In fair rent division, the problem is to assign rooms to roommates and fairly split the rent based on roommates' reported valuations for the rooms. Envy-free rent division is the most popular application on the fair division website Spliddit. The standard model assumes that agents can correctly report their valuations for each room. In practice, agents may be unsure about their valuations, for example because they have had only limited time to inspect the rooms. Our goal is to find a robust rent division that remains fair even if agent valuations are slightly different from the reported ones. We introduce the lexislack solution, which selects a rent division that remains envy-free for valuations within as large a radius as possible of the reported valuations. We also consider robustness notions for valuations that come from a probability distribution, and use results from learning theory to show how we can find rent divisions that (almost) maximize the probability of being envy-free, or that minimize the expected envy. We show that an almost optimal allocation can be identified based on polynomially many samples from the valuation distribution. Finding the best allocation given these samples is NP-hard, but in practice such an allocation can be found using integer linear programming.

We believe datacenters can benefit from more focus on per-node efficiency, performance, and predictability, versus the more common focus so far on scalability to a large number of nodes. Improving per-node efficiency decreases costs and fault recovery because fewer nodes are required for the same amount of work. We believe that the use of complex, general-purpose operating systems is a key contributing factor to these inefficiencies.

An implemented system for designing pipe layouts automatically using robot path planning techniques is described. The authors introduce a new approach to pipe layout design automation in which pipe routes are treated as paths left behind by rigid objects (robots). They have implemented this approach in a basic pipe router, which is also described, and have extended this router in order to make it capable of treating a variety of other constraints which are typical of practical pipe layout design problems. These constraints relate to the process carried out in the pipes, to the design of their mechanical support, and to the constructability and the ease of operation and maintenance of the designed pipe systems.>

The authors consider one of the most popular approaches to path planning: hierarchical approximate cell decomposition. This approach consists of constructing successive decompositions of the robot's configuration space into rectangloid cells and searching the connectivity graph built at each level of decomposition for a path. Despite its conceptual simplicity, an efficient implementation of this approach raises many delicate questions that have not yet been addressed. The major contributions this work are (1) a novel approach to cell decomposition based on constraint reformulation and (2) a new algorithm for hierarchical search with a mechanism for recording failure conditions. These algorithms have been implemented in a path planner, and experiments with this planner have been carried out on various examples. These experiments show that the proposed planner is significantly (approximately 10 times) faster than previous planners based on the same general approach.>

Robot path planning consists of approximating the set of free configurations of the robot by a collection of rectangloid cells at successive levels of approximation and, at each level, searching the graph representing the adjacency relation among these cells. A set of algorithms which specifically address the main two computational issues underlying this approach, cell decomposition and graph searching, has been developed. The authors have implemented a planner which incorporates these algorithms and have experimented with it on examples. The experiments show that the planner is significantly faster than previous planners based on the same general approach. The authors focus on the planner's cell-decomposition algorithms. They use a constraint reformulation technique that consists of approximating the obstacles intersecting the cell to be decomposed by a collection of rectangloids and computing their complements in the cell. Two types of approximations are used, bounding and bounded approximations. This technique produces much less cells than previously proposed techniques, resulting in smaller search graphs. Experimental results are presented.>