On Reconfiguration of Disks in the Plane and Related Problems
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Reconfiguration of List Edge-Colorings in a Graph
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Reconfiguration of list edge-colorings in a graph
Discrete Applied Mathematics
On reconfiguration of disks in the plane and related problems
Computational Geometry: Theory and Applications
k-color multi-robot motion planning
International Journal of Robotics Research
| Hi-index | 0.00 |
Let $G$ be a connected graph, and let $V$ and $V'$ be two $n$-element subsets of its vertex set $V(G)$. Imagine that we place a chip at each element of $V$ and we want to move them into the positions of $V'$ ($V$ and $V'$ may have common elements). A move is defined as shifting a chip from $v_1$ to $v_2$ ($v_1,v_2 \in V(G)$) on a path formed by edges of $G$ so that no intermediate vertices are occupied. We give upper and lower bounds on the number of moves that are necessary and analyze the computational complexity of this problem under various assumptions: labeled versus unlabeled chips, arbitrary graphs versus the case when the graph is the rectangular (infinite) planar grid, etc. We prove hardness and inapproximability results for several variants of the problem. We also give a linear time algorithm which performs an optimal (minimum) number of moves for the unlabeled version in a tree, and a constant-ratio approximation algorithm for the unlabeled version in a graph. The graph algorithm uses the tree algorithm as a subroutine.