We have a C++ application for which we try to improve performance. We identified that data retrieval takes a lot of time, and want to cache data. We can't store all data in memory as it is huge. We want to store up to 1000 items in memory. This items can be indexed by a long key. However, when the cache size goes over 1000, we want to remove the item that was not accessed for the longest time, as we assume some sort of "locality of reference", that is we assume that items in the cache that was recently accessed will probably be accessed again.
Can you suggest a way to implement it?
My initial implementation was to have a map<long, CacheEntry> to store the cache, and add an accessStamp member to CacheEntry which will be set to an increasing counter whenever an entry is created or accessed. When the cache is full and a new entry is needed, the code will scan the entire cache map and find the entry with the lowest accessStamp, and remove it.
The problem with this is that once the cache is full, every insertion requires a full scan of the cache.
Another idea was to hold a list of CacheEntries in addition to the cache map, and on each access move the accessed entry to the top of the list, but the problem was how to quickly find that entry in the list.
Can you suggest a better approach?
Thankssplintor
Have your map<long,CacheEntry> but instead of having an access timestamp in CacheEntry, put in two links to other CacheEntry objects to make the entries form a doubly-linked list. Whenever an entry is accessed, move it to the head of the list (this is a constant-time operation). This way you will both find the cache entry easily, since it's accessed from the map, and are able to remove the least-recently used entry, since it's at the end of the list (my preference is to make doubly-linked lists circular, so a pointer to the head suffices to get fast access to the tail as well). Also remember to put in the key that you used in the map into the CacheEntry so that you can delete the entry from the map when it gets evicted from the cache.
Scanning a map of 1000 elements will take very little time, and the scan will only be performed when the item is not in the cache which, if your locality of reference ideas are correct, should be a small proportion of the time. Of course, if your ideas are wrong, the cache is probably a waste of time anyway.
An alternative implementation that might make the 'aging' of the elements easier but at the cost of lower search performance would be to keep your CacheEntry elements in a std::list (or use a std::pair<long, CacheEntry>. The newest element gets added at the front of the list so they 'migrate' towards the end of the list as they age. When you check if an element is already present in the cache, you scan the list (which is admittedly an O(n) operation as opposed to being an O(log n) operation in a map). If you find it, you remove it from its current location and re-insert it at the start of the list. If the list length extends over 1000 elements, you remove the required number of elements from the end of the list to trim it back below 1000 elements.
Update: I got it now...
This should be reasonably fast. Warning, some pseudo-code ahead.
// accesses contains a list of id's. The latest used id is in front(),
// the oldest id is in back().
std::vector<id> accesses;
std::map<id, CachedItem*> cache;
CachedItem* get(long id) {
if (cache.has_key(id)) {
// In cache.
// Move id to front of accesses.
std::vector<id>::iterator pos = find(accesses.begin(), accesses.end(), id);
if (pos != accesses.begin()) {
accesses.erase(pos);
accesses.insert(0, id);
}
return cache[id];
}
// Not in cache, fetch and add it.
CachedItem* item = noncached_fetch(id);
accesses.insert(0, id);
cache[id] = item;
if (accesses.size() > 1000)
{
// Remove dead item.
std::vector<id>::iterator back_it = accesses.back();
cache.erase(*back_it);
accesses.pop_back();
}
return item;
}
The inserts and erases may be a little expensive, but may also not be too bad given the locality (few cache misses). Anyway, if they become a big problem, one could change to std::list.
In my approach, it's needed to have a hash-table for lookup stored objects quickly and a linked-list for maintain the sequence of last used.
When an object are requested.
1) try to find a object from the hash table
2.yes) if found(the value have an pointer of the object in linked-list), move the object in linked-list to the top of the linked-list.
2.no) if not, remove last object from the linked-list and remove the data also from hash-table then put object into hash-table and top of linked-list.
For example
Let's say we have a cache memory only for 3 objects.
The request sequence is 1 3 2 1 4.
1) Hash-table : [1]
Linked-list : [1]
2) Hash-table : [1, 3]
Linked-list : [3, 1]
3) Hash-table : [1,2,3]
Linked-list : [2,3,1]
4) Hash-table : [1,2,3]
Linked-list : [1,2,3]
5) Hash-table : [1,2,4]
Linked-list : [4,1,2] => 3 out
Create a std:priority_queue<map<int, CacheEntry>::iterator>, with a comparer for the access stamp.. For an insert, first pop the last item off the queue, and erase it from the map. Than insert the new item into the map, and finally push it's iterator onto the queue.
I agree with Neil, scanning 1000 elements takes no time at all.
But if you want to do it anyway, you could just use the additional list you propose and, in order to avoid scanning the whole list each time, instead of storing just the CacheEntry in your map, you could store the CacheEntry and a pointer to the element of your list that corresponds to this entry.
