I need to read from a dataset which is very large, highly interlinked, the data is fairly localized, and reads are fairly expensive. Specifically:
The data sets are 2gigs - 30gigs in size, so I have to map sections of the file into memory to read. This is very expensive compared to the rest of the work I do in the algorithm. From profiling I've found roughly 60% of the time is spent reading the memory, so this is the right place to start optimizing.
When operating on a piece of this dataset, I have to follow links inside of it (imagine it like being similar to a linked list), and while those reads aren't guaranteed to anywhere near sequential, they are fairly localized. This means:
Let's say, for example, we operate on 2 megs of memory at a time. If you read 2 megs of data into memory, roughly 40% of the reads I will have to subsequently do will be in that same 2 megs of memory. Roughly 20% of the reads will be purely random access in the rest of the data, and the other 40% very likely links back into the 2meg segment which pointed to this one.
From knowledge of the problem and from profiling, I believe that introducing a cache to the program will help greatly. What I want to do is create a cache which holds N chunks of X megs of memory (N and X configurable so I can tune it) which I can check first, before having to map another section of memory. Additionally, the longer something has been in the cache, the less likely it is that we will request that memory in the short term, and so the oldest data will need to be expired.
After all that, my question is very simple: What data structure would be best to implement a cache of this nature?
I need to have very fast lookups to see if a given address is in the cache. With every "miss" of the cache, I'll want to expire the oldest member of it, and add a new member. However, I plan to try to tune it (by changing the amount that's cached) such that 70% or more of reads are hits.
My current thinking is to use either an AVL tree (LOG2 n for search/insert/delete) would be the safest (no degenerate cases). My other option is a sparse hashtable such that lookups would be O(1) in the best case. In theory this could degenerate into O(n), but in practice I could keep collisions low. The concern here would be how long it takes to find and remove the oldest entry in the hashtable.
Does anyone have any thoughts or suggestions on what data structure would be best here, and why?
Put the cache into two sorted trees (AVL or any other reasonably balanced tree implementation is fine--you're better off using one from a library than creating your own).
One tree should sort by position in the file. This lets you do log(n) lookups to see if your cache is there.
The other tree should sort by time used (which can be represented by a number that increments by one on each use). When you use a cached block, you remove it, update the time, and insert it again. This will take log(n) also. When you miss, remove the smallest element of the tree, and add the new block as the largest. (Don't forget to also remove/add that block to the by-position-in-file tree.)
If your cache doesn't have very many items in it, you'll be better off still by just storing everything in a sorted array (using insertion sort to add new elements). Moving 16 items down one spot in an array is incredibly fast.
Seems like you are looking for an LRU (Least Recently Used) cache: LRU cache design
If 60% of your algorithm is I/O, I suggest that the actual cache design doesn't really matter that much- any sort of cache could be a substantial speed-up.
However, the design depends a lot on what data you're using to access your chunks. String, int, etc. If you had an int, you could do a hashmap into a linked list, erase the back on cache miss, erase and then push on top if cache hit.
hashmaps are provided under varying names (most commonly, unordered map) in many implementations. Boost has one, there's one in TR1, etc. A big advantage of a hash_map is less performance loss with growing numbers, and more flexibility about key values.
Related
I am looking for suggestions on how best to implement my code for the following requirements. During execution of my c++ code, I frequently need to access data stored in a dictionary, which itself is stored in a text file. The dictionary contains 100 million entries, and at any point in time, my code would query data corresponding to some particular entry among those 100 million entries. There is no particular pattern in which those queries are made, and further during the lifetime of the program execution, not all entries in the dictionary are queried. Also, the dictionary will remain unchanged during the program's lifetime. The data corresponding to each entry is not all of the same length. The file size of my dictionary is ~24 GB, and I have only 16 GB of RAM memory. I need my application to be very fast, so I would like to know how best to implement such a system so that read access times can be minimized.
