Andrew Adler

The bit complexity of randomized leader election on a ring

The inherent bit complexity of leader election on asynchronous unidirectional rings of processors is examined under various assumptions about global knowledge of the ring. If processors have unique identities with a maximum of

Randomized function evaluation on a ring

m

Probabilistic leader election on rings of known size

bits, then the expected number of communication bits sufficient to elect a leader with probability 1, on a ring of (unknown) size

F-Planar graphs

n

Probabilistic solitude verification on a ring

is

Tight lower bounds for probabilistic solitude verification on anonymous rings

O(nm)

Some results on one-dimensional tilings

. If the ring size is known to within a multiple of 2, then the expected number of communication bits sufficient to elect a leader with probability 1 is

Randomized Function Evaluation on a Ring

O(n \log n)

Probabilistic Solitude Detection II: Ring Size Known Exactly

. These upper bounds are complemented by lower bounds on the communication complexity of a related problem called solitude verification that reduces to leader election in

Optimal Algorithms for Probabilistic Solitude Detection on Anonymous Rings

O(n)