The LCS of two rooted, ordered, and labeled trees F and G is the largest forest that can be
obtained from both trees by deleting nodes. We present algorithms for computing tree LCS
which exploit the sparsity inherent to the tree LCS problem. Assuming G is smaller than F,
our first algorithm runs in time O (r⋅ height (F)⋅ height (G)⋅ lglg| G|), where r is the number
of pairs (v∈ F, w∈ G) such that v and w have the same label. Our second algorithm runs in
time O (Lrlgr⋅ lglg| G|), where L is the size of the LCS of F and G. For this algorithm we …

The LCS of two rooted, ordered, and labeled trees F and G is the largest forest that can be
obtained from both trees by deleting nodes. We present algorithms for computing tree LCS
which exploit the sparsity inherent to the tree LCS problem. Assuming G is smaller than F,
our first algorithm runs in time O(r⋅\rmheight(F)⋅\rmheight(G)⋅\lg\lg|G|), where r is the
number of pairs (v∈ F, w∈ G) such that v and w have the same label. Our second algorithm
runs in time O(Lr\lgr⋅\lg\lg|G|), where L is the size of the LCS of F and G. For this algorithm …