1 research outputs found
A Self-Stabilizing Minimal k-Grouping Algorithm
We consider the minimal k-grouping problem: given a graph G=(V,E) and a
constant k, partition G into subgraphs of diameter no greater than k, such that
the union of any two subgraphs has diameter greater than k. We give a silent
self-stabilizing asynchronous distributed algorithm for this problem in the
composite atomicity model of computation, assuming the network has unique
process identifiers. Our algorithm works under the weakly-fair daemon. The time
complexity (i.e., the number of rounds to reach a legitimate configuration) of
our algorithm is O(nD/k) where n is the number of processes in the network and
\diam is the diameter of the network. The space complexity of each process is
O((n +n_{false})log n) where n_{false} is the number of false identifiers,
i.e., identifiers that do not match the identifier of any process, but which
are stored in the local memory of at least one process at the initial
configuration. Our algorithm guarantees that the number of groups is at most
after convergence. We also give a novel composition technique to
concatenate a silent algorithm repeatedly, which we call loop composition.Comment: This is a revised version of the conference paper [6], which appears
in the proceedings of the 18th International Conference on Distributed
Computing and Networking (ICDCN), ACM, 2017. This revised version slightly
generalize Theorem