mih-rs

Rust implementation of multi-index hashing (MIH) for neighbor searches on binary codes in the Hamming space, described in the paper

Norouzi, Punjani, and Fleet, Fast exact search in Hamming space with multi-index hashing, IEEE TPAMI, 36(6):1107– 1119, 2014.

As the benchmark result shows, on 10 million 64-bit codes, mih-rs can perform top-k searches 19−94 times faster than linear search when k = 1..100.

Features

• Two types of neighbor searches: mih-rs provides the two search operations:

  • Range search finds neighbor codes whose Hamming distances to a given code are within a radius.
  • Top-K search finds the top-K codes that are closest to a given code.

• Fast and memory-efficient implementation: The data structure is built on sparse hash tables, following the original implementation.

• Parameter free: mih-rs automatically sets an optimal parameter of MIH depending on a given database (although you can also set this manually).

• Serialization: mih-rs supports to serialize/deserialize the index.

Example

use mih_rs::Index;

// Database of codes
let codes: Vec<u64> = vec![
    0b1111111111111111111111011111111111111111111111111011101111111111, // #zeros = 3
    0b1111111111111111111111111111111101111111111011111111111111111111, // #zeros = 2
    0b1111111011011101111111111111111101111111111111111111111111111111, // #zeros = 4
    0b1111111111111101111111111111111111111000111111111110001111111110, // #zeros = 8
    0b1101111111111111111111111111111111111111111111111111111111111111, // #zeros = 1
    0b1111111111111111101111111011111111111111111101001110111111111111, // #zeros = 6
    0b1111111111111111111111111111111111101111111111111111011111111111, // #zeros = 2
    0b1110110101011011011111111111111101111111111111111000011111111111, // #zeros = 11
];

// Query code
let qcode: u64 = 0b1111111111111111111111111111111111111111111111111111111111111111; // #zeros = 0

// Construct the index
let index = Index::new(codes).unwrap();

// Find the ids of neighbor codes whose Hamming distances are within 2
let mut searcher = index.range_searcher();
let answers = searcher.run(qcode, 2);
assert_eq!(answers, vec![1, 4, 6]);

// Find the ids of the top-4 nearest neighbor codes
let mut searcher = index.topk_searcher();
let answers = searcher.run(qcode, 4);
assert_eq!(answers, vec![4, 1, 6, 0]);

// Serialization/Deserialization
let mut data = vec![];
index.serialize_into(&mut data).unwrap();
let other = Index::<u64>::deserialize_from(&data[..]).unwrap();
assert_eq!(index, other);

Binary code types

mih_rs::Index can be built from a vector of type mih_rs::CodeInt that is a primitive integer trait supporting a popcount operation. Currently, this library defines mih_rs::CodeInt for u8, u16, u32, and u64.

Benchmark

timeperf_topk.rs offers the benchmark of top-K search for MIH and LinearSearch algorithms on binary code types u32 and u64.

The following table shows the result of average search times in milliseconds per query, in the settings:

• Database: N random codes from a uniform distribution.
• Query set: 100 random codes from a uniform distribution.
• Machine: MacBook Pro (2019) of Quad-Core Intel Core i5 @2.4 GHz with 16 GB of RAM.
• Library version: v0.2.0

Result for u32

Algorithm	N=10,000	N=100,000	N=1,000,000	N=10,000,000
MIH (K=1)	0.01	0.02	0.07	0.38
MIH (K=10)	0.04	0.08	0.30	1.06
MIH (K=100)	0.13	0.22	1.22	4.35
LinearSearch	0.36	4.40	50.96	626.87

Result for u64

Algorithm	N=10,000	N=100,000	N=1,000,000	N=10,000,000
MIH (K=1)	0.10	0.36	1.46	6.7
MIH (K=10)	0.20	0.76	3.72	14.8
MIH (K=100)	0.41	1.53	7.02	33.2
LinearSearch	0.36	4.36	52.28	629.1

Licensing

This library is free software provided under MIT.