Abstract
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.
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Notes
An ordinal tree is a rooted one in which the children of a node are ordered.
It also supports two other operations: the ancestor of \(x\) closest to root with a given label and the first descendant of \(x\) with a given label in preorder. Both operations can be easily supported using \(\mathtt{{pre\_rank}}_\alpha \), \(\mathtt{{pre\_select}}_\alpha \), \(\mathtt{{depth}}_\alpha \) and \(\mathtt{{level\_anc}}_\alpha \), and thus we do not list them in Table 1.
Another query supported by their structure is SubPathSearch, which can count or list nodes whose upward paths start with a given query string.
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We thank anonymous reviewers for their fruitful comments and suggestions.
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The preliminary version of this article was published in Proceedings of the 23rd International Symposium on Algorithms and Computation (ISAAC 2012) [15]. This work was supported by NSERC and the Canada Research Chairs Program.
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He, M., Munro, J.I. & Zhou, G. A Framework for Succinct Labeled Ordinal Trees over Large Alphabets. Algorithmica 70, 696–717 (2014). https://doi.org/10.1007/s00453-014-9894-4
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DOI: https://doi.org/10.1007/s00453-014-9894-4