I am also the one who is creating the dictionary, so I do have the flexibility in breaking down my dictionary into several smaller volumes. While thinking about what I can do, I came up with the following, but not sure if either are good.
If I store the line offset for each entry in my dictionary from the beginning of the file, then to read the data for the corresponding entry, I can directly jump to the corresponding offset. Is there a way to do this using say ifstream without looping through all lines until the offset line? A quick search on the web seems to suggest this is not possible atleast with ifstream, are there are other ways this can be done?
The other extreme thought was to create a single file for each entry in the dictionary, so I would have 100 million files. This approach has the obvious drawback of overhead in opening and closing the file stream.
In general I am not convinced either of the approaches I have in mind are good, and so I would like some suggestions.
Well, if you only need key value accesses, and if the data is larger than what can fit in memory, the answer is a NoSQL database. That mean a hash type index for the key and arbitrary values. If you have no other constraint like concurrent accesses from many clients or extended scalability, you can roll your own. The most important question for a custom NoSQL database is the expected number of keys that will give the size of the index file. You can find rather good hashing algorithms around, and will have to make a decision between a larger index file and a higher risk of collisions. Anyway, unless you want to use a tera bytes index files, your code must be prepared to possible collisions.
A detailed explaination with examples is far beyond what I can write in a SO answer, but it should give you a starting point.
The next optimization will be what should be cached in memory. It depends on the way you expect the queries. If it is unlikely to query more than one time the same key, you can probably just rely on the OS and filesystem cache, and a slight improvement would be memory mapped files, else caching (of index and/or values) makes sense. Here again you can choose and implement a caching algorithm.
Or if you think that it is too complex for little gain, you can search if one of the free NoSQL databases could meet your requirement...
Once you decide using on-disk data structure it becomes less a C++ question and more a system design question. You want to implement a disk-based dictionary.
You should consider the following factors from now on are - what's your disk parameters? is it SSD? HDD? what's your average lookup rate per second? Are you fine having 20usec - 10ms latencies for your Lookup() method?
On-disk dictionaries require random disk seeks. Such seeks have a latency of dozens of microseconds for SSD and 3-10ms for HDD. Also, there is a limit on how many such seeks you can make a second. You can read this article for example. CPU stops being a bottleneck and IO becomes important.
If you want to pursue this direction - there are state of art C++ libraries that give you on-disk key-value store (no need for out-of- process database) or you can do something simple yourself.
If your application is a batch process and not a server/UI program, i.e. you have another finite stream of items that you want to join with your dictionary then I recommend reading about external algorithms like Hash Join or a MapReduce. In these cases, it's possible to organize your data in such way that instead of having 1 huge dictionary of 24GB you can have 10 dictionaries of size 2.4GB and sequentially load each one of them and join. But for that, I need to understand what kind of problem you are trying to solve.
To summarize, you need to design your system first before coding the solution. Using mmap or tries or other tricks mentioned in the comments are local optimizations (if at all), they are unlikely game-changers. I would not rush exploring them before doing back-on-the-envelope computations to understand the main direction.
I'm currently playing around with RocksDB (C++) and was curious about some performance metrics I've experienced.
For testing purposes, my database keys are file paths and the values are filenames. My database has around 2M entries in it. I'm running RocksDB locally on a MacBook Pro 2016 (SSD).
My use case is dominated by reads. Full key scans are quite common as are key scans that include a "significant" number of keys. (50%+)
I'm curious about the following observations:
1. An Iterator is dramatically faster than calling Get when performing full key scans.
When I want to look at all of the keys in the database, I'm seeing a 4-8x performance improvement when using an Iterator instead of calling Get for each key. The use of MultiGet makes no difference.
In the case of calling Get roughly 2M times, the keys have been previously fetched into a vector and sorted lexicographically. Why is calling Get repeatedly so much slower than using an Iterator? Is there a way to narrow the performance gap between the two APIs?
