Characterizing Universal Reconfigurability of Modular Pivoting Robots

Autor: Akitaya, Hugo A., Demaine, Erik D., Gonczi, Andrei, Hendrickson, Dylan H., Hesterberg, Adam, Korman, Matias, Korten, Oliver, Lynch, Jayson, Parada, Irene, Sacristán, Vera
Rok vydání: 2020
Předmět:
Druh dokumentu: Working Paper
Popis: We give both efficient algorithms and hardness results for reconfiguring between two connected configurations of modules in the hexagonal grid. The reconfiguration moves that we consider are "pivots", where a hexagonal module rotates around a vertex shared with another module. Following prior work on modular robots, we define two natural sets of hexagon pivoting moves of increasing power: restricted and monkey moves. When we allow both moves, we present the first universal reconfiguration algorithm, which transforms between any two connected configurations using $O(n^3)$ monkey moves. This result strongly contrasts the analogous problem for squares, where there are rigid examples that do not have a single pivoting move preserving connectivity. On the other hand, if we only allow restricted moves, we prove that the reconfiguration problem becomes PSPACE-complete. Moreover, we show that, in contrast to hexagons, the reconfiguration problem for pivoting squares is PSPACE-complete regardless of the set of pivoting moves allowed. In the process, we strengthen the reduction framework of Demaine et al. [FUN'18] that we consider of independent interest.
Databáze: arXiv