Yingxi Li

Yingxi Li, Ellen Vitercik, Mingwei Yang

In the online metric matching problem, $n$ servers and $n$ requests lie in a metric space. Servers are available upfront, and requests arrive sequentially. An arriving request must be matched immediately and irrevocably to an available server, incurring a cost equal to their distance. The goal is to minimize the total matching cost. We study this problem in the Euclidean metric $[0, 1]^d$, when servers are adversarial and requests are independently drawn from distinct distributions that satisfy a mild smoothness condition. Our main result is an $O(1)$-competitive algorithm for $d \neq 2$ that requires no distributional knowledge, relying only on a single sample from each request distribution. To our knowledge, this is the first algorithm to achieve an $o(\log n)$ competitive ratio for non-trivial metrics beyond the i.i.d. setting. Our approach bypasses the $Ω(\log n)$ barrier introduced by probabilistic metric embeddings: instead of analyzing the embedding distortion and the algorithm separately, we directly bound the cost of the algorithm on the target metric of a simple deterministic embedding. We then combine this analysis with lower bounds on the offline optimum for Euclidean metrics, derived via majorization arguments, to obtain our guarantees.

Connor Lawless, Yingxi Li, Anders Wikum et al.

Mixed integer linear programming (MILP) solvers expose hundreds of parameters that have an outsized impact on performance but are difficult to configure for all but expert users. Existing machine learning (ML) approaches require training on thousands of related instances, generalize poorly and can be difficult to integrate into existing solver workflows. We propose a large language model (LLM)-based framework that configures cutting plane separators using problem descriptions and solver-specific separator summaries. To reduce variance in LLM outputs, we introduce an ensembling strategy that clusters and aggregates candidate configurations into a small portfolio of high-performing configurations. Our method requires no custom solver interface, generates configurations in seconds via simple API calls, and requires solving only a small number of instances. Extensive experiments on standard synthetic and real-world MILPs show our approach matches or outperforms state-of-the-art configuration methods with a fraction of the data and computation.

Yu He, Yingxi Li, Colin White et al.

As large language models (LLMs) take on increasingly complex tasks, understanding their algorithmic reasoning abilities has become essential. However, existing evaluations focus on distinct and isolated tasks. We propose a unified diagnostic lens: structural reasoning--understanding and manipulating relationships like order, hierarchy, and connectivity. We introduce DSR-Bench, the first benchmark to systematically evaluate LLM structural reasoning through canonical data structures, which serve as interpretable, algorithmically meaningful abstractions. DSR-Bench spans 20 data structures, 35 operations, and 4,140 synthetically generated problem instances with minimal contamination. The benchmark's hierarchical design pinpoints specific failure modes, while its fully automated evaluation ensures objective and consistent assessment. Benchmarking ten state-of-the-art LLMs reveals critical limitations: the top-performing model scores only 0.498 out of 1 on challenging instances. Three additional evaluation suites reveal further weaknesses: models perform poorly on spatial data and natural language scenarios, and fail to reason over their own generated code. DSR-Bench offers a principled diagnostic tool for structural reasoning, helping expose reasoning bottlenecks and guide the development of more capable and reliable LLMs.