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).

Example

```rust use mih_rs::Index;

// Database of codes let codes: Vec = 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.rangesearcher(); let answers = searcher.run(qcode, 2); asserteq!(answers, vec![1, 4, 6]);

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

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.