As a simpler alternative, you could create a map that grows indefinitely and clears itself out every 10 minutes or so (adjust time for expected traffic).
You could also log some very interesting stats this way.
I believe this is a good candidate for treaps. The priority would be the time (virtual or otherwise), in ascending order (older at the root) and the long as the key.
There's also the second chance algorithm, that's good for caches. Although you lose search ability, it won't be a big impact if you only have 1000 items.
The naïve method would be to have a map associated with a priority queue, wrapped in a class. You use the map to search and the queue to remove (first remove from the queue, grabbing the item, and then remove by key from the map).
Another option might be to use boost::multi_index. It is designed to separate index from data and by that allowing multiple indexes on the same data.
I am not sure this really would be faster then to scan through 1000 items. It might use more memory then good. Or slow down search and/or insert/remove.
Related
I have a linked list like this:
Head->A->B->C->D->Tail.
There can be N (1<N<10^5) items in the list.
The current cursor position is, cursor->B which is 2 if we think like an array.
I have to perform the following operation on my list:
insert x characters in the list at the cursor position and update the
cursor.
delete y (y < N) characters starting from the
cursor position and update the cursor.
move the cursor to a specific position within in the list.
I want all this operation in constant time.
Can anyone kindly help by suggesting any data structure model?
There isn't. Searching / iterating is linear in complexity - O(n). If you want a constant complexity, you need to use the different data structure. Since you are using C++, you should utilize one from the Containers library.
If the data can be sorted then by using "skip lists" a speed up can be achieved.
The principle is that extra pointers are used to skip ahead.
skip list is a data structure that allows fast search within an ordered sequence of elements. Fast search is made possible by maintaining a linked hierarchy of subsequences, with each successive subsequence skipping over fewer elements than the previous one ...
wikipedia
Therefore, with O(√n) extra space, we are able to reduce the time complexity to O(√n).
Skip-list
Of course it is not possible to use the linked list for that. As said before a linked list has a linear complexity.
You can try to use a more complex data structure like a hash as a lookup-container for the items in your list, which has a complexity of - O(n). Instead of storing the items itself the stored item can contain a pointer / index showing to the next item. But you have to keep in mind that the deletion will be still expensive because when removing one item you have to refresh the links showing to this item as well, So the item itself will need to know, if any other items are pointing to it.
I know that I can use various container classes in STL but it's an overkill and expensive for this purpose.
We have over 1M+ users online and per user we need to maintain 8 unrelated 32-bit data items. The goal is to
find if an item exists in the list,
if not, insert. Remove oldest entry if full.
Brute Force approach would be to maintain a last write pointer and iterate (since only 8 items) but I am looking for inputs to better analyze and implement.
Look forward to some interesting suggestions in terms of design pattern and algorithm.
Don Knuth gives several interesting and very efficient approximations in The Art of Computer Proramming.
Self-organizing list I: when you find an entry, move it to the head of the list; delete from the end.
Self-organizing list II: when you find an entry, move it up one spot; delete from the end.
[Both the above in Vol. 3 §6.1(A).]
Another scheme involves maintaining the list circularly with 1 extra bit per entry, which is set when you find that entry, and cleared when you skip past it to find something else. You always start searching at the last place you stopped, and if you don't find the entry you replace the one with the next clear bit with it, i.e. it hasn't been used since one entire trip around the list.
[Vol. 1 §2.5(G).]
You want to use here a combination of a Hash table and a doubly linked list.
Each item is accessible via the hash table that holds the key you need plus a pointer to the element in the list.
Algorithm:
Given new item x, do:
1. Add x to the head of the list, save pointer as ptr.
2. Add x to the hash table where the data is stored, and add ptr.
3. If the list is bigger than allowed, take the last element (from the tail of the list) and remove it. Use the key of this element to remove it from the Hash table as well.
If you want a C implementation of LRU cache try this link
The idea is that we use two data structures to implement an LRU Cache.
Queue which is implemented using a doubly linked list. The maximum size of the queue will be equal to the total number of frames available (cache size).The most recently used pages will be near front end and least recently pages will be near rear end.
A Hash with page number as key and address of the corresponding queue node as value.
When a page is referenced, the required page may be in the memory. If it is in the memory, we need to detach the node of the list and bring it to the front of the queue.
If the required page is not in the memory, we bring that in memory. In simple words, we add a new node to the front of the queue and update the corresponding node address in the hash. If the queue is full, i.e. all the frames are full, we remove a node from the rear of queue, and add the new node to the front of queue.
I personally would either go with the self organising lists as proposed by EJP or, as we only have eight elements, simply store them together with a timestamp sequentially.
When accessing an element, just update the timestamp, when replacing, replace the one with oldest timestamp (one linear search). This is less efficient on replacements, but more efficient on access (no need to move any elements around). And it might be the easiest to implement...
