A Simple and Optimal Ancestry Labeling Scheme for Trees (original) (raw)

We present a lg n`2 lg lg n`3 ancestry labeling scheme for trees. The problem was first presented by Kannan et al. [STOC 88'] along with a simple 2 lg n solution. Motivated by applications to XML files, the label size was improved incrementally over the course of more than 20 years by a series of papers. The last, due to Fraigniaud and Korman [STOC 10'], presented an asymptotically optimal lg n`4 lg lg nÒ p1q labeling scheme using non-trivial tree-decomposition techniques. By providing a framework generalizing interval based labeling schemes, we obtain a simple, yet asymptotically optimal solution to the problem. Furthermore, our labeling scheme is attained by a small modification of the original 2 lg n solution.