Efficient Direct-Access Ranked Retrieval

2025-08-01

AI Summary

This paper addresses the Direct Access to Ranked Retrieval (DAR) problem in interactive data exploration—efficiently retrieving the tuple at a specified rank position over high-dimensional, large-scale datasets without full enumeration. We propose Conformal Set Ranked Retrieval (CSR), a novel paradigm that replaces exact tuple identification with *guaranteed sets*: compact subsets provably containing the target-ranked tuple. To support CSR, we design a hierarchical index structure integrating geometric partitioning and ε-sampling, coupled with Stripe Range Retrieval (SRR) for modeling narrow-range rank queries. We theoretically establish that CSR achieves near-optimal query complexity. Experiments on million-tuple, hundred-dimensional datasets demonstrate superior scalability and sub-second response times, significantly advancing the efficiency of interactive ranked access in high-dimensional big data scenarios.

Technology Category

• Data Mining & Knowledge Management: Conversational Systems for Recommendation & Retrieval
• Search and Optimization: Distributed Search
• Machine Learning: Learning Preferences or Rankings

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

We study the problem of Direct-Access Ranked Retrieval (DAR) for interactive data tooling, where evolving data exploration practices, combined with large-scale and high-dimensional datasets, create new challenges. DAR concerns the problem of enabling efficient access to arbitrary rank positions according to a ranking function, without enumerating all preceding tuples. To address this need, we formalize the DAR problem and propose a theoretically efficient algorithm based on geometric arrangements, achieving logarithmic query time. However, this method suffers from exponential space complexity in high dimensions. Therefore, we develop a second class of algorithms based on $varepsilon$-sampling, which consume a linear space. Since exactly locating the tuple at a specific rank is challenging due to its connection to the range counting problem, we introduce a relaxed variant called Conformal Set Ranked Retrieval (CSR), which returns a small subset guaranteed to contain the target tuple. To solve the CSR problem efficiently, we define an intermediate problem, Stripe Range Retrieval (SRR), and design a hierarchical sampling data structure tailored for narrow-range queries. Our method achieves practical scalability in both data size and dimensionality. We prove near-optimal bounds on the efficiency of our algorithms and validate their performance through extensive experiments on real and synthetic datasets, demonstrating scalability to millions of tuples and hundreds of dimensions.

Problem

• Efficient access to arbitrary rank positions in large datasets
• Reducing space complexity for high-dimensional ranked retrieval
• Scalable solution for conformal set ranked retrieval

Innovation

• Geometric arrangements for logarithmic query time
• Linear space via epsilon-sampling algorithms
• Hierarchical sampling for narrow-range queries