Fine-Grain parallel algorithm for LU-decomposition
It will be clearer if you look at 1 slide before (10/42). The algorithm does not decide on how do you assign to node. It just says that the algorithm can be consisted of many parallel tasks. Each task has identification of $(i,j)$ and each executes the algorithm in slide (12/42). 

More specifically, each task is assigned an entry $a_{ij}$ of the matrix ($n^2$ number of tasks), and at the end of the algorithm that entry becomes $u_{ij}$ if $i \le j$ or $l_{ij}$ if $i&gt;j$.