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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. 

We study a variation of facility location problems (FLPs) that aims to improve the accessibility of agents to the facility within the context of mechanism design without money. In such a variation, agents have preferences on the ideal locations of the facility on a real line, and the facility’s location is fixed in advance where (re)locating the facility is not possible due to various constraints (e.g., limited space and construction costs). To improve the accessibility of agents to facilities, existing mechanism design literature in FLPs has proposed to structurally modify the real line (e.g., by adding a new interval) or provide shuttle services between two points when structural modifications are not possible. In this paper, we focus on the latter approach and propose to construct an accessibility range to extend the accessibility of the facility. In the range, agents can receive accommodations (e.g., school buses, campus shuttles, or pickup services) to help reach the facility. Therefore, the cost of each agent is the distance from their ideal location to the facility (possibility) through the range. We focus on designing strategyproof mechanisms that elicit true ideal locations from the agents and construct accessibility ranges (intervals) to approximately minimize the social cost or the maximum cost of agents. For both social and maximum costs, we design group strategyproof mechanisms and strong group strategyproof mechanisms with (asymptotically) tight bounds on the approximation ratios.