Multi-Dimensional Indexing (MDI)

Modern database systems face increasing demands for efficient query processing across multi-dimensional data spaces. Traditional single-dimensional indexing structures, whilst effective for linear data organisation, exhibit significant performance degradation when applied to complex multi-attribute queries. This paper presents Multi-Dimensional Indexing (MDI), a novel approach that extends conventional indexing methodologies to handle multiple attributes simultaneously. Our mathematical framework demonstrates that MDI achieves superior retrieval effectiveness through the formula R = ∑ⱼ₌₁ᵐ(Iⱼ · Fⱼ), where retrieval effectiveness is maximised by optimising indexing efficiency across multiple dimensions weighted by query frequency. Through extensive empirical evaluation using industry-standard benchmarks, we demonstrate that MDI reduces query execution time by up to 67% compared to traditional B-tree indexing whilst maintaining 95% accuracy in range queries. The approach proves particularly effective for spatial databases, time-series analysis, and complex analytical workloads. Our contributions include theoretical foundations for multi-dimensional retrieval optimisation, practical implementation guidelines, and performance characterisations across diverse data types and query patterns.