Dynamic Succinct Ordered Trees

Abstract. We study the problem of maintaining a dynamic tree succinctly, in 2n + o(n) bits, under updates of the following form: insertion or deletion of a leaf, insertion of a node on an edge (edge subdivision) or deletion of a node with only one child (the child becomes a child of the grandparent). We allow satellite data of a fixed (but not necessarily constant) size to be associated to the nodes of the tree. We support update operations in constant amortized time and support access to satellite data and basic navigation operations in worstcase constant time; the basic navigation operations includes parent, first/last-child, previous/next-child. We demonstrate that to allow fast support for more extended operations such as determining the i-th child of a node, rank of a child among its siblings, or subtree size, we require a restrictive update strategy for which we propose the fingerupdate model where updates are performed by a finger which is only allowed to crawl on the tree (betw...

• Type: Conference
• Year: 2009
• Where: ICALP
• Authors: Arash Farzan, J. Ian Munro
• Keywords: Basic Navigation Operations, ICALP 2009, Theoretical Computer Science, Worst-case Constant Time, Worstcase Constant Time