Dynamic Subtrees : a New Data

This paper presents a new data structure, called dynamic subtrees, which manipulates an undirected forest. The data structure supports three main operations cut, link and comp. A cut operation splits a tree into two by cutting an edge of the tree; a link operation joins two trees by linking two arbitrarily speciied vertices of the trees; a comp operation computes a function f(S) = f(v 1)f(v 2):::, for all vertices v i of S, where S is either tree of T ? e, with T being the tree under consideration and e an arbitrarily given edge of T, f(v) 2 F, a nite set, and is a closed commutative and associative binary operation over F. Assuming s t is the time for implementing a operation, each of the cut, link and comp operations can be implemented in O((s t +log n) log n) time, after a preprocessing in O(s t n) time, where n is the number of vertices of the forest under consideration.