2. When fetching around half the keys, the performance between using an Iterator and Get starts to become negligible.
As the number of keys to fetch is reduced, then making multiple calls to Get starts to take about as long as using an Iterator as the iterator is paying the price of scanning over keys that aren't in the desired keyset.
Is there some "magic" ratio where this becomes true for most databases? For example, if I need to scan over 25% of the keys, then calling Get is faster, but if it's 75% of the keys, then an Iterator is faster. But those numbers are just "made up" by rough testing.
3. Fetching keys in sorted order does not appear to improve performance.
If I pre-sort the keys I want to fetch into the same order that an Iterator would return them in, that does not appear to make calling Get multiple times any faster. Why is that? It's mentioned in the documentation that it's recommended to sort keys before doing a batch insert. Does Get not benefit from the same look-ahead caching that an Iterator benefits from?
4. What settings are recommended for a read-heavy use case?
Finally, are there any specific settings recommended for a read-heavy use case that might involve scanning a significant number of keys at once?
macOS 10.14.3, MacBook Pro 2016 SSD, RocksDB 5.18.3, Xcode 10.1
RocksDB internally represents its data as a log-structured merge tree which has several sorted layers by default (this can be changed with plugins/config). The intuition from Paul's first answer holds, except there is no classical index; the data is actually sorted on disk with pointers to the next files. The lookup operation has on average logarithmic complexity, but advancing an iterator in a sorted range is constant time. So for dense sequential reads, iterating is much faster.
The point where the costs balance out is determined not only by the number of keys you read, but also by the size of the database. As the database grows, the lookup becomes slower, while Next() remains constant. Very recent inserts are likely to be read very fast, since they may still be in memory (memtables).
Sorting the keys actually just improves your cache hit-rate. Depending on your disk, the difference may be very small, e.g., if you have an NVMe SSD, the difference in access time is just not as drastic anymore as it was when it was RAM vs. HDD. If you have to do several operations over the same or even different key-sets doing them by key-order (f(a-c) g(a-c) f(d-g)...) instead of sequentially should improve your performance, since you will have more cache-hits and also benefit from the RocksDB block cache.
The tuning guide is a good starting point, especially the video on database solutions, but if RocksDB is too slow for you also consider using a DB based on a different storage algorithm. LSM is typically better for write-heady workloads, and while RocksDB lets you control read vs. write vs. space amplification very well, a b-tree or ISAM based solution may just be much faster for range-reads/repeated reads.
I don't know anything about RocksDB per-se, but I can answer a lot of this from first principles.
An Iterator is dramatically faster than calling Get when performing full key scans.
This is likely to be because Get has to do a full lookup in the underlying index (starting from the top) whereas advancing an iterator can be achieved by just moving from the current node to the next. Assuming the index is implemented as a red-black tree or similar, there's a lot less work in the second method than the first.
When fetching around half the keys, the performance between using an Iterator and Get starts to become negligible.
So you are skipping entries by calling iterator->Next () multiple times? If so, then there will come a point where it's cheaper to call Get for each key instead, yes. Exactly when that happens will depend on the number of entries in the index (since that determines the number of levels in the tree).
Fetching keys in sorted order does not appear to improve performance.
No, I would not expect it to. Get is (presumably) stateless.
What settings are recommended for a read-heavy use case?
That I don't know, sorry, but you might read:
https://github.com/facebook/rocksdb/wiki/RocksDB-Tuning-Guide
I was soving a competitive programming problem with the following requirements:
I had to maintain a list of unqiue 2d points (x,y), the number of unique points would be less than 500.
My idea was to store them in a hash table (C++ unordered set to be specific) and each time a node turned up i would lookup the table and if the node is not already there i would insert it.
I also know for a fact that i wouldn't be doing more than 500 lookups.
So i saw some solutions simply searching through an array (unsorted) and checking if the node was already there before inserting.
My question is is there any reasonable way to guess when should i use a hash table over a manual search over keys without having to benchmark them?
My question is is there any reasonable way to guess when should i use a hash table over a manual search over keys without having to benchmark them?
