Fully-Functional Succinct Trees

We propose new succinct representations of ordinal trees, which have been studied extensively. It is known that any n-node static tree can be represented in 2n + o(n) bits and a large number of operations on the tree can be supported in constant time under the word-RAM model. However existing data structures are not satisfactory in both theory and practice because (1) the lower-order term is (n log log n/ log n), which cannot be neglected in practice, (2) the hidden constant is also large, (3) the data structures are complicated and difficult to implement, and (4) the techniques do not extend to dynamic trees supporting insertions and deletions of nodes. We propose a simple and flexible data structure, called the range min-max tree, that reduces the large number of relevant tree operations considered in the literature to a few primitives, which are carried out in constant time on sufficiently small trees. The result is then extended to trees of arbitrary size, achieving 2n + O(n/polyl...

• Type: Conference
• Year: 2010
• Where: SODA
• Authors: Kunihiko Sadakane, Gonzalo Navarro
• Keywords: Discrete Algorithms, Dynamic Succinct Trees, Relevant Tree Operations, SODA 2010, Trees Supporting Insertions