Can a B tree have more solutions? - c

I have this values
10,15,20,25,30,33,38,40,43,45,50
and then I insert 34
I tried 2 generators
https://s3.amazonaws.com/learneroo/visual-algorithms/BTree.html
http://ysangkok.github.io/js-clrs-btree/btree.html
and they gave me different results
On paper I tried to create the tree inserting those consecutive values 1 by1 and get a totally different result.
If the elements were in random order would the result be the same?
My result is this
The problem is when on the right I have 38|40|45 and I add 50 I have to put 40 a level higher but in the internet generators they also put 33 a level down and I don't see why

Can a B tree have more solutions?
I think you're asking whether there can be more than one one way to store a given set of keys in a b-tree, but you have already answered that yourself. Both of the generated examples you present contain the same keys and are valid 1-3 b-trees. The first is also a valid 1-2 b-tree. With the correction, your attempt is also a valid 1-3 b-tree.
Note well that there are different flavors of b-tree, based on how many keys the internal nodes are permitted to contain, and also that even binary trees, with which you may be more familiar, afford many different structures for the same set of two or more keys.
If the elements were in random order would the result be the same?
Very likely so, yes, but that's not a question of the b-tree form and structure, but rather about the implementation of the software used to construct and maintain it.
You seem confused that
in the internet generators they also put 33 a level down and I don't see why
, but we can only speculate about the implementation of the software supporting those trees. It's unlikely that anyone here can tell you with certainty why they produce the particular b-tree forms they do, but those forms are valid, and so, now, is yours.

Related

Multiple Keys for exact and approximate lookups in C

I am trying to develop a network resource manager component in C which keeps track of various network elements over TCP/UDP sockets. For this, I use three values :
Hardware Location Number
Service Group Number
Node Number
The rule is that no two elements on a network may have the same set of these three numbers. Thus, each location's identity will be unique on the network. This information needs to be saved in the program (non-persistently) in a way so that given any of the parameters (could be just a single number, or a combination of any two, or all three) the program returns the eligible candidates by performing a quick search.
The addition and deletion should also be efficient, but given that there will be few insertions or deletions after the initial transient phase if they are a bit slower than search, it should be OK. Using trees is one option, but the answer of 'Which one to use?' still eludes me (Not that I know of many, but I look forward to learning newer ones if they serve my purpose).
To do this, I could have three different trees maintained separately with similar nodes pointing to a same structure in memory, but I feel that is inefficient and not compact. I am looking for a unified data set which can handle these variations like multiple keys.
Or I could have a single AVL tree with multiple keys (if that is allowed).
The number of elements in the network is dynamic, so using a 3D array is out of option.
A friend also suggested hashing, but I am not too sure.
Please help.
Hashing seems like a silly choice for this. Perhaps the most significant reason is that you seem interested in approximate lookups. Hashing your values will likely mean iterating through the entire collection to find a group of nodes that have a common prefix, or a similar prefix.
PATRICIA is commonly used in routing tables, and makes itself quite amenable to searching for items that have similar keys. Note that I have found much misleading information about PATRICIA tries, which I've written about here. I found this resource to be particularly helpful.
Similarly to an AVL tree, you'll need to combine the three keys to form one (without hashing, preferably).
unsigned int key[3] = { hardware_location_number, service_group_number, node_number };
/* ^------- Use something like this as your key */

how to remember multiple indexes in a buffer to later access them for modification one by one...keeping optimization in mind

i have a scenario where i have to set few records with field values to a constant and then later access them one by one sequentially .
The records can be random records.
I dont want to use link list as it will be costly and don't want to traverse the whole buffer.
please give me some idea to do that.
When you say "set few records with field values to a constant" is this like a key to the record? And then "later access them one by one" - is this to recall them with some key? "one-by-one sequentially" and "don't want to traverse the whole buffer" seems to conflict, as sequential access sounds a lot like traversal.
But I digress. If you in fact do have a key (and it's a number), you could use some sort of Hash Table to organize your records. One basic implementation might be an array of linked lists, where you mod the key down into the array's range, then add it to the list there. This might increase performance assuming you have a good distribution of keys (your records spread across the array well).
Another data structure to look into might be a B-Tree or a binary search tree, which can access nodes in logarithmic time.
However, overall I agree with the commenters that over-optimizing is usually not a good idea.

