Efficient union-find for planar graphs and other sparse graph classes

Jens Gustedt
1998 Theoretical Computer Science  
We solve the Union-Find Problem (UF) efficiently for the case the input is restricted to several graph classes, namely partial k-trees for any fixed k, d-dimensional grids for any fixed dimension d and for planar graphs. The result on grids allows us to perform region growing techniques that are used for image segmentation in linear time. For planar graphs we develop a technique of decomposing such a graph into small subgraphs, patching, that might be useful for other algorithmic problems on
more » ... nar graphs, too. By efficiency we do not only mean linear time in a theoretical setting but also a practical reorganization of memory such that a dynamic data structures for UF is allocated consecutively.
doi:10.1016/s0304-3975(97)00291-0 fatcat:zc2ae36f7zgqpjfh7a5ic3j5wm