I am guessing you are familiar with basic algorithmics & time complexity and C++ standard containers and know that with luck hash table access is O(1)
If the hash table code (or some balanced tree code, e.g. using std::map - assuming there is an easy order on keys) is more readable, I would prefer it for that readability reason alone.
Otherwise, you might make some guess taking into account the approximate timing for various operations on a PC. BTW, the entire http:///norvig.com/21-days.html page is worth reading.
Basically, memory accesses are much more slow than everything else in the CPU. The CPU cache is extremely important. A typical memory access with cache fault requiring fetching data from DRAM modules is several hundreds times slower than some elementary arithmetic operation or machine instruction (e.g. adding two integers in registers).
In practice, it does not matter that much, as long as your data is tiny (e.g. less than a thousand elements), since in that case it is likely to sit in L2 cache.
Searching (linearly) in an array is really fast (since very cache friendly), up to several thousand of (small) elements.
IIRC, Herb Sutter mentions in some video that even inserting an element inside a vector is practically -but unintuitively- faster (taking into account the time needed to move slices) than inserting it into some balanced tree (or perhaps some other container, e.g. an hash table), up to a container size of several thousand small elements. This is on typical tablet, desktop or server microprocessor with a multimegabyte cache. YMMV.
If you really care that much, you cannot avoid benchmarking.
Notice that 500 pairs of integers is probably fitting into the L1 cache!
My rule of thumb is to assume the processor can deal with 10^9 operations per second.
In your case there are only 500 entries. An algorithm up to O(N^2) could be safe. By using contiguous data structure like vector you can leverage the fast cache hit. Also hash function sometimes can be costly in terms of constant. However if you have a data size of 10^6, the safe complexity might be only O(N) in total. In this case you might need to consider O(1) hashmap for a single lookup.
You can use Big O Complexity to roughly estimate the performance. For the Hash Table, Searching an element is between O(1) and O(n) in the worst case. That means, that in the best case your access time is independant of the number of elements in your map but in the worst case it is linear dependant on the size of your hash table.
A Binary tree has a guaranteed search complexity of O(nlog(n)). That means, that searching an element always depends on the size of the array, but in the Worst Case its faster than a hash table.
You can look up some Big O Complexities at this handy website here: http://bigocheatsheet.com/
I'm reading up on datastructures, especially immutable ones like the append-only B+ tree used in CouchDB and the Hash array mapped trie used in Clojure and some other functional programming languages.
The main reason datastructures that work well in memory might not work well on disk appears to be time spent on disk seeks due to fragmentation, as with a normal binary tree.
However, HAMT is also very shallow, so doesn't require any more seeks than a B tree.
Another suggested reason is that deletions from a array mapped trie are more expensive tha from a B tree. This is based on the assumption that we're talking about a dense vector, and doesn't apply when using either as a hash map.
What's more, it seems that a B tree does more rebalancing, so using it in an append-only manner produces more garbage.
So why do CouchDB and practically every other database and filesystem use B trees?
[edit] fractal trees? log-structured merge tree? mind = blown
[edit] Real-life B trees use a degree in the thousands, while a HAMT has a degree of 32. A HAMT of degree 1024 would be possible, but slower due to popcnt handling 32 or 64 bits at a time.
B-trees are used because they are a well-understood algorithm that achieves "ideal" sorted-order read-cost. Because keys are sorted, moving to the next or previous key is very cheap.
HAMTs or other hash storage, stores keys in random order. Keys are retrieved by their exact value, and there is no efficient way to find to the next or previous key.
Regarding degree, it is normally selected indirectly, by selecting page size. HAMTs are most often used in memory, with pages sized for cache lines, while B-trees are most often used with secondary storage, where page sizes are related to IO and VM parameters.
Log Structured Merge (LSM) is a different approach to sorted order storage which achieves more optimal write-efficiency, by trading off some read efficiency. That hit to read efficiency can be a problem for read-modify-write workloads, but the fewer uncached reads there are, the more LSM provides better overall throughput vs B-tree - at the cost of higher worst case read latency.
