Implicit data structure

In computer science, an implicit data structure or space-efficient data structure is a data structure that stores very little information other than the main or required data: a data structure that requires low overhead. They are called "implicit" because the position of the elements carries meaning and relationship between elements; this is contrasted with the use of pointers to give an explicit relationship between elements. Definitions of "low overhead" vary, but generally means constant overhead; in big O notation, O(1) overhead. A less restrictive definition is a succinct data structure, which allows greater overhead.

Formally, an implicit data structure is one with constant (O(1)) space overhead (above the information-theoretic lower bound).

Historically, Munro, & Suwanda (1980) defined an implicit data structure (and algorithms acting on one) as one "in which structural information is implicit in the way data are stored, rather than explicit in pointers." They are somewhat vague in the definition, defining it most strictly as a single array, with only the size retained (a single number of overhead), or more loosely as a data structure with constant overhead (O(1)). This latter definition is today more standard, and the still-looser notion of a data structure with non-constant but small (o(N)) overhead is today known as a succinct data structure, as defined by Jacobson (1988); it was referred to as semi-implicit by Munro, & Suwanda (1980).

A fundamental distinction is between static data structures (read-only) and dynamic data structures (which can be modified). Simple implicit data structures, such as representing a sorted list as an array, may be very efficient as a static data structure, but inefficient as a dynamic data structure, due to modification operations (such as insertion in the case of a sorted list) being inefficient.

A trivial example of an implicit data structure is an array data structure, which is an implicit data structure for a list, and requires only the constant overhead of the length; unlike a linked list, which has a pointer associated with each data element, which explicitly gives the relationship from one element to the next. Similarly, a null-terminated string is an implicit data structure for a string (list of characters). These are considered very simple because they are static data structures (read-only), and only admit the simple operation of iteration over the elements.

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