Convergence
Robots must get arbitrarily close to a common point; they need not ever meet.
Problem statement and measuresexpand
\(n\) robots start at arbitrary points. For every \(\varepsilon > 0\) there must be a time after which all robots stay within distance \(\varepsilon\) of each other (equivalently, of a common limit point). Robots never need to coincide.
Measures: Time, rounds (FSYNC, SSYNC) or epochs (ASYNC) until the task is done; "finite" when only solvability is known; Colours, colours of the light per robot (0 for oblivious robots).
Progress map
tight near-optimal polynomial gap unknown impossible· rows follow the assumption tree; each cell: best upper bound vs lower bound, and what forces the lower bound
Setting
Time
Colours
unknown
\(\text{finite}\) vs —
tight
\(0\) vs —
unknown
\(\text{finite}\) vs —
tight
\(0\) vs —
unknown
\(\text{finite}\) vs —
tight
\(0\) vs —
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