Lotustree

Lotustree is a term used in computer science to describe a family of hierarchical, multi-level data structures inspired by the growth pattern of the lotus plant. The structure emphasizes broad branching at higher levels with more compact arrangements near the leaves, mirroring the way lotus petals radiate from a center. There is no universally accepted specification, and implementations vary among researchers and projects.

Typical lotustrees are composed of a root and several levels of internal nodes. Each internal node can have multiple children, often organized in circular or ring-like arrangements to facilitate parallel traversal and locality. Leaf nodes store pointers to records or data blocks, while internal nodes store routing keys and compact summaries, such as minimum or maximum values, to guide searches toward relevant subtrees.

Core operations include insertion, search, and deletion. When a node reaches capacity, it can split into two nodes, and routing keys are updated to preserve ordering. Rebalancing schemes may relocate subtrees to maintain balanced height and to preserve the lotus-like symmetry of the structure. Some variants employ lazy updates to amortize reorganization costs.

Performance depends on the chosen fan-out and balancing strategy. In balanced forms, search and insertion costs approach logarithmic time with respect to the number of stored items. Several variants have been proposed, sometimes under names such as RadixLotus or CompactLotus, each optimizing for cache locality, disk I/O, or concurrent access.

Lotustrees have been discussed in database indexing, spatial data management, and file systems where hierarchical indexing and locality are beneficial. The term appears in academic discussions and some open source projects but lacks a standardized specification, so implementations vary widely.

See also: B-tree, B+-tree, R-tree, quad-tree, k-d tree.