LSM also offers the promise of a wider-performance envelope. Putting new data into its proper place is "deferred", offering the possibility to tune read-to-write efficiency by controlling the proportion of deferred cleanup work to live work. In theory, an ideal-LSM with zero-deferral is a B-tree and with 100%-deferral is a log.
However, LSM is more of a "family" of algorithms than a specific algorithm like a B-tree. Their usage is growing in popularity, but it is hindered by the lack of a de-facto optimal LSM design. LevelDB/RocksDB is one of the more practical LSM implementations, but it is far from optimal.
Another approach to achieving write-throughput efficiency is to write-optimize B-trees through write-deferral, while attempting to maintain their optimal read-throughput.
Fractal-trees, shuttle-trees, stratified-trees are this type of design, and represent a hybrid gray area between B-tree and LSM. Rather than deferring writes to an offline process, they amortize write-deferral in a fixed way. For example, such a design might represent a fixed 60%-write-deferral fraction. This means they can't achieve the 100% write-deferral performance of an LSM, but they also have a more predictable read-performance, making them more practical drop-in replacements for B-trees. (As in the commercial Tokutek MySQL and MongoDB fractal-tree backends)
Btrees are ordered by their key while in a hash map similar keys have very different hash values so are stored far each other. Now think of a query that do a range scan "give me yesterday's sales": with a hash map you have to scan all the map to find them, with a btree on the sales_dtm columns you'll find them nicely clustered and you exactly know where to start and stop reading.
How to implement Radix sort on multi-GPU – same way as on single GPU i.e. by splitting the data then building histograms on separate GPUs and then use merge data back (like bunch of cards)?
That method would work, but I don't think it would be the fastest approach. Specifically, merging histograms for every K bits (K=4 is currently best) would require the keys to be exchanged between GPUs 32/K = 8 times to sort 32-bit integers. Since the memory bandwidth between GPUs (~5GB/s) is much lower than the memory bandwidth on a GPU (~150GB/s) this will kill performance.
A better strategy would be to split the data into multiple parts, sort each part in parallel on a different GPU, and then merge the parts once at the end. This approach requires only one inter-GPU transfer (vs. 8 above) so it will be considerably faster.
Unfortunately this question is not adequately posed. It depends on element size, where the elements begin life in memory, and where you want the sorted elements to end up residing.
Sometimes it's possible to compress the sorted list by storing elements in groups sharing the same common prefix, or you can unique elements on the fly, storing each element once in the sorted list with an associated count. For example, you might sort a huge list of 32-bit integers into 64K distinct lists of 16-bit values, cutting your memory requirement in half.
The general principle is that you want to make the fewest number of passes over the data as possible and that your throughput will almost always correspond to bandwidth constraints associated with your storage policy.
If your data set exceeds the size of fast memory, you probably want to finish with a merge pass rather than continue to radix sort, as another person has already answered.
I'm just getting into GPU architecture and I don't understand the K=4 comment above. I've never seen an architecture yet where such a small K would prove optimal.
I suspect merging histograms is also the wrong approach. I'd probably let the elements fragment in memory rather than merge histograms. Is it that hard to manage meso-scale scatter/gather lists in the GPU fabric? I sure hope not.
Finally, it's hard to conceive of a reason why you would want to involve multiple GPUs for this task. Say your card has 2GB of memory and 60GB/s write bandwidth (that's what my mid-range card is showing). A three pass radix sort (11-bit histograms) requires 6GB of write bandwidth (likely your rate limiting factor), or about 100ms to sort a 2GB list of 32-bit integers. Great, they're sorted, now what? If you need to ship them anywhere else without some kind of preprocessing or compression, the sorting time will be small fish.
In any case, just compiled my first example programs today. There's still a lot to learn. My target application is permutation intensive, which is closely related to sorting. I'm sure I'll weigh in on this subject again in future.