Establish theoretical guarantees for Multi-Probe LSH

Establish formal theoretical guarantees for Multi-Probe LSH in Euclidean-space approximate near neighbor search, specifying provable bounds (e.g., success probability and query time/space complexities) under its multi-probing strategy of querying multiple nearby hash buckets, so that its performance can be grounded comparably to E2LSH’s guarantees.

Background

The paper surveys LSH variants that reduce index size compared to E2LSH. Multi-Probe LSH improves practical performance by probing multiple nearby buckets instead of building many hash tables, but unlike E2LSH it lacks established theoretical guarantees. The authors explicitly note this gap while contrasting methods’ guarantees and practical performance.

Formal guarantees (success probability, time and space bounds) are central to LSH methods’ appeal, and their absence for Multi-Probe LSH is highlighted as an unresolved issue in the literature referenced by the paper.