Online makespan minimization is a fundamental problem in scheduling. In this paper, we investigate its over-time formulation, where each job has a release time and a processing time. A job becomes known only at its release time and must be scheduled on a machine thereafter. The Longest Processing Time First (LPT) algorithm, established by Chen and Vestjens (1997), achieves a competitive ratio of $1.5$. For the special case of two machines, Noga and Seiden introduced the SLEEPY algorithm, which achieves a tight competitive ratio of $1.382$. However, for $m \geq 3$, no known algorithm has convincingly surpassed the long-standing $1.5$ barrier. We propose a natural generalization of SLEEPY and show this simple approach can beat the $1.5$ barrier and achieve $1.482$-competitive when $m=3$. However, when $m$ becomes large, we prove this simple generalization fails to beat $1.5$. Meanwhile, we introduce a novel technique called dynamic locking to overcome this new challenge. As a result, we achieve a competitive ratio of $1.5-\frac{1}{O(m^2)}$, which beats the LPT algorithm ($1.5$-competitive) for every constant $m$.

cs.DS↗

arXiv2025

The Long Arm of Nashian Allocation in Online $p$-Mean Welfare Maximization

We study the online allocation of divisible items to $n$ agents with additive valuations for $p$-mean welfare maximization, a problem introduced by Barman, Khan, and Maiti~(2022). Our algorithmic and hardness results characterize the optimal competitive ratios for the entire spectrum of $-\infty \le p \le 1$. Surprisingly, our improved algorithms for all $p \le \frac{1}{\log n}$ are simply the greedy algorithm for the Nash welfare, supplemented with two auxiliary components to ensure all agents have non-zero utilities and to help a small number of agents with low utilities. In this sense, the long arm of Nashian allocation achieves near-optimal competitive ratios not only for Nash welfare but also all the way to egalitarian welfare.

cs.GT↗