Develop Reference

BTrees and Disk Persistance

For some time i am working on creating index for very large data sets (around 190 million). I have a BTree which can insert data sets (typically an object)/search for key and while i searched how to persist the data into files in disk, i came across this amazing article (http://www.javaworld.com/article/2076333/java-web-development/use-a-randomaccessfile-to-build-a-low-level-database.html#resources). This pretty much gives me the starting point.
Here they are indexing String key to binary object (blob). They have the file format where they have divided it into 3 regions, header(stores start point of indexes), index(stores index and its corresponding location) and data region (stores data). They are using RandomAccessFile to get the data.
How do i define similar file format for btree. All i know is for every read made to disk, i have to get one node(typically one block 512 bytes). There are many similar questions on how to persist but it is little difficult to understand the big picture on why we decide on something that we implemented like this question (Persisting B-Tree nodes to RandomAccessFile -[SOLVED]). Please share your thoughts.

Here is an alternative take on the question, based on problem specifics that have become known in the meantime. This post is based on the following assumptions:
record count about 190 million, fixed
keys are 64-byte hashes, like SHA-256
values are filenames: variable length, but sensible (average length < 64 bytes, max < page)
page size 4 KiByte
Efficient representation of filenames in a database is a different topic that cannot be addressed here. Should the filenames be awkward - longish on average and/or Unicode - then the hashing solution will punish you with increased disk read counts (more overflows, more chaining) or reduced average occupancy (more wasted space). A B-tree solution reacts somewhat more benignly, though, since an optimum tree can be constructed in any case.
The most efficient solution in this situation - and the simplest to implement by a wide margin - is hashing, since your keys are perfect hashes already. Take the first 23 bits of the hash as the page number, and lay out the pages like this:
page header
uint32_t next_page
uint16_t key_count
key/offset vector
uint16_t value_offset;
byte key[64];
... unallocated space ...
last arrived filename
...
2nd arrived filename
1st arrived filename
Values (filenames) are stored from the end of the page downwards, prefixed with their 16-bit length, and the key/offset vector grows upwards. That way neither low/high key counts nor short/long values can cause unnecessary waste of space, as would be the case with fixed-size structures. Nor do you have to parse variable-length structures during key searches. Apart from that I've aimed for the greatest possible simplicity - no premature optimisation. The bottom of the heap can be stored in the page header, in KO.[PH.key_count].value_offset (my preference), or computed as KO.Take(PH.key_count).Select(r => r.value_offset).Min(), whatever pleases you most.
The key/offset vector needs to be kept sorted on the keys so that you can use binary search but the values can be written as they arrive, they do not need to be in any particular order. If the page overflows, allocate a new one just like it at the current end of the file (growing the file by one page) and stash its page number in the appropriate header slot. This means that you can binary search within a page but all chained pages need to be read and searched one by one. Also, you do not need any kind of file header, since the file size is otherwise available and that's the only piece of global management information that needs to be maintained.
Create the file as a sparse file with the number of pages as indicated by your chosen number of hash key bits (e.g. 8388608 pages for 23 bits). Empty pages in a sparse file don't take up any disk space and read as all 0s, which works perfectly fine with our page layout/semantics. Extend the file by one page whenever you need to allocate an overflow page. Note: the 'sparse file' thing isn't very important here since almost all pages will have been written to when you're done building the file.
For maximum efficiency you need to run some analyses on your data. In my simulation - with random numbers as stand-ins for the hashes, and on the assumption that average filename size is 62 bytes or less - the optimum turned out to be making 2^23 = 8388608 buckets/pages. This means that you take the first 23 bit of the hash as the page number to load. Here are the details:
# bucket statistics for K = 23 and N = 190000000 ... 7336,5 ms
average occupancy 22,6 records
0 empty buckets (min: 3 records)
310101/8388608 buckets with 32+ records (3,7%)
That keeps the chaining to a minimum, on average you need to read just 1.04 pages per search. Increasing the hash key size by one single bit to 24 reduces the expected number of overflowing pages to 3 but doubles the file size and reduces average occupancy to 11.3 records per page/bucket. Reducing the key to 22 bits means that almost all pages (98.4%) can be expected to overflow - meaning the file is virtually the same size as that for 23 bits but you have to do twice as many disk reads per search.
Hence you see how important it is to run a detailed analysis on the data to decide on the proper number of bits to use for hash addressing. You should run an