Partitioning
Robots must partition themselves into \(k\) groups of exactly \(n/k\) robots each, each group at its own point.
Problem statement and measuresexpand
\(n\) robots, with \(k\) dividing \(n\), must partition themselves into \(k\) groups of exactly \(n/k\) robots, each group gathered at its own point, and stay there. The \(k\) points, and so the group size \(n/k\), are given (the papers' \(k\)-EPF and \(k\)-circle formation name the group size \(k\), which is \(n/k\) here).
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
Exactly \(n/k\) robots at each fixed point + point, + unlimited visibility, + transparent, + no faults, + one axis
1 open · 1 results
unknown
\(\text{finite}\) vs —
tight
\(0\) vs —
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