🤖 AI Summary
This work addresses the high computational cost of exact range queries and the excessive false positive rates of existing approximate methods such as SRC. To this end, we propose c-DAG, a tunable 1D-Tree–enhanced structure featuring densely overlapping nodes with at least three branches per node, enabling efficient approximate range queries. Theoretical analysis demonstrates that c-DAG reduces the average false positive rate by a logarithmic factor. Furthermore, we introduce a general extension framework tailored to empirical query distributions and prove its superiority over baseline approaches in structural privacy preservation. Experimental evaluation on the Gowalla dataset confirms that c-DAG significantly lowers false positive rates while maintaining comparable time and memory overheads, highlighting its potential for applications in searchable encryption and multimedia retrieval.
📝 Abstract
Range queries are simple and popular types of queries used in data retrieval. However, extracting exact and complete information using range queries is costly. As a remedy, some previous work proposed a faster principle, {\em approximate} search with range queries, also called single range cover (SRC) search. It can, however, produce some false positives. In this work we introduce a new SRC search structure, a $c$-DAG (Directed Acyclic Graph), which provably decreases the average number of false positives by logarithmic factor while keeping asymptotically same time and memory complexities as a classic tree structure. A $c$-DAG is a tunable augmentation of the 1D-Tree with denser overlapping branches ($c \geq 3$ children per node). We perform a competitive analysis of a $c$-DAG with respect to 1D-Tree and derive an additive constant time overhead and a multiplicative logarithmic improvement of the false positives ratio, on average. We also provide a generic framework to extend our results to empirical distributions of queries, and demonstrate its effectiveness for Gowalla dataset. Finally, we quantify and discuss security and privacy aspects of SRC search on $c$-DAG vs 1D-Tree, mainly mitigation of structural leakage, which makes $c$-DAG a good data structure candidate for deployment in privacy-preserving systems (e.g., searchable encryption) and multimedia retrieval.