Determining the Similarity Between Items in a Database

We have a database with hundreds of millions of records of log data. We're attempting to 'group' this log data as being likely to be of the same nature as other entries in the log database. For instance:
Record X may contain a log entry like:
Change Transaction ABC123 Assigned To Server US91
And Record Y may contain a log entry like:
Change Transaction XYZ789 Assigned To Server GB47
To us humans those two log entries are easily recognizable as being likely related in some way. Now, there may be 10 million rows between Record X and Record Y. And there may be thousands of other entries that are similar to X and Y, and some that are totally different but that have other records they are similar to.
What I'm trying to determine is the best way to group the similar items together and say that with XX% certainty Record X and Record Y are probably of the same nature. Or perhaps a better way of saying it would be that the system would look at Record Y and say based on your content you're most like Record X as apposed to all other records.
I've seen some mentions of Natural Language Processing and other ways to find similarity between strings (like just brute-forcing some Levenshtein calculations) - however for us we have these two additional challenges:
The content is machine generated - not human generated
As opposed to a search engine approach where we determine results for a given query - we're trying to classify a giant repository and group them by how alike they are to one another.
Thanks for your input!
Interesting problem. Obviously, there's a scale issue here because you don't really want to start comparing each record to every other record in the DB. I believe I'd look at growing a list of "known types" and scoring records against the types in that list to see if each record has a match in that list.
The "scoring" part will hopefully draw some good answers here -- your ability to score against known types is key to getting this to work well, and I have a feeling you're in a better position than we are to get that right. Some sort of soundex match, maybe? Or if you can figure out how to "discover" which parts of new records change, you could define your known types as regex expressions.
At that point, for each record, you can hopefully determine that you've got a match (with high confidence) or a match (with lower confidence) or very likely no match at all. In this last case, it's likely that you've found a new "type" that should be added to your "known types" list. If you keep track of the score for each record you matched, you could also go back for low-scoring matches and see if a better match showed up later in your processing.
I would suggest indexing your data using a text search engine like Lucene to split your log entries into terms. As your data is machine generated use also word bigrams and tigrams, even higher order n-grams. A bigram is just a sequence of consecutive words, in your example you would have the following bigrams:
Change_Transaction, Transaction_XYZ789, XYZ789_Assigned, Assigned_To, To_Server, Server_GB47
For each log prepare queries in a similar way, the search engine may give you the most similar results. You may need to tweek the similarity function a bit to obtain best results but I believe this is a good start.
Two main strategies come to my mind here:
the ad-hoc one. Use an information retrieval approach. Build an index for the log entries, eventually using a specialized tokenizer/parser, by feeding them into a regular text search engine. I've heard people do this with Xapian and Lucene. Then you can "search" for a new log record and the text search engine will (hopefully) return some related log entries to compare it with. Usually the "information retrieval" approach is however only interested in finding the 10 most similar results.
the clustering approach. You will usually need to turn the data into numerical vectors (that may however be sparse) e.g. as TF-IDF. Then you can apply a clustering algorithm to find groups of closely related lines (such as the example you gave above), and investigate their nature. You might need to tweak this a little, so it doesn't e.g. cluster on the server ID.
Both strategies have their ups and downs. The first one is quite fast, however it will always just return you some similar existing log lines, without much quantities on how common this line is. It's mostly useful for human inspection.
The second strategy is more computationally intensive, and depending on your parameters could fail completely (so maybe test it on a subset first), but could also give more useful results by actually building large groups of log entries that are very closely related.
It sounds like you could take the lucene approach mentioned above, then use that as a source for input vectors into the machine learning library Mahout (http://mahout.apache.org/). Once there you can train a classifier, or just use one of their clustering algorithms.
If your DBMS has it, take a look at SOUNDEX().

