Before revision:  To implement } Kruskal's MST algorithm on it. To achieve this with limited workspace, we introduce a compact representation of planar graphs , called an s-net which allows us to manipulate its component structure during the execution of the algorithm .
After revision:  To implement } Kruskal's algorithm with O(s) cells of workspace, we introduce a compact representation of planar graphs , called an s-net which allows us to manipulate its component structure during the execution of the algorithm .