Disk-Based Interval Indexes Under the Increasing Ending Time Assumption

2026-06-21

AI Summary

This work addresses the lack of disk-based index structures for large-scale interval data in time-series databases that simultaneously support efficient querying, fast insertion, and compact storage. The authors propose CEB and TIDE, two novel two-level append-only B⁺-tree indexes that, for the first time, map intervals into a two-dimensional corner space by leveraging interval centroids or durations together with monotonically increasing end timestamps to establish ordering and indexing mechanisms. This approach significantly improves insertion throughput and reduces storage overhead while preserving high query efficiency. Experimental results demonstrate that both CEB and TIDE outperform existing solutions in terms of index size and insertion speed, with TIDE consistently achieving superior query performance—accelerating queries by up to several orders of magnitude.

Abstract

Indexes for large collections of intervals are common in temporal databases, where each record has a lifespan, or validity interval. Despite their conceptual differences, we demonstrate that interval indexes can be captured by some corner structure in a 2D space. This representation facilitates the optimization of query processing by identifying nodes that must contain query results versus nodes that may contain results. In addition, we explore the assumption that intervals arrive in order of increasing ending time (IET) to develop disk-based indexes that have compact size, efficient insertions, and fast query processing. Specifically, we first develop CEB, an index in the corner space defined by the interval center and endpoint. Our second contribution is TIDE, which organizes intervals by their duration and endpoint. CEB and TIDE adopt a two-layer architecture, where the leaf nodes of a top tree (ordering intervals by their center or duration) correspond to the root nodes of bottom trees, ordering intervals by their endpoints. Both top and bottom trees are append-only B+-trees to facilitate fast insertions. CEB and TIDE outperform state-of-the-art competitors in terms of index size and insertion speed. In addition, TIDE is always faster in query processing, sometimes by orders of magnitude.

Problem

• interval indexes
• disk-based indexing
• increasing ending time
• temporal databases
• query processing

Innovation

• interval index
• corner structure
• increasing ending time
• append-only B+-tree
• two-layer architecture