Compressed Bit vectors Based on Variable-to-Fixed Encodings

Abstract

We consider practical implementations of compressed bitvectors, which support rank and select operations on a given bit-string, while storing the bit-string in compressed form. Our approach relies on variable-to-fixed encodings of the bit-string, an approach that has not yet been considered systematically for practical encodings of bitvectors. We show that this approach leads to fast practical implementations with low redundancy (i.e., the space used by the bitvector in addition to the compressed representation of the bit-string), and is a flexible and promising solution to the problem of supporting rank and select on moderately compressible bit-strings, such as those encountered in real-world applications.

Indexing structures for the PLS blockchain

“…Tunstall in his PhD thesis [13] proposed a greedy search which at the same time builds a compact dictionary structure (the Tunstall tree) that can be used for encoding/decoding efficiently, without sharing the dictionary (as long as p is known to both the encoder and the decoder). The greedy search turns out to be of excellent quality, too, delivering the entropy limit asymptotically [13], and, as a recent study shows [9], with a rapidly decreasing redundancy as w increases. The redundancy formula from [9] being useful for our analysis, we present it below (without derivation and rewritten in our notation):…”

“…The greedy search turns out to be of excellent quality, too, delivering the entropy limit asymptotically [13], and, as a recent study shows [9], with a rapidly decreasing redundancy as w increases. The redundancy formula from [9] being useful for our analysis, we present it below (without derivation and rewritten in our notation):…”

“…The idea there is to choose a (pseudo)random element of a sequence of source items and exchange it with the first element on the sequence. Clearly, if this is repeated enough times then any possible permutation could be achieved 9 . A recent paper [3] presents a fast, parallel algorithm that mimics the technique of merge-sort except the merge makes a pseudorandom choice when ordering two elements for the output.…”