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Linear time distributed swap edge algorithms
Information Processing Letters ( IF 0.5 ) Pub Date : 2020-06-02 , DOI: 10.1016/j.ipl.2020.105979
A.K. Datta , P. Ferragina , L. Larmore , L. Pagli , G. Prencipe

In this paper, we consider the all best swap edges problem in a distributed environment. We are given a 2-edge connected positively weighted network X, where all communication is routed through a rooted spanning tree T of X. If a tree edge e={x,y} fails, the communication network will be disconnected. However, since X is 2-edge connected, communication can be restored by replacing e by non-tree edge e, called a swap edge of e, whose ends lie in different components of T{e}. Of all possible swap edges of e, we would like to choose the best, according to four different objective functions.

Overall, the problem is to identify the best swap edge for every tree edge, so that in case of any edge failure, the best swap edge can be activated quickly. There are solutions to this problem for a number of cases in the literature. A major concern for all these solutions is to minimize the number of messages. However, especially in fault-transient environments, time is a crucial factor. In this paper we present a novel technique that addresses this problem from a time perspective; in fact, we present a distributed solution that works in linear time with respect to the height h of T for a number of different criteria, while retaining the optimal number of messages and O(δx) space per each processor x of degree δx.

To the best of our knowledge, there is no prior algorithm for the all best swap edges problem whose asymptotic complexity matches ours in all three measures: time, space, and number of messages.



中文翻译:

线性时间分布交换边缘算法

在本文中,我们考虑了分布式环境中的所有最佳交换边问题。我们给了一个2边连接的正加权网络X,其中所有通信都通过X的根生成树T进行路由。如果树边Ë={Xÿ}失败,通讯网络将被断开。但是,由于X是2边连接的,因此可以通过用非树边替换e来恢复通信。Ë称为一个交换边ë,其端部位于不同的部件Ť{Ë}。在e的所有可能交换边中,我们希望根据四个不同的目标函数选择最佳的交换边。

总体而言,问题在于为每个树边缘确定最佳交换边缘,以便在发生任何边缘故障的情况下,可以快速激活最佳交换边缘。对于文献中的许多情况,都有解决此问题的方法。所有这些解决方案的主要关注点是最大程度地减少消息数量。但是,尤其是在故障瞬态环境中,时间是至关重要的因素。在本文中,我们提出了一种从时间角度解决此问题的新颖技术。事实上,我们提出了一种分布式的解决方案是,在线性时间相对于所述高度作品ħŤ用于许多不同的条件,同时保持消息的最佳数量和ØδX每个处理器的空间xδX

据我们所知,没有关于所有最佳交换边问题的先验算法,其渐近复杂度在时间,空间和消息数量这三个方面均与我们的渐进复杂性相匹配。

更新日期:2020-06-02
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