Optimal top dag compression

Abstract

It is shown that for a given ordered node-labelled tree of size $n$ and with $s$ many different node labels, one can construct in linear time a top dag of height $O(\log n)$ and size $O(n / \log_\sigma n) \cap O(d \cdot \log n)$, where $\sigma = \max\{ 2, s\}$ and $d$ is the size of the minimal dag. The size bound $O(n / \log_\sigma n)$ is optimal and improves on previous bounds.