In this article, we focus on extending the notion of lattice linearity to self-stabilizing programs. Lattice linearity allows a node to execute its actions with old information about the state of other nodes and still preserve correctness. It increases the concurrency of the program execution by eliminating the need for synchronization among its nodes. The extension -- denoted as eventually lattice linear algorithms -- is performed with an example of the service-demand based minimal dominating set (SDDS) problem, which is a generalization of the dominating set problem; it converges in $2n$ moves. Subsequently, we also show that the same approach could be used in various other problems including minimal vertex cover, maximal independent set and graph coloring.

翻译：在本文中,我们侧重于将线性线性概念扩展至自稳定程序。 光性线性允许节点用关于其他节点状况的旧信息来实施其行动, 并且仍然保持正确性。 它通过消除节点之间同步的必要性来增加程序执行的共通度。 扩展( 被称为最终拉蒂线性算法) 是以服务- 需求为基础的最低支配性集( SDDS) 问题( SDDS) 为例来进行, 这是对主导性集成问题的概括化; 它以 $2 $ 的移动相交汇 。 随后, 我们还表明, 同一方法可以用于其他各种问题, 包括最小的顶层覆盖、 最大独立的集和图形颜色 。