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Aguri: Coolest Data Structure You've Never Heard Of
- mojuba 19y agoRadix tries are nice. Use them when (1) you need fast lookup and fast inserts (2) you need to preserve the lexicograhpic order of your elements - something that a hash table won't give you (3) you are afraid of DoS attacks or maybe just "bad" data - hash tables can be attacked easily if the implementation is known (4) you don't care about memory usage that much. I compared a simple 8-bit radix tree with some standard hash table implementation - the former took roughly ten times more memory. I then changed my radix to be based on 4 bits (each char is just split into 2 parts) and the memory usage improved twice. Now I'm wondering if radix tries have more room for improvement. So this is something to consider. And thanks for the article - never heard of Aguri, it's beautiful. Upd. sorted lists basically give you same advantages except for fast inserts
- tptacek 19y agoCompressed binary radix tries (also known as PATRICIA trees) give you excellent memory usage characteristics and pretty much optimal search time characteristics: both wins come from only storing the edges corresponding to significant bit differences. Since hash tables by necessity have to allocate enough storage to keep table load down and minimize collisions, you could find a PATRICIA tree has even better memory footprint than whatever hash table you use. Of course, all data structures share the DoS problem. There's an input to a PATRICIA tree that pessimizes lookup and memory usage: the one that creates a full 32 bits of fanout for every key. In all cases, the attack degrades performance to linear search. Of all the "mainstream" data structures, balanced binary trees are probably the hardest to attack this way.
- tptacek 19y agoI am, of course, an idiot; you can't make a PATRICIA lookup worse than O(k).
- mojuba 19y agoboth wins come from only storing the edges corresponding to significant bit differences. Of course I used compressed suffixes, but it didn't help much as compared with hash tables. you could find a PATRICIA tree has even better memory footprint than whatever hash table you use I don't think you can demonstrate that Patricia has a better memory footprint than a good hashtable. In fact best radix trees are much worse. Of course, all data structures share the DoS problem. You can attack radix trees in terms of memory usage, while hash tables are prone to serious performance attacks. In all cases, the attack degrades performance to linear search. Not true. I don't think you understand these algorithms and O(n) complexity very well. The question how a hash table degrades when attacked highly depends on how exactly conflict resolution is implemented. Among other methods is, for example, expansion and rehashing, and you can't tell for sure if it degrades to linear search or not. And radix never degrades to linear search - never. Of all the "mainstream" data structures, balanced binary trees are probably the hardest to attack this way. They are prone to a very specific attack when you make the tree to re-balance often.
- tptacek 19y agoYou're ignoring table load factor in your memory comparison, you can attack any dictionary "in terms of memory", I conceded the O(n)/O(k) lookup thing before you wrote this, and why do you think "balancing" a red-black tree is expensive?
- mojuba 19y agoYou're ignoring table load factor in your memory comparison I believe I don't ignore anything, I'm measuring precise memory usage by two identical programs doing same thing but based on different algorithms. I also believe I got the most out of radix in my tests. The 4-bit version of radix wasn't trivial, but it was reasonably fast and the mem usage was twice as better than the 8-bit one, as I said before. But even speculatively, on paper if you wish, radix consumes more memory than some good hash table implementation. Upd. forgot to mention, I did some more optimizations as well, like compressing the pointer tables in tree nodes.
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- jwp 19y agoSuffix array.
- andrewf 19y agoA couple of years back, googling for "suffix array" got you advertisements for jobs@google. I'm not sure whether Google HR ended the program, or just migrated to more obscure search terms :)
- dfranke 19y agoKnuth has a pretty good treatment of tries in volume 3.
- Xichekolas 19y agoHe says binary trees are better default search table than hash table... binary tree search is O(lg(n)) while hash table is O(1)... so hash table is better for search, binary trees win in other ways (like ordered traversal if you need that), but no way you could say one is always better than the other. Also confused how he proposes to build his Radix Trie in less than linear time... just seems like he ditches his original premise and launches into routing. There are selection algorithms that will find things in an unsorted array in O(lg(n))... but pretty sure building a tree of any sort is not part of it. Radix Tries are sweet fun... so is just good old Radix Sort, but he starts with something that doesn't really make sense for the topic (the unsorted array he wants to pull three out of), then makes some weird claims, then jumps into routing with Radix Tries... not sure what is insightful here.
- aston 19y agoThere aren't any algorithms to find things in an unsorted array in less than worst case linear time. I think you're confusing search (for some value) with select (a value with a given index in the sorted array).
- Xichekolas 19y agoYeah, yeah I was... was just thinking about that over breakfast.
- eru 19y agoIf you want to do several searches on the same data - that is initially unsorted - you can get better than O(n) per query. But like you said - not for the first one.
- tptacek 19y agoHash tables are NOT O(1). You just failed the job interview. You're like the 4th person I've seen that read (some) of this article and pulled this tree vs. hash thing out of it. It's a throwaway point. Binary trees provide comparable performance to hash tables, but also provide efficient access to ranges of keys. Binary trees support more operations efficiently than hash tables. The article isn't about some war I've declared on hash tables.
- garret 19y agoD. J. Bernstein uses these too. http://cr.yp.to/critbit.html http://cr.yp.to/critbit.html
- codeslinger 19y agoThe point of the data structure in this case was not the radix trie alone but rather the combination of the use of tries in concert with the aggregation characteristics of IP traffic. This type of innovative combination is common in the network world due to the necessity of providing ever more introspection and functionality over ever higher throughputs and ever lower latencies. For some serious treatment of the subject, check out the book "Network Algorithmics" by George Varghese.
- tptacek 19y agoThis is an awesome, awesome, awesome book. Aguri isn't in it; aguri doesn't even rate for this book. That's how awesome this book is.
- anupamkapoor 19y agonetwork-algorithmics is just soooo cool. really, what you must be reading after stevens.
- hisham 19y agoWow reading this post was like replaying one of my interviews with Google...
- deleted 19y ago[deleted]
- RajendranB 19y agoThe time space trade off between hashtables and binary trees are not touched upon in all the above writings. Hashtables will require continuous memory locations and hence from stack and hence won't work for large sets of data and binary search trees or their derivatives will allocate memory from heap and take more time (logn) for get and put than the constant time(O(1)) for hashtables.
- bayareaguy 19y agoIt sounds like you're making a lot of assumptions about the storage hierarchy and addressing scheme.