hierarchiescoordinate

hierarchiescoordinate is a concept used to describe a coordinate-based representation for items arranged in a hierarchy. It refers to encoding the location of a node within a tree-like structure as a vector of integers, where each element indicates the position of the node among its siblings at a given level. There is no single standard for hierarchiescoordinate; implementations vary in how depth is encoded and how missing levels are represented.

In a typical scheme, coordinates are sequences of nonnegative integers. The root node may be represented by an empty sequence or by a designated zero-length coordinate; the root's first child is [1], the second child [2], and so on. A node's coordinate extends from its parent by appending the child index, e.g., [2] -> [2,1] for its first child. Depth limits can be enforced, and schemes may allow ragged coordinates with optional delimiters.

Semantics for comparison and navigation are usually defined lexicographically by the coordinate vectors. A is ancestor of B if A's coordinate is a prefix of B's coordinate; siblings differ at the last element; distance can be defined in terms of tree edges. Operations include computing a parent (remove last element), obtaining a child (append a new index), and enumerating descendants (generate extended coordinates).

Common uses include compactly encoding hierarchical keys in databases, file systems, or ontologies; enabling efficient range queries and neighborhood queries by lexicographic order; and simplifying serialization without maintaining separate tree pointers. Limitations include the need to update coordinates when the tree structure changes, potential growth of coordinate length with depth, and ambiguity if unequal depths are not consistently handled.

Other terms with similar goals include path encoding, nested sets, and hierarchical label indexing. hierarchiescoordinate emphasizes a path-like vector representation rather than a flat numeric label, and its exact form depends on the domain and implementation.