Package it.unimi.dsi.sux4j.bits
This package provides a number of implementations of rank/select queries for bits vectors. Ranking is counting the number of ones in an initial segment of a bit vector. Selection is finding the position of the rth one. Both operation can be performed in constant time on an array of n bits using o(n) additional bits, but in practice linear data structures with small constants and theoretically nonconstant time work much better. Sux4J proposes a number of new, very efficient implementation of rank and select oriented to 64bit processors (in other words: they will be fairly slow on 32bit processors). The implementations are based on broadword programming and described in Sebastiano Vigna, “Broadword Implementation of Rank/Select Queries”, in Proc. of the 7th International Workshop on Experimental Algorithms, WEA 2008, volume 5038 of Lecture Notes in Computer Science, pages 154−168. Springer, 2008.
For dense arrays, Rank9
is the basic rank implementation;
Rank16
is slightly slower but occupies much less space. Selection
can be performed using SimpleSelect
for reasonably uniform bit
arrays, or using Select9
, which occupies more space but
guarantees practical constanttime evaluation.
For sparse arrays (e.g., representation of pointers in a bitstream) we provide
SparseRank
and SparseSelect
.
Their main feature is that they do not require the original bit array, as they use an
EliasFanoMonotoneLongBigList
to implement a succint dictionary
containing the positions of bits set. If the bit array is sufficiently sparse, such a
representation provides significant gains in space occupancy.
All structures can be serialized. Since in some cases the original bit vector is stored inside
the structure, to avoid saving and loading twice the same vector we suggest to pack all
structures into a RankSelect
instance.
Note that all methods in this package are considered lowlevel and do not perform bound checks on their arguments. Bound checks can be enabled, however, by enabling assertions.

Interface Summary Interface Description BalancedParentheses A data structure providing primitives for balanced parentheses represented in a bit array.Rank A data structure providing ranking over a bit array.Select A data structure providing selection over a bit array.SelectZero A data structure providing zero selection over a bit array. 
Class Summary Class Description AbstractRank An abstract implementation ofRank
providing a few obvious derived methods.HintedBsearchSelect A hinted binarysearch select implementation.JacobsonBalancedParentheses An implementation of Jacobson's balanced parentheses data structure.Rank11 Arank11
implementation.Rank16 Arank16
implementation.Rank9 Arank9
implementation.RankSelect A serialisationoriented container for associated rank/select(zero) structures.Select9 Aselect9
implementation.SimpleSelect A simple select implementation based on a twolevel inventory, a spill list and broadword bit search.SimpleSelectZero A simple zeroselect implementation based on a twolevel inventory, a spill list and broadword bit search.SparseRank A rank implementation for sparse bit arrays based on the Elias–Fano representation of monotone functions.SparseSelect A select implementation for sparse bit arrays based on the Elias–Fano representation of monotone functions.