Succinct Trees in Practice

We implement and compare the major current techniques for representing general trees in succinct form. This is important because a general tree of n nodes is usually represented in pointer form, requiring O(n log n) bits, whereas the succinct representations we study require just 2n + o(n) bits and carry out many sophisticated operations in constant time. Yet, there is no exhaustive study in the literature comparing the practical magnitudes of the o(n)-space and the O(1)-time terms. The techniques can be classified into three broad trends: those based on BP (balanced parentheses in preorder), those based on DFUDS (depth-first unary degree sequence), and those based on LOUDS (level-ordered unary degree sequence). BP and DFUDS require a balanced parentheses representation that supports the core operations findopen, findclose, and enclose, for which we implement and compare three major algorithmic proposals. All the tree representations require also core operations rank and select on bit...

• Type: Conference
• Year: 2010
• Where: ALENEX
• Authors: Diego Arroyuelo, Rodrigo Cánovas, Gonzalo Navarro, Kunihiko Sadakane
• Keywords: ALENEX 2010, Algorithms, Core Operations, General Tree, Unary Degree Sequence