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. The concept was originally introduced by Jacobson^[1] to encode bit vectors, (unlabeled) trees, and planar graphs. Unlike general lossless data compression algorithms, succinct data structures retain the ability to use them in-place, without decompressing them first. A related notion is that of a compressed data structure, insofar as the size of the stored or encoded data similarly depends upon the specific content of the data itself.

Suppose that ${\displaystyle Z}$ is the information-theoretical optimal number of bits needed to store some data. A representation of this data is called:

• implicit if it takes ${\displaystyle Z+O(1)}$ bits of space,
• succinct if it takes ${\displaystyle Z+o(Z)}$ bits of space, and
• compact if it takes ${\displaystyle O(Z)}$ bits of space.

For example, a data structure that uses ${\displaystyle 2Z}$ bits of storage is compact, ${\displaystyle Z+{\sqrt {Z}}}$ bits is succinct, ${\displaystyle Z+\lg Z}$ bits is also succinct, and ${\displaystyle Z+3}$ bits is implicit.

Implicit structures are thus usually reduced to storing information using some permutation of the input data; the most well-known example of this is the heap.