Self-Stabilizing Token Distribution with Constant-Space for Trees
Self-stabilizing and silent distributed algorithms for token distribution in rooted tree networks are given. Initially, each process of a graph holds at most l tokens. Our goal is to distribute the tokens in the whole network so that every process holds exactly k tokens. In the initial configuration, the total number of tokens in the network may not be equal to nk where n is the number of processes in the network. The root process is given the ability to create a new token or remove a token from the network. We aim to minimize the convergence time, the number of token moves, and the space complexity. A self-stabilizing token distribution algorithm that converges within O(n l) asynchronous rounds and needs Theta(nh epsilon) redundant (or unnecessary) token moves is given, where epsilon = min(k,l-k) and h is the height of the tree network. Two novel ideas to reduce the number of redundant token moves are presented. One reduces the number of redundant token moves to O(nh) without any additional costs while the other reduces the number of redundant token moves to O(n), but increases the convergence time to O(nh l). All algorithms given have constant memory at each process and each link register.
token distribution
self-stabilization
constant-space algorithm
Theory of computation~Self-organization
31:1-31:16
Regular Paper
The brief announcement version of this paper is published in [Sudo and Datta, 2018].
Yuichi
Sudo
Yuichi Sudo
Graduate School of Information Science and Technology, Osaka University, Japan
Ajoy K.
Datta
Ajoy K. Datta
Department of Computer Science, University of Nevada, Las Vegas, USA
Lawrence L.
Larmore
Lawrence L. Larmore
Department of Computer Science, University of Nevada, Las Vegas, USA
Toshimitsu
Masuzawa
Toshimitsu Masuzawa
Graduate School of Information Science and Technology, Osaka University, Japan
10.4230/LIPIcs.OPODIS.2018.31
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Yuichi Sudo, Ajoy K. Datta, Lawrence L. Larmore, and Toshimitsu Masuzawa
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