Evacuation
Robots start at the centre of a disk (or a polygon) and must all leave through an exit at an unknown point of the boundary, as fast as possible.
Problem statement and measuresexpand
\(k\) unit-speed robots start together at the centre of a unit disk (or the centroid of a unit equilateral triangle or square). An exit lies at an unknown point of the boundary; a robot recognises it only on reaching it. Time is the worst case, over exit positions, of the time until the last robot reaches the exit (in priority evacuation, where one robot is the queen: until the queen does).
Measures: Evacuation time, worst-case time until the last robot (or the queen) reaches the exit; unit disk, unit speed.
Two robots, two exits, face-to-face
verifiedWith two exits at unknown positions and communication only on meeting, the optimal evacuation time is \((1+\pi/2)R \approx 2.57R\).
Assumed (added on the last edge are outlined)
Not assumed
Formal definitions of this setting
- Domain: disk
- The unit disk; robots start at its centre; the exit is a point of the boundary circle.
- Number of robots: two robots
- Two robots.
- Goal: all robots
- The task ends when the last robot reaches the exit.
- Exits: two exits
- Two exits at unknown points of the boundary; the task ends when every robot has reached one of them.
- Communication: face-to-face
- Face-to-face: two robots exchange information only when they are at the same point at the same time.
- Faults: no faults
- Every robot detects and reports the target.
- Speeds: equal speeds
- All robots move at most at unit speed.
- Randomness: deterministic
- Trajectories are fixed functions of the information received.
What is known
- two robots start at the centre
- radius \(R=1\); oblivious robots
Results, in order of publication
Introductory and current best; optimal.
Open questions
None recorded for this variant.
Notes
Bounds from the full version, supplied by the catalogue owner (a co-author); the robots are oblivious.
What carries over from neighbouring settings
Read off the order of assumptions, not checked case by case: results may carry extra assumptions (shown on their pages), and asynchronous time is measured in epochs.
Algorithms from weaker settings work here
Lower bounds from stronger settings hold here
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