Memory efficient, self-stabilizing algorithm to construct BFS spanning trees

Abstract

A self-stabilizing BFS spanning tree construction algorithm which requires only 0(1) bits of memory per link is presented. The algorithm uses neither the distance variable for any special data structure to achieve the memory requirement. The r_color of the current three is used to distinguish the processors that are from those that are not part of the current tree. Two error-handling strategies is designed one for destroying illegal trees and the other for breaking the cycles.