Roaring bitmap using more storage than normal bitset

Question

I have a bitset which i am using to track whether an item is present or not example

b = 01100110000

it represents that 2nd and 3rd items are present and 1st and 4th item are not present.

While searching for library which can optimise this bitset array. I came across Roaring bitmaps which sounded very exciting.

I did a quick test with it,

    public static void main(String[] args) throws IOException {
        RoaringBitmap roaringBitMap = new RoaringBitmap();
        BitSet bitSet = new BitSet(5000);
        double prob = 0.001;
        Random random = new Random();
        for (int i = 0; i < 5000; i++) {
            if (random.nextDouble() < prob) {
                bitSet.set(i);
                roaringBitMap.add(i);
            }
        }
        System.out.println(bitSet.cardinality());
        System.out.println("bitset bytes: "+ bitSet.size());
        System.out.println("RoaringBitmap bytes: " + roaringBitMap.getSizeInBytes() * 8);
    }

Basically we are setting some values and check overall size of data structure.

when we run this with multiple prob values. I got

prob byte	bitset bytes	RoaringBitmap bytes
0.001	5056	288
0.01	5056	944
0.1	5056	7872
0.999	5056	65616

If you see as we insert more and more numbers, the memory footprint of RoaringBitmap increases.

1. Is this expected?
2. In the worst case should it not just fall back to bitset based implementaiton?
3. can't 0.999 be treated as inverse of 0.001 and we would be able to store it in 288 bytes?
4. What is the most optimal way to represent these bitset as String when we are making inter service calls and using jackson library (but not byte based serialisation libraries)

Answer 1

this seems to be the case when number of entries are small, But as we increase the number of entries, the different becomes less visible. Although it is not confirmed by the lib author ( i asked here and followed up here)

prob	number of entries	bitset bits	RoaringBitmap bits	saving %
0.001	50000	50048	928	98
0.01	50000	50048	7744	84
0.1	50000	50048	65616	-31
0.999	50000	50048	65616 <- NOTE it does not increase	-31
0.001	500000	500032	8704	98
0.01	500000	500032	80720	83
0.1	500000	500032	524480	-4
0.999	500000	500032	524480 <- NOTE it does not increase	-4
0.001	50000000	50000000	835232	98
0.01	50000000	50000000	8036368	83
0.1	50000000	50000000	50016240	-0.03
0.999	50000000	50000000	50016240 <- NOTE it does not increase	-0.03

looking at this it seems like as number of entries grows they might be using bitmap only behind the scene. The take away is that don't blindly use the library, test for your use case.