Concept

Compressed bit vector — where it appears

A bit vector stored as each block's class and an offset within that class, so a block that is all ones or all zeros costs nothing beyond its class. It reaches the entropy of the block classes rather than of the bits, which is why a vector with runs compresses and one of independent coin flips does not.

Named by 3 essays across 3 fields — each of them below, with the objects they name alongside it.

A block, a class and an offset

Replacing each block of a bit vector by how many ones it holds and which arrangement it is takes 7.6% off the grid. On a permutation with no structure at all it takes 2.6%, so five of the seven points are the data and two of them are the encoding.

indexes · Grid

Twenty bits apart

Two representations of one sparse set, six thousand seven hundred and forty-five bits against six thousand seven hundred and sixty-five. One exploits sparsity and the other exploits runs, and on this set at this density they price identically.

machine · Space

A code word is at least one bit

A wavelet tree of plain vectors reaches the entropy by its shape, and a Huffman code word cannot be shorter than one bit. On a collection whose document array has an entropy of 1.69 the tree costs 1.98, and the gap is a floor rather than an inefficiency.

bounds · Index

Named alongside it

The objects these essays reach for when they reach for this one.

Index size Entropy Wavelet tree Compression Control Crossing point Document array Elias fano Grid Huffman code Lower bound Measurement

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