Modification of self organising lists, if based on some array data structure: Sure, on update, you have to shift several elements (variant I) or at least swap two of them (variant II) - but if you organize the data as ring buffer, on replacement we just replace the last element with the new one and move the buffer's pointer to this new element:
a, b, c, d
^
Accessing a:
d, b, a, c
^
New element e:
d, e, a, c
^
Special case: accessing the oldest element (d in this case) - we then simply can move the pointer, too:
d, e, a, c
^
Just: with only 8 elements, it might not be worth the effort to implement all this...
I agree with Drop and Geza's comments. The straightforward implementation will take one cache line read, and cause one cache line write.
The only performance question left is going to be the lookup and update of that 32 bit value in 256 bits. Assuming modern x86, the lookup itself can be two instructions: _mm256_cmp_epi32_mask finds all equal values in parallel, _mm256_lzcnt_epi32 counts leading zeroes = number of older non-matching items*32. But even with older SIMD operations, the cache line read/write operations will dominate the execution time. And that's in turn is dominated by finding the right user. Which in turn is dominated by the network I/O involved.
You should use Cuckoo's Filter which is a probabilistic data structure that supports fast set membership testing. It is a hash-based data structure.
Time Complexity of Cuckoo's Filter:
Lookup: O(1)
Deletion: O(1)
Insertion: O(1)
For reference here is how the cuckoo filter works.
Parameters of the filter
1. Two Hash Functions: h1 and h2
2. An array B with n Buckets. The i-th Bucket will be called B[i]
Input : L, a list of elements to inserted into the cuckoo filter.
Algorithm:
while L is not empty:
Let x be the 1st item in the list L. Remove x from the list.
if (B[h1(x)] == empty)
place x in B[h1(x)];
else if (B[h2(x)] == empty)
place x in B[h2(x)];
else
Let y be the element in B[h2(x)]
Prepend y to L
place x in B[h2(x)]
For LRU you can use time stamping in your hash function by keeping just a local variable.
This is the best approach for very large data sets to date.
A skip list is a data structure in which the elements are stored in sorted order and each node of the list may contain more than 1 pointer, and is used to reduce the time required for a search operation from O(n) in a singly linked list to O(lg n) for the average case. It looks like this:
Reference: "Skip list" by Wojciech Muła - Own work. Licensed under Public domain via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:Skip_list.svg#mediaviewer/File:Skip_list.svg
It can be seen as an analogy to a ruler:
In a skip list, searching an element and deleting one is fine, but when it comes to insertion, it becomes difficult, because according to Data Structures and Algorithms in C++: 2nd edition by Adam Drozdek:
To insert a new element, all nodes following the node just inserted have to be restructured; the number of pointers and the value of pointers have to be changed.
I can construe from this that although choosing a node with random number of pointers based on the likelihood of nodes to insert a new element, doesn't create a perfect skip list, it gets really close to it when large number of elements (~9 million for example) are considered.
My question is: Why can't we insert the new element in a new node, determine its number of pointers based on the previous node, attach it to the end of the list, and then use efficient sorting algorithms to sort just the data present in the nodes, thereby maintaining the perfect structure of the skip list and also achieving the O(lg n) insert complexity?
Edit: I haven't tried any code yet, I'm just presenting a view. Simply because implementing a skip list is somewhat difficult. Sorry.
There is no need to modify any following nodes when you insert a node. See the original paper, Skip Lists: A Probabilistic Alternative to Balanced Trees, for details.
I've implemented a skip list from that reference, and I can assure you that my insertion and deletion routines do not modify any nodes forward of the insertion point.
I haven't read the book you're referring to, but out of context the passage you highlight is just flat wrong.
You have a problem on this point and then use efficient sorting algorithms to sort just the data present in the nodes. Sorting the data will have complexity O(n*lg(n)) and thus it will increase the complexity of insertion. In theory you can choose "perfect" number of links for each node being inserted, but even if you do that, when you perform remove operations, the perfectness will be "broken". Using the randomized approach is close enough to perfect structure to perform well.
You need to have function / method that search for location.
It need to do following:
if you insert unique keys, it need to locate the node. then you keep everything, just change the data (baggage). e.g. node->data = data.
if you allow duplicates, or if key is not found, then this function / method need to give you previous node on each height (lane). Then you determine height of new node and insert it after the found nodes.
Here is my C realisation:
https://github.com/nmmmnu/HM2/blob/master/hm_skiplist.c
You need to check following function:
static const hm_skiplist_node_t *_hm_skiplist_locate(const hm_skiplist_t *l, const char *key, int complete_evaluation);
it stores the position inside hm_skiplist_t struct.
complete_evaluation is used to save time in case you need the data and you are not intend to insert / delete.
