Distributed leader election and computation of local identifiers for programmable matter

Deterministic Leader Election in Programmable Matter

“…The current paper adapts and uses a sub-routine from their paper. Gastineau et al [17] presented a leader election algorithm that assumed common chirality and a connected hole-free shape of particles and elected a leader with the additional property of assigning an identifier to each particle that is unique within a radius of k particles. Their result holds for triangular, square, and king grids, while the current paper focuses on the triangular grid alone.…”

“…7 The type of asynchronous scheduler used affects the leader election results. Typically in the literature [6,13,17], the scheduler provides conflict resolution mechanisms for movement and communication such that particle activations can be analyzed sequentially, i.e., the activation of each particle is atomic. However, when a scheduler is allowed to schedule such particles simultaneously [2,15], it becomes impossible to elect deterministically a unique leader in some cases.…”

“…When a receives an accept/reject message from all its neighbors and an acknowledgement message from its successor in the segment, if any, a sends an acknowledgement message to its successor node in the segment. 17 Termination detection of this phase is coordinated by seg-heads P 1 to P k as follows. Once some P i receives an acknowledgement message from its successor, if any, and accept/reject messages from its neighbors, it sends a terminate message to the remaining k − 1 other seg-heads.…”

“…The length of the largest boundary in the initial configuration is Lmax. The length of the outer boundary in the initial configuration is L. The number of particles in the configuration is denoted by n. The terms r and mtree are unique to paper[17].…”