Dynamizing succinct tree representations

Abstract

We consider succinct, or space-efficient, representations of ordinal trees. Representations exist that take 2n + o(n) bits to represent a static n-node ordinal tree - close to the information-theoretic minimum - and support navigational operations in O(1) time on a RAM model; and some implementations have good practical performance. The situation is different for dynamic ordinal trees. Although there is theoretical work on succinct dynamic ordinal trees, there is little work on the practical performance of these data structures. Motivated by applications to representing XML documents, in this paper, we report on a preliminary study on dynamic succinct data structures. Our implementation is based on representing the tree structure as a sequence of balanced parentheses, with navigation done using the min-max tree of Sadakane and Navarro (SODA '10). Our implementation shows promising performance for update and navigation, and our findings highlight two issues that we believe will be important to future implementations: the difference between the finger model of (say) Farzan and Munro (ICALP '09) and the parenthesis model of Sadakane and Navarro, and the choice of the balanced tree used to represent the min-max tree. © 2012 Springer-Verlag.