Dynamizing Succinct Tree Representations

Abstract

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.

A General Framework for Dynamic Succinct and Compressed Data Structures

“…Determining whether different self-balancing trees, such as splay trees [28] (as in Joannou and Raman [20]) or rank balanced trees [16] would perform better is an interesting direction.…”

“…We note that these data structures do not explicitly manage memory, but are instead designed to be avoid bad sequences of allocations/deallocations. In a later work [20], the same authors also describe an implementation of dynamic succinct trees, with the targeted application of representing dynamic XML documents. Their dynamic tree occupies 2n + o(n) bits, and is combination of the min-max tree [25,24] and a splay tree [28].…”

Succinct Representations of Ordinal Trees

“…A key feature is that operations on a node are specified by the position of that node in the BP bit-string. As noted by Joannou and Raman [28], when using this approach, any navigation operation has several steps that are known require Ω(lg n/ lg lg n) time (unless updates are allowed to take more than poly-log time). However, the resulting dynamization does support the full range of navigational operations supported by the FF representation, together with the updates, in O(lg n/ lg lg n) time.…”

“…Joannou and Raman [28] observe that the reason that the simple O(lg n)-time excess search of Arroyuelo et al performs comparably to the O(1)-time implementation of Geary et al for navigation is that navigation in ordinal trees (i.e. a sequence of steps moving from a node to an adjacent one) induces a kind of locality of access in the BP sequence; consequently, the O(lg n)-time worst-case cost may not be paid frequently.…”

FLOUDS: A Succinct File System Structure

“…In nearly all cases, attempts were made at practical implementations, with successful results [20], [24], [31].…”