Graph), a comprehensive benchmark of graph-based problem solving designed in natural language.

Here we cover the full specification of the experiments. Some details were omitted from the main text. If there were separate training and test sets, they were combined before creating the random 10-fold split. All attributes are normalized to mean 0 and standard deviation 1. Additional details for each model type follow.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. Thanks to your rebuttal, I think I now understand your algorithm, and I think it is correct. But why did you present in Figure 2 algorithm 2 with CB and not TCB? The algorithm with CB does not work, and it is misleading to put CB in Figure 2. I would recommend changing this and putting TCB in the presentation of your algorithm. Also, please comment on the necessity of knowing L(u_1,...,u_n) (or rather an upper bound on this, and rewrite the Thm with an upper bound since it is not realistic to have truly this quantity available).

Traditionally, these would be made according to hard-coded expert heuristics implemented in solvers.

This paper introduces GraphOmni, a comprehensive benchmark designed to evaluate the reasoning capabilities of LLMs on graph-theoretic tasks articulated in natural language. GraphOmni encompasses diverse graph types, serialization formats, and prompting schemes, significantly exceeding prior efforts in both scope and depth. Through extensive systematic evaluation, we identify critical interactions among these dimensions, demonstrating their substantial impact on model performance. Our experiments reveal that state-of-the-art models like Claude-3.5 and o4-mini consistently outperform other models, yet even these leading models exhibit substantial room for improvement. Performance variability is evident depending on the specific combinations of factors we considered, underscoring the necessity of comprehensive evaluations across these interconnected dimensions. Additionally, we observe distinct impacts of serialization and prompting strategies between open-source and closed-source models, encouraging the development of tailored approaches. Motivated by the findings, we also propose a reinforcement learning-inspired framework that adaptively selects the optimal factors influencing LLM reasoning capabilities. This flexible and extendable benchmark not only deepens our understanding of LLM performance on structured tasks but also provides a robust foundation for advancing research in LLM-based graph reasoning. The code and datasets are available at https://github.com/GAI-Community/GraphOmni.

A total of more than 3400 public shootings have occurred in the United States between 2016 and 2022. Among these, 25.1% of them took place in an educational institution, 29.4% at the workplace including office buildings, 19.6% in retail store locations, and 13.4% in restaurants and bars. During these critical scenarios, making the right decisions while evacuating can make the difference between life and death. However, emergency evacuation is intensely stressful, which along with the lack of verifiable real-time information may lead to fatal incorrect decisions. To tackle this problem, we developed a multi-route routing optimization algorithm that determines multiple optimal safe routes for each evacuee while accounting for available capacity along the route, thus reducing the threat of crowding and bottlenecking. Overall, our algorithm reduces the total casualties by 34.16% and 53.3%, compared to our previous routing algorithm without capacity constraints and an expert-advised routing strategy respectively. Further, our approach to reduce crowding resulted in an approximate 50% reduction in occupancy in key bottlenecking nodes compared to both of the other evacuation algorithms.

Game-theoretic resource allocation on graphs (GRAG) involves two players competing over multiple steps to control nodes of interest on a graph, a problem modeled as a multi-step Colonel Blotto Game (MCBG). Finding optimal strategies is challenging due to the dynamic action space and structural constraints imposed by the graph. To address this, we formulate the MCBG as a Markov Decision Process (MDP) and apply Reinforcement Learning (RL) methods, specifically Deep Q-Network (DQN) and Proximal Policy Optimization (PPO). To enforce graph constraints, we introduce an action-displacement adjacency matrix that dynamically generates valid action sets at each step. We evaluate RL performance across a variety of graph structures and initial resource distributions, comparing against random, greedy, and learned RL policies. Experimental results show that both DQN and PPO consistently outperform baseline strategies and converge to a balanced $50\%$ win rate when competing against the learned RL policy. Particularly, on asymmetric graphs, RL agents successfully exploit structural advantages and adapt their allocation strategies, even under disadvantageous initial resource distributions.