A Framework for Succinct Labeled Ordinal Trees over Large Alphabets

We consider succinct representations of labeled ordinal trees that support a rich set of operations. Our new representations support a much broader collection of operations than previous work. In our approach, labels of nodes are stored in a preorder label sequence, which can be compressed using any succinct representation of strings that supports $$\mathtt{{access}}$$ , $${\mathtt{{rank}}}$$ and $$\mathtt{{select}}$$ operations. Thus, we present a framework for succinct representations of labeled ordinal trees that is able to handle large alphabets. This answers an open problem presented by Geary et al., which asks for representations of labeled ordinal trees that remain space-efficient for large alphabets. We further extend our work and present the first succinct representations for dynamic labeled ordinal trees that support several label-based operations including finding the level ancestor with a given label.