A quasi self-stabilizing algorithm for detecting fundamental cycles in a graph with DFS spanning tree given

This paper presents a linear time quasi self-stabilizing algorithm for detecting the set of fundamental cycles on an undirected connected graph modeling asynchronous distributed system. Previous known algorithm has O(n²) time complexity, whereas we prove that our stabilizes after O(n) moves. Distributed adversarial scheduler is considered. Both algorithms assume that the depth-first search (DFS) spanning tree (DFST) of the graph is given. The output is given in a distributed manner as a state of variables in the nodes.