subpath

Subpath is a term used in mathematics and computer science to denote a contiguous portion of a path. A path is a sequence of connected elements—such as vertices in a graph or components of a string—and a subpath is a segment of that sequence that itself forms a valid path. The defining feature is contiguity: the elements of a subpath appear consecutively in the original path. In many contexts, a subpath can be the entire path (the trivial case) or a shorter segment.

In graph theory, if P = (v0, v1, ..., vn) is a path, then for any i ≤ j, the sequence (vi, vi+1, ..., vj) is a subpath of P. This notion is useful in dynamic programming, shortest-path analyses, and path decompositions where segments are combined or compared.

In routing and network contexts, a subpath refers to a segment of a route between two intermediate points. Algorithms may optimize or evaluate costs on subpaths and then concatenate them to form longer routes.

In software and data processing, subpath appears in path-handling APIs. Many languages offer a method to extract a subpath from a larger path by selecting a consecutive range of path components. For example, some APIs treat a file system path as a sequence of name elements and provide a subpath method to obtain a subset of those elements.

Subpaths are distinct from substrings or subsequences in that they preserve order and contiguity; substrings and subsequences may skip elements, while a subpath maintains consecutive elements from the original path. See also path, substring, subsequence, segment.