Lecture 7 - Dynamic Trees Lecturer : Michel

1 Overview In this lecture, we discuss dynamic trees, a sophisticated data structure introduced by Sleator and Tarjan. Dynamic trees allow to provide the fastest worst-case running times for many network flow algorithms. In particular, it will allow us to efficiently perform the Cancel operation in the Cancel and Tighten algorithm. Dynamic trees build upon splay trees, which we introduced in the previous lecture. Dynamic trees manage a set of node-disjoint (not necessarily binary) rooted trees. With each node v is associated a cost. In our use of dynamic trees, the cost will be coming from the edge (p(v), v), where p(v) denotes the parent of v; the cost of the root in that case will be set arbitrarily large (larger than the cost of any other node), say +∞.