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.
Disk, priority evacuation, queen and two servants
verifiedA queen and two servants evacuate the queen in about \(3.833\) against a lower bound of about \(3.631\).
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: three robots
- Three robots.
- Goal: priority (queen)
- One designated robot (the queen) must reach the exit; the others (servants) only help; the task ends when the queen exits.
- Exits: one exit
- One exit, at an unknown point of the boundary.
- Communication: wireless
- Wireless: every robot can send messages to every other robot instantly at any distance.
- Faults: no faults
- Every robot detects and reports the target.
- Speeds: distinct speeds
- Each robot \(i\) has its own maximum speed \(v_i\), known to all.
- Randomness: deterministic
- Trajectories are fixed functions of the information received.
What is known
Results, in order of publication
Introductory and current best (Theorem 10).
Open questions
None recorded for this variant.
Notes
Checked against the full text.
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