A simpl(istic) Java implementation of the Elias-Fano compression schema

As a coding exercise, I have implemented in Java a simple version of the Elias-Fano compression schema. This is a technique for compressing arrays of monotonically increasing integers. The interesting aspect is that the Elias-Fano compression schema permits to retrieve the i-th element in the compressed data, without decompressing the whole array. Similarly, it permits to find the index of the first element in the compressed data which is greater or equal to a given value — without decompressing the whole array. You can find the code on my github (here).


 int[] a = ...; //an array of monotonically increasing integers; 
//compress the array 
EliasFano ef = new EliasFano(); 
int u = a[a.length - 1]; //the maximum value in a; 
int size = ef.getCompressedSize(u, a.length); //the size of the compressed array
byte[] compressed = new byte[size]; 
ef.compress(a, 0, a.length, compressed, 0); 
//decompress the array 
int[] b = new int[a.length]; 
int L = ef.getL(u, a.length); //the number of lower bits (see references) 
ef.decompress(compressed, 0, a.length, L, b, 0); 
//get the value of the 4-th element in the compressed data 
int val = ef.get(compressed, 0, a.length, L, 3); 
//get the index of the first element, in the compressed data, greater or equal than 1000 
int idx = ef.select(compressed, 0, a.length, L, 1000); 

So, I can’t use it to compress non-increasing arrays, isn’t it?
Sure you can! You just need to transform your array into a monotonically increasing one, by adding to the i-th value the sum of the previous values in the array. Then, you can recompute the original i-th element doing i-th minus (i-1)-th value.

EliasFano ef = new EliasFano();
int[] a1 = ...; //a generic array
//make a2 monotonically increasing
int[] a2 = new int[a1.length];
a2[0] = a1[0];
for (int i = 1; i < a1.length; i++) a2[i]=a1[i]+a2[i-1];
//compress a2
int u = a2[a2.length-1]; //the max value in a2
int size = ef.getCompressedSize(u, a2.length);
byte[] compressed = new byte[size];
ef.compress(a2, 0, a2.length, compressed, 0);
//get the original i-th value of a1, as i-th minus (i-1)-th of a2
int L = ef.getL(u, a2.length);
int val = ef.get(compressed, 0, a2.length, L, i)-ef.get(compressed, 0, a2.length, L, i-1);

– JUnit 4

For a general understanding of the Elias-Fano technique, see:
Sebastiano Vigna, “The Revenge of Elias and Fano” (here)

More advanced material:
Sebastiano Vigna, “Quasi-succinct indices”, WSDM’13
Giuseppe Ottaviano and Rossano Venturini, “Partitioned Elias-Fano indexes”, SIGIR’14