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Compact : O (OPT) bits . This is easier to achieve, and acts more as a warmup for succinct data structures. Succinct : O PT + o(OPT) bits . T his is what we will focus on. Labeled Trees First let's examine the space complexity of trees in pointer form. Above is an n-node (n = 12) tree in pointer form. A general tree of n nodes requires O (nw ) Succinct data structure In computer science, a succinct data structure is a data structure which uses an amount of space that is "close" to the information-theoretic lower bound, but (unlike other compressed representations) still allows for efficient query operations. Operations rank and select are fundamental to succinct data structures. Given a string t of length n on an alphabet Σ, rank a ( t, i) ( i ≥ 0, a ∈ Σ) returns the number of occurrences of a in the prefix of t ending at position i; select a ( t, c) ( c ≥ 1) returns the position of the c -th occurrence of a in t. supporting access/rank/select operations efficiently. Our high-order entropy compressed text index provides more efficient support for searches than previous results that occupy essentially the same amount of space. Our succinct representation for labeled trees support more operations than previous results do. We also design the first succinct representations of labeled graphs. To design succinct data structures Introduction Rank&Select Plan LOUDS Primitives First attempt Second try Perspectives Dynamic data Principle Simply typed Perspectives Proving tree algorithms for succinct data structures Reynald A eldt 1 Jacques Garrigue 2 Xuanrui Qi 2 Kazunari Tanaka 2 1National Institute of Advanced Industrial Science and Technology, Japan 2Graduate Scool of Mathematics, Nagoya Bit vectors are fundamental building blocks of many succinct data structures. They can be used to represent graphs, are an important part of many text indices in the form of the wavelet tree, and can be used to encode ordered sequences of integers as Elias-Fano codes. To do so, two queries have to be answered: namely rank and select queries. Given a position in the bit vector, a rank query Succinct data structures provide the same functionality as their corresponding traditional data structure in compact space. We improve on functions rank and select, which are the basic building blocks of FM-indexes and other succinct data structures. First, we present a cache-optimal, uncompressed bitvector representation that outperforms all Rank & select data structures are one of the fundamental building blocks for many modern succinct data structures. With the continued growth of massive-scale information services, the space efficiency of succinct data structures is becoming increasingly attractive in practice. In this paper, we re-examine the design of rank & select data structures from the bottom up, applying an architectural The deep connection between the Burrows-Wheeler transform (BWT) and the so-called rank and select data structures for symbol sequences is the basis of most successful approaches to compressed text This problem