Transfer Time Complexity of Conflict-free Vehicle Routing with no Communications
International Journal of Robotics Research
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We consider permutation routing problems on 2D and 3D mesh-connected computers with side lenth n. Our main result is a deterministic on-line algorithm routing on 2D meshes, operating in worst-case time T = 2n + O(1) and with queue size Q = 3. We also develop off-line routing algorithms with performance bounds T = 2n + O(1) and with queue size Q = 3. We also develop off-line routing algorithms with performance bounds T = 2n - 1 and Q = 2 for 2D meshes, and T = 3n - 2 and Q = 4 for 3D meshes. We also show that is it possible to route most of the permutations on 2D meshes off-line in time T = 2n- 2 with Q = 1.