String Covers of a Tree.

We consider covering labeled trees by a collection of paths with the same string label, called a (string) cover of a tree. We show how to compute all covers of a directed (rooted) labeled tree in O ( n log n / log log n ) time and all covers of an undirected labeled tree in O ( n 2 ) time and space or in O ( n 2 log n ) time and O ( n ) space. We also show several essential differences between covers in standard strings and covers in trees.