Combinatorial optimization (CO) problems, central to decision-making scenarios like logistics and manufacturing, are traditionally solved using problem-specific algorithms requiring significant domain expertise. While large language models (LLMs) have shown promise in automating CO problem solving, existing approaches rely on intermediate steps such as code generation or solver invocation, limiting their generality and accessibility. This paper introduces a novel framework that empowers LLMs to serve as end-to-end CO solvers by directly mapping natural language problem descriptions to solutions.

We consider the problem of scheduling mjobs on nunrelated strategic machines to minimize the maximum load of any machine. As the machines are strategic they may misreport processing times to minimize their own load. The pioneering work of Nisan and Ronen gave an n-approximate deterministic strategyproof mechanism for this setting, and this was recently shown to be best possible by the breakthrough results of Christodoulou et al. This large approxation guarantee begs the question: how can we avoid these large worst-case results. In this work, we use the powerful framework of algorithms with (machine-learned) predictions to bypass these strong impossibility results. We show how we can predict O(m+n)values to obtain a deterministic strategyproof algorithm whose makespan is within a constant factor of the optimal makespan when the predictions are correct, and O(n) times the optimum no matter how poor the predictions are.

In non-clairvoyant scheduling, the goal is to minimize the total job completion time without prior knowledge of individual job processing times. This classical online optimization problem has recently gained attention through the framework of learning-augmented algorithms. We introduce a natural setting in which the scheduler receives continuous feedback in the form of progress bars--estimates of the fraction of each job completed over time. We design new algorithms for both adversarial and stochastic progress bars and prove strong competitive bounds. Our results in the adversarial case surprisingly induce improved guarantees for learning-augmented scheduling with job size predictions. We also introduce a general method for combining scheduling algorithms, yielding further insights in scheduling with predictions. Finally, we propose a stochastic model of progress bars as a more optimistic alternative to conventional worst-case models, and present an asymptotically optimal scheduling algorithm in this setting.

This study considers a novel problem setting, referred to as bandit task assignment, that incorporates the processing time of each task in the bandit setting. In this problem setting, a player sequentially chooses a set of tasks to start so that the set of processing tasks satisfies a given combinatorial constraint. The reward and processing time for each task follow unknown distributions, values of which are revealed only after the task has been completed.

A procedure of IHT consists of two main parts in an iteration.

Recent language models have shown impressive multilingual performance, even when not explicitly trained for it. Despite this, there are concerns about the quality of their outputs across different languages. In this paper, we show how disparity in the treatment of different languages arises at the tokenization stage, well before a model is even invoked. The same text translated into different languages can have drastically different tok-enization lengths, with differences up to 15 times in some cases. These disparities persist even for tokenizers that are intentionally trained for multilingual support.

There aretwointeresting andwell-studied computational paradigms aimed attackling uncertainty.

The machines gain possibly different utilities by processing different jobs, and alljobs assigned tothesame machine should beprocessed without overlap.