Self-stabilizing depth-first token circulation in arbitrary rooted networks

2000 ◽  
Vol 13 (4) ◽  
pp. 207-218 ◽  
Author(s):  
Ajoy K. Datta ◽  
Colette Johnen ◽  
Franck Petit ◽  
Vincent Villain
Keyword(s):  
Token Circulation

Self-stabilizing depth-first token circulation on networks

1993 ◽  
Vol 7 (1) ◽  
pp. 61-66 ◽  
Author(s):  
Shing-Tsaan Huang ◽  
Nian-Shing Chen
Keyword(s):  
Token Circulation

SELF-STABILIZING DEPTH-FIRST MULTI-TOKEN CIRCULATION IN TREE NETWORKS

2001 ◽  
Vol 16 (1) ◽  
pp. 17-35 ◽  
Author(s):  
GHEORGHE ANTONOIU ◽  
PRADIP K. SRIMANI
Keyword(s):  
Tree Networks ◽  
Token Circulation

OPTIMALITY AND SELF-STABILIZATION IN ROOTED TREE NETWORKS

1999 ◽  
Vol 09 (03) ◽  
pp. 313-323
Author(s):  
FRANCK PETIT ◽  
VINCENT VILLAIN
Keyword(s):  
Rooted Tree ◽  
The State ◽  
Extra Cost ◽  
Tree Networks ◽  
Token Circulation ◽  
Self Stabilization ◽  
Legitimate State ◽  
Arbitrary Tree

In this paper, we consider arbitrary tree networks where every processor, except one, called the root, executes the same program. We show that, to design a depth-first token circulation protocol in such networks, it is necessary to have at least [Formula: see text] configurations, where n is the number of processors in the network and Δi is the degree of processor pi. We then propose a depth-first token circulation algorithm which matches the above minimal number of configurations. We show that the proposed algorithm is self-stabilizing, i.e., the system eventually recovers itself to a legitimate state after any perturbation modifying the state of the processors. Hence, the proposed algorithm is optimal in terms of the number of configurations and no extra cost is involved in making it stabilizing.

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