Persisting a Large List for Membership Testing in C

Each item is an array of 17 32-bit integers. I can probably produce 120-bit unique hashes for them.
I have an algorithm that produces 9,731,643,264 of these items, and want to see how many of these are unique. I speculate that at most 1/36th of these will be unique but can't be sure.
At this size, I can't really do this in memory (as I only have 4 gigs), so I need a way to persist a list of these, do membership tests, and add each new one if it's not already there.
I am working in C(gcc) on Linux so it would be good if the solution can work from there.
Any ideas?
This reminds me of some of the problems I faced working on a solution to "Knight's Tour" many years ago. (A math problem which is now solved, but not by me.)
Even your hash isn't that much help . . . at the nearly the size of a GUID, they could easily be unique accross all the the known universe.
It will take approximately .75 Terrabytes just to hold the list on disk . . . 4 Gigs of memory or not, you'd still need a huge disk just to hold them. And you'd need double that much disk or more to do the sort/merge solutions I talk about below.
If you could SORT that list, then you could just go threw the list one item at a time looking for unique copies next to each other. Of course sorting that much data would required a custom sort routine (that you wrote) since it is binary (coverting to hex would double the size of your data, but would allow you to use standard routines) . . . though likely even there they would probably choke on that much data . . . so your are back to your own custom routines.
Some things to think about:
Sorting that much data will take weeks, months or perhaps years. While you can do a nice heap sort or whatever in memory, because you only have so much disk space, you will likely be doing a "bubble" sort of the files regardless of what you do in memory.
Depending on what your generation algorithm looks like, you could generate "one memory load" worth of data, sort it in place then write it out to disk in a file (sorted). Once that was done, you just have to "merge" all those individual sorted files, which is a much easier task (even thought there would be 1000s of files, it would still be a relatively easier task).
If your generator can tell you ANYTHING about your data, use that to your advantage. For instance in my case, as I processed the Knight's Moves, I know my output values were constantly getting bigger (because I was always adding one bit per move), that small knowledge allowed me to optimize my sort in some unique ways. Look at your data, see if you know anything similar.
Making the data smaller is always good of course. For instance you talk about a 120 hash, but is that has reversable? If so, sort the hash since it is smaller. If not, the hash might not be that much help (at least for my sorting solutions).
I am interested in the machanics of issues like this and I'd be happy to exchange emails on this subject just to bang around ideas and possible solutions.
You can probably make your life a lot easier if you can place some restrictions on your input data: Even assuming only 120 significant bits, the high number of duplicate values suggests an uneven distribution, as an even distribution would make duplicates unlikely for a given sample size of 10^10:
2^120 = (2^10)^12 > (10^3)^12 = 10^36 >> 10^10
If you have continuous clusters (instead of sparse, but repeated values), you can gain a lot by operating on ranges instead of atomic values.
What I would do:
fill a buffer with a batch of generated values
sort the buffer in-memory
write ranges to disk, ie each entry in the file consists of start and end value of a continuous group of values
Then, you need to merge the individual files, which can be done online - ie as the files become available - the same way a stack-based mergesort operates: associate to each file a counter equal to the number of ranges in the file and push each new file on a stack. When the file on top of the stack has a counter greater or equal to the previous file, merge the files into a new file whose counter is the number of ranges in the merged file.

Can triple stores be made scalable

Most triple stores I read about are said to be scalable to around .5 billion triples.
I am interested to know if people think there is a theoretical reason to why they have to have an upper limit, and whether you know of any particular ways to make them more scalable.
I am curious to know if existing triple stores do things like this:
Represent URIs with integers
Integers in order
Search the integers instead of the URIs which I would imagine must be faster (because you can do things like a binary search etc.)
Thoughts ...
Just to get to 500million a triple store has to do all of that and more. I have spent several years working on a triple store implementation, and I can tell you that breaking 1 billion triples is not as simple as it may seem.
The problem is that many rdf queries are 2nd or 3rd order (and higher-orders are far from unheard of). This means that you are not only querying a set of entities, but simultaneously the data about the set of entities; data about the entities schemas; data describing the schema language used to describe the entities schemas.
All of this without any of the constraints available to a relational database to allow it to make assumptions about the shape of this data/metadata/metametadata/etc.
There are ways to get beyond 500 million, but they are far from trivial, and the low hanging fruit (ie. the approaches you have mentioned) were required just to get to where we are now.
That being said, the flexibility provided by an rdf-store, combined with a denotational semantic available via its interpretation in Description Logics, makes it all worthwhile.

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