Gathering
Robots must meet at a single point that is not fixed in advance, and stay there.
Problem statement and measuresexpand
\(n\) robots start at distinct points and must all reach the same point in finite time and remain there. For \(n = 2\) the problem is called rendezvous. Time is counted in rounds (FSYNC, SSYNC) or in epochs (ASYNC: intervals in which every robot completes at least one full Look–Compute–Move cycle); colours count light colours.
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).
Rendezvous, external light (FCOM), SSYNC
verifiedWith a light only the other robot sees, two robots meet in SSYNC with 3 colours, and 2 colours are impossible.
Assumed (added on the last edge are outlined)
Not assumed
Formal definitions of this setting
- Body: point
- Each robot is a point of the plane: several robots may share a point (multiplicity), and a robot hides only what lies exactly behind it on a line of sight.
- Visibility: unlimited visibility
- A robot sees all robots (subject to opacity).
- Opacity: transparent
- Robots do not obstruct each other's view.
- Faults: no faults
- All robots follow the algorithm forever.
- Scheduler: SSYNC
- SSYNC: time is divided into rounds; in each round a non-empty subset of robots, chosen by a fair adversary, executes one atomic Look–Compute–Move cycle. Called Atom by Prencipe Prencipe 2007.
- Lights (persistent memory): external light (FCOM)
- FCOM: each robot has a light with \(c\) colours that only the others can see (constant communication, no persistent memory of its own). Also called an external light.
- Agreement on coordinates: disoriented
- Each robot \(r\) observes in its own coordinate system, obtained from the global one by an unknown similarity (translation, rotation, uniform scaling, and possibly reflection); systems may differ between robots and, in some models, between cycles. Papers that call robots disoriented do not always mean this: Défago and Souissi use the word while assuming chirality Défago & Souissi 2008. Some papers also let the adversary change a robot's rotation, reflection and unit at every Look (variable disorientation) Flocchini et al. 2023 Masuzawa et al. 2026.
- Movement: non-rigid
- In a Move phase the adversary may stop a robot before its destination, but only after it has travelled at least \(\delta>0\) (a constant unknown to the robots) or reached the destination.
- Multiplicity detection: no multiplicity detection
- A snapshot is a set of points: a point occupied by several robots looks like a single robot.
- Randomness: deterministic
- The destination computed in a cycle is a function of the snapshot (and the light, if any).
- Identifiers: anonymous
- Robots are indistinguishable and run the same algorithm.
- Number of robots: \(n = 2\)
- Exactly two robots (rendezvous).
What is known
- Theorem 1: 2 colours are impossible for external lights, for every \(n \ge 2\)
- holds even with rigid moves, chirality and a common unit
- Theorem 8: for colour-only (class L) algorithms, rigid SSYNC
Results, in order of publication
Introductory and current best (Theorem 16): self-stabilizing, non-rigid moves, no common unit.
Open questions
None recorded for this variant.
Notes
Checked against the full texts.
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
No catalogued stronger setting.
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