linesrows

Linesrows is a theoretical data representation used in discussions of two-dimensional data storage and processing. It combines two organizational axes—lines and rows—to allow efficient access and compression for datasets where meaningful segments align along both dimensions.

In a linesrows model, data is partitioned into a lines component, which records contiguous line segments with coordinates and value ranges, and a rows component, which indexes rows that contain data and stores per-row metadata. The two components reference each other to reconstruct the full matrix when needed. This separation supports selective retrieval by line or by row without scanning the entire matrix.

Algorithms in linesrows focus on maintaining consistency between line and row indices during updates and on performing range or neighborhood queries efficiently. The representation can be implemented by adapting established sparse-matrix formats, such as CSR or CSC, augmented with line-segment metadata to mark line extents and transitions.

Applications include sparse matrices with structured sparsity, geographic grids with linear features, time-series tabular data with spatial relationships, and streaming pipelines where partial window access is common. Limitations include added encoding complexity and potential overhead when data density is high or when both axes lack structure.

See also: sparse matrix formats, CSR, CSC, run-length encoding, grid data structures.