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Self-stabilizing token distribution on trees with constant space
Journal of Parallel and Distributed Computing ( IF 3.4 ) Pub Date : 2020-08-24 , DOI: 10.1016/j.jpdc.2020.07.007
Yuichi Sudo , Ajoy K. Datta , Lawrence L. Larmore , Toshimitsu Masuzawa

Self-stabilizing and silent distributed algorithms for token distribution in rooted tree networks are given. Initially, each process of a graph holds at most tokens. Our goal is to distribute the tokens uniformly 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 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. First, a self-stabilizing token distribution algorithm that converges within O(n) asynchronous rounds and needs Θ(nhϵ) redundant (or unnecessary) token moves is given, where ϵ=min(k,k) and h is the height of the tree network. Next, two novel mechanisms 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). All given algorithms have constant memory at each process and each link register.



中文翻译:

自稳定令牌在具有恒定空间的树上的分布

给出了在树状树网络中令牌分配的自稳定和静默分布式算法。最初,图的每个过程最多容纳令牌。我们的目标是将令牌均匀分布在整个网络中,以便每个进程都能准确地容纳ķ令牌。在初始配置中,网络中的令牌总数可能不是ñķ 哪里 ñ是网络中的进程数。根进程具有创建新令牌或从网络中删除令牌的能力。我们的目标是最小化收敛时间,令牌移动的数量和空间复杂度。首先,一种在内部收敛的自稳定令牌分配算法Øñ 异步回合和需求 ΘñHϵ 给出了多余的(或不必要的)令牌移动,其中 ϵ=ķ-ķH是树状网络的高度。接下来,提出了两种减少冗余令牌移动数量的新颖机制。一个减少了冗余令牌移动到的数量ØñH 无需支付任何额外费用,而另一种则减少了向 Øñ,但将收敛时间增加到 ØñH。所有给定的算法在每个进程和每个链接寄存器中都有恒定的内存。

更新日期:2020-08-24
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