I want to have a hit parameter for objects that are received, showing its frequency. and being able to have the most frequent, top hit, objects.
Unordered_map fits the first part, having object as the key and hit as the value.
unordered_map<object,int>
It enables searching fast for object and incrementing its hit. But how about sorting? priority_queue enables having the top hit object. But how about incrementing the object's hit?
I would suggest you have a look at splay tree that keeps objects in a way that most recent and most frequnetly accessed objects are closer to the top. This relies on several euristicts and thus will give you an approximation of the perfect solution.
For an exact solution it is better to implement your own binary heap and implement the operation icrement priority. In theory the same is used for backing for priority_queue, but there is no cahnge priority operation, while it can be done without affecting the complexity of the data structure's operations.
I managed to solved it by keeping track of sorted list of objects by their hit number as I insert the objects. So there is always the list of the most N top hits. There are 3,000,000 objects and I want to have the top 20.
Here are the structures I used:
key_hit to keep track of hits (by key, a string, I mean the object):
unordered_map<string, int> key_hit;
two arrays : hits[N], keys[N] which contains the top hits and their corresponding key (object).
idx, hits, keys
0, 212, x
1, 200, y
...
N, 12, z
and another map key_idx to keep the key and its corresponding index:
unordered_map<string,int> key_idx;
Algorithm (without details):
key is input.
search the key in key_hit, find its hit and increment (this is fast enough).
if hit<hits[N], ignore it.
else, idx=key_idx[key], (if not found, add it to structures and delete the existing one. it too long to write all details)
H=h[idx]++
check whether it is greater than the above entry, h[idx-1]<H. if yes, swap idx and idx-1 in key_idx,hits,keys.
I tried to make it fast. but I don't know how far it's fast.
In a graph class I need to handle nodes with integer values (1-1000 mostly). In every step I want to remove a node and all its neighbors from the graph. Also I want to always begin with the node of the minimal value. I thought long about how to do this in the fastest possible manner and decided to do the following:
The graph is stored using adjancency lists
There is a huge array std::vector<Node*> bucket[1000] to store the nodes by its value
The index of the lowest nonempty bucket is always stored and kept track off
I can find the node of minimal value very fast by picking a random element of that index or if the bucket is already empty increase the index
Removing the selected node from the bucket can clearly done in O(1), the problem is that for removing the neighbors I need to search the bucket bucket[value of neighbor] first for all neighbor nodes, which is not really fast.
Is there a more efficient approach to this?
I thought of using something like std::list<Node*> bucket[1000], and assign every node a pointer to its "list element", such that I can remove the node from the list in O(1). Is this possible with stl lists, clearly it can be done with a normal double linked list that I could implement by hand?
I recently did something similar to this for a priority queue implementation using buckets.
What I did was use a hash tables (unordered_map), that way, you don't need to store 1000 empty vectors and you still get O(1) random access (general case, not guaranteed). Now, if you only need to store/create this graph class one time, it probably doesn't matter. In my case I needed to create the priority queue tens/hundreds of time per second and using the hash map made a huge difference (due to the fact that I only created unordered_sets when I actually had an element of that priority, so no need to initialize 1000 empty hash sets). Hash sets and maps are new in C++11, but have been available in std::tr1 for a while now, or you could use the Boost libraries.
The only difference that I can see between your & my usecase, is that you also need to be able to remove neighboring nodes. I'm assuming every node contains a list of pointers to it's neighbors. If so, deletion of the neighbors should take k * O(1) with k the number of neighbors (again, O(1) in general, not guaranteed, worst case is O(n) in an unordered_map/set). You just go over every neighboring node, get its priority, that gives you the correct index into the hash map. Then you find the pointer in the hash set which the priority maps to, this search in general will be O(1) and removing the element is again O(1) in general.
All in all, I think you got a pretty good idea of what to do, but I believe that using hash maps/sets will speed up your code by quite a lot (depends on the exact usage of course). For me, the speed improvement of an implementation with unordered_map<int, unordered_set> versus vector<set> was around 50x.
Here's what I would do. Node structure:
struct Node {
std::vector<Node*>::const_iterator first_neighbor;
std::vector<Node*>::const_iterator last_neighbor;
int value;
bool deleted;
};
Concatenate the adjacency lists and put them in a single std::vector<Node*> to lower the overhead of memory management. I'm using soft deletes so update speed is not important.
Sort pointers to the nodes by value into another std::vector<Node*> with a counting sort. Mark all nodes as not deleted.
Iterate through the nodes in sorted order. If the node under consideration has been deleted, go to the next one. Otherwise, mark it deleted and iterate through its neighbors and mark them deleted.
If your nodes are stored contiguously in memory, then you can omit last_neighbor at the cost of an extra sentinel node at the end of the structure, because last_neighbor of a node is first_neighbor of the succeeding node.