Man-made and natural disruptions such as planned constructions on roads, suspensions of bridges, and blocked roads by trees/mudslides/floods can often create obstacles that separate two connected regions. As a result, the traveling and reachability of agents from their respective regions to other regions can be affected. To minimize the impact of the obstacles and maintain agent accessibility, we initiate the problem of constructing a new pathway (e.g., a detour or new bridge) connecting the regions disconnected by obstacles from the mechanism design perspective. In the problem, each agent in their region has a private location and is required to access the other region. The cost of an agent is the distance from their location to the other region via the pathway. Our goal is to design strategyproof mechanisms that elicit truthful locations from the agents and approximately optimize the social or maximum cost of agents by determining locations in the regions for building a pathway. We provide a characterization of all strategyproof and anonymous mechanisms. For the social and maximum costs, we provide upper and lower bounds on the approximation ratios of strategyproof mechanisms.

Large Language Models (LLMs) have demonstrated amazing capabilities in language generation, comprehension, and knowledge reasoning. However, relying on a single model can result in biased and unstable outcomes in many tasks. Multi-model collaboration has been introduced to enhance reasoning abilities on various tasks, but obtaining the correct answer from multiple candidate responses remains a challenge. To address this issue, we propose multi-model brainstorming based on prompt. It incorporates different models into a group for brainstorming, to reach a consensus answer after multiple rounds of reasoning elaboration and re-inference. Our experiments on diverse datasets demonstrate that the brainstorming can substantially improve the effectiveness in logical reasoning. Further, we observe that two small-parameter models can achieve accuracy comparable to a larger-parameter model through brainstorming, presenting a novel approach for the distributed deployment of LLMs.