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In the modular robot reconfiguration problem, we are given n cube-shaped modules (or robots) as well as two configurations, i.e., placements of the n modules so that their union is face-connected. The goal is to find a sequence of moves that reconfigures the modules from one configuration to the other using "sliding moves," in which a module slides over the face or edge of a neighboring module, maintaining connectivity of the configuration at all times. For many years it has been known that certain module configurations in this model require at least Ω(n²) moves to reconfigure between them. In this paper, we introduce the first universal reconfiguration algorithm - i.e., we show that any n-module configuration can reconfigure itself into any specified n-module configuration using just sliding moves. Our algorithm achieves reconfiguration in O(n²) moves, making it asymptotically tight. We also present a variation that reconfigures in-place, it ensures that throughout the reconfiguration process, all modules, except for one, will be contained in the union of the bounding boxes of the start and end configuration. 

We study the investment incentives created by truthful mechanisms that allocate resources using approximation algorithms. Some approximation algorithms guarantee nearly 100% of the optimal welfare in the allocation problem but guarantee nothing when accounting for investment incentives. An algorithm's allocative and investment guarantees coincide if and only if itsconfirming negative externalitiesare sufficiently small. We introduce fast approximation algorithms for the knapsack problem that have no confirming negative externalities and guarantees close to 100% for both allocation and investment. 

Abstract We analyze the effects of taxation in two‐sided matching markets where agents have heterogeneous preferences over potential partners. Our model provides a continuous link between models of matching with and without transfers. Taxes generate inefficiency on the allocative margin, by changing who matches with whom. This allocative inefficiency can be nonmonotonic, but is weakly increasing in the tax rate under linear taxation if each worker has negative nonpecuniary utility of working. We adapt existing econometric methods for markets without taxes to our setting, and estimate preferences in the college‐coach football market. We show through simulations that standard methods inaccurately measure deadweight loss.