new bloom filter post

Author: mugulmd

_posts/2025-11-29-bloom-filter.md

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+---
+layout: post
+title:  "bloom filter"
+date:   2025-11-29 14:43:00 +0200
+categories: tech
+---
+
+I had a lot of topics in mind for this 1st tech post, each one more complex (and fascinating) than the other, but in the end I chose the simplest one: Bloom filters.
+
+Start simple and small, then build up to something more intricate. When in doubt, that's always a good way to go (in my experience at least).
+
+Anyway, Bloom filters: what about them?
+
+I didn't know about their existence until quite recently, and I was surprised that none of my teacher ever mentionned them while I was studying computer science.
+
+You can see them as an optimization structure to accelerate some queries on a *set*.
+In particular, if you have a set of objects and you want to know if some other object belongs to that set or not, then a Bloom filter can tell you two things:
+- no, the object is definitely not in the set
+- maybe, you'll have to ask the actual set interface for a more precise answer.
+And the whole point is that it can give you this answer *very quickly*, and the filter's memory footprint is also super light.
+
+How does it work?
+
+The filter is composed of B bits and H (independent) hash functions, all of them taking an object as input and returning an integer between 0 and M-1.
+Initially all M bits are set to 0.
+When an object is added to the set, we compute it's H hashes, all of which providing a bit position that will be set to 1.
+
+Now when you want to know if some object belongs to the set, compute it's H hashes and check that all corresponding bits are all 1s.
+If not, then this object is definitely not in the set. Otherwise well...we don't know, so we pass the query onto the actual set interface!
+
+Since the hash functions are independant, any object should be mapped to M "random" bit positions, therefore it's very unlikely that an object that is **not** in the set actually passes the filter test.
+And that's where the true beauty of Bloom filter is: since this model is pretty simple, we can actually quantify this probability (with actual math and calculus yes!), depending on B, H, and the number of items in the set.
+
+I'm not gonna do the maths here, mainly because I haven't figured out yet how to make math expressions work with Jekyll, but they're easy to find online.
+