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

TL;DR

This paper introduces a trie-based deterministic top-k retrieval method using LCP similarity that is space-efficient and significantly reduces energy consumption and latency on GPUs, enabling scalable and reliable sequence retrieval.

Contribution

It presents a new O(N*L) space index for deterministic retrieval, proves a tight space lower bound, and introduces TAL for energy-efficient range scans on modern hardware.

Findings

308x energy reduction per query

329x latency improvement on range scans

scalable deterministic retrieval with near-peak hardware utilization

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.