Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Deterministic Retrieval at Scale: Optimal-Space LCP Indexing and 308x Energy Reduction on Modern GPUs

Stanislav Byriukov

TL;DR

This work tackles deterministic top-$k$ retrieval under Longest Common Prefix (LCP) similarity for datasets of $N$ sequences length $L$, proving a space lower bound and delivering a trie-based index that uses $O(NL)$ space with $O(L+k)$ query time. It introduces Thermal-Aware Logic (TAL) to transform prefix structures into energy-efficient, range-bounded scans, achieving $308\times$ energy reduction and $329\times$ latency improvements on a 20M-item benchmark on NVIDIA GPUs while maintaining near-peak utilization. The authors also establish a determinism guarantee for all executions and provide extensive hardware validation, showing that the LCP-Index both preserves exact results and operates efficiently enough for safety-critical, edge, and distributed systems. The combination of provable optimality, deterministic retrieval, and substantial energy savings has direct implications for certification-compliant memory retrieval in aerospace, automotive, and multi-agent robotics contexts. These results advance a practical deterministic primitive for scalable similarity retrieval where approximate methods are unacceptable. All math is presented with $...$ delimiters where used, and the work emphasizes a path toward reproducible, certifiable high-performance retrieval primitives.

Abstract

We study deterministic top-k retrieval under Longest Common Prefix (LCP) similarity for N sequences of length L. We prove a tight Omega(N) space lower bound (cell-probe model) and present a trie-based index using O(N*L) space with O(L+k) query time. We contrast this with pairwise materialization (Theta(N^2)), which hits a practical OOM wall at scale, while our indexed approach remains O(N) in memory. We then introduce Thermal-Aware Logic (TAL), which turns prefix structure into range-bounded scans. In hardware measurements, TAL reduces energy per query by 308x (0.0145 J vs 4.46 J) and cuts p95 latency by 329x (0.114 ms vs 37.5 ms) on a 20M-item range-scan benchmark, while sustaining near-peak utilization (~99%) under long runs. The result is a deterministic retrieval primitive with receipts in regimes where approximate methods are unacceptable.

Deterministic Retrieval at Scale: Optimal-Space LCP Indexing and 308x Energy Reduction on Modern GPUs

TL;DR

This work tackles deterministic top- retrieval under Longest Common Prefix (LCP) similarity for datasets of sequences length , proving a space lower bound and delivering a trie-based index that uses space with query time. It introduces Thermal-Aware Logic (TAL) to transform prefix structures into energy-efficient, range-bounded scans, achieving energy reduction and latency improvements on a 20M-item benchmark on NVIDIA GPUs while maintaining near-peak utilization. The authors also establish a determinism guarantee for all executions and provide extensive hardware validation, showing that the LCP-Index both preserves exact results and operates efficiently enough for safety-critical, edge, and distributed systems. The combination of provable optimality, deterministic retrieval, and substantial energy savings has direct implications for certification-compliant memory retrieval in aerospace, automotive, and multi-agent robotics contexts. These results advance a practical deterministic primitive for scalable similarity retrieval where approximate methods are unacceptable. All math is presented with delimiters where used, and the work emphasizes a path toward reproducible, certifiable high-performance retrieval primitives.

Abstract

We study deterministic top-k retrieval under Longest Common Prefix (LCP) similarity for N sequences of length L. We prove a tight Omega(N) space lower bound (cell-probe model) and present a trie-based index using O(N*L) space with O(L+k) query time. We contrast this with pairwise materialization (Theta(N^2)), which hits a practical OOM wall at scale, while our indexed approach remains O(N) in memory. We then introduce Thermal-Aware Logic (TAL), which turns prefix structure into range-bounded scans. In hardware measurements, TAL reduces energy per query by 308x (0.0145 J vs 4.46 J) and cuts p95 latency by 329x (0.114 ms vs 37.5 ms) on a 20M-item range-scan benchmark, while sustaining near-peak utilization (~99%) under long runs. The result is a deterministic retrieval primitive with receipts in regimes where approximate methods are unacceptable.
Paper Structure (79 sections, 16 theorems, 21 equations, 2 figures, 11 tables, 6 algorithms)

This paper contains 79 sections, 16 theorems, 21 equations, 2 figures, 11 tables, 6 algorithms.

Table of Contents

  1. Introduction
  2. Motivation
  3. Contributions
  4. Paper Organization
  5. Preliminaries
  6. Notation and Definitions
  7. Computational Model
  8. Related Work
  9. Approximate Nearest Neighbor Search
  10. Locality-Sensitive Hashing (LSH).
  11. Hierarchical Navigable Small World (HNSW).
  12. Product Quantization and IVF.
  13. Exact Nearest Neighbor
  14. k-d Trees and Ball Trees.
  15. Metric Trees.
  16. ...and 64 more sections

Key Result

Theorem 1

The distance $d$ satisfies the strong triangle inequality: for all $s, t, u \in \Sigma^L$.

Figures (2)

  • Figure 1: Memory scaling: materialization vs LCP-Index. The dashed line shows H100 memory limit.
  • Figure 2: TAL energy reduction scales with bucket count, matching theoretical $O(1/B)$.

Theorems & Definitions (40)

  • Example 1: GNC Sensor Fusion
  • Definition 1: LCP Similarity
  • Definition 2: Top-$k$ LCP Retrieval
  • Definition 3: LCP-Induced Ultrametric
  • Theorem 1: Ultrametric Property
  • proof
  • Definition 4: Cell-Probe Complexity
  • Theorem 2: Space Lower Bound
  • proof
  • Theorem 3: Query Lower Bound
  • ...and 30 more