Quasi-Optimal Elimination Trees for 2D Grids with Singularities

Algorithm 1

()   Create forest of   one-element trees,

()    sorted according to the numbering of elements, from largest to smallest

()   Store list of neighbors for each tree

()   Compute area =   for each tree

()   repeat

()    Select sub-forest of elements with minimum area

()    Find maximum number of common edges between all pairs in the selected sub-forest

()    Loop  through all pairs of trees (v,w) in the sub-forest with number of common edges

()      equal to the maximum number of common edges found

()   Create new root node r

()   Assign v and w as children nodes of r

()   Update area of r: area(r) = area(v) + area(w)

()   Update list of neighbors of r (merge the lists)

()   Add new tree   to the forest in such a way

()    that the forest is still sorted according to area of trees

()     end for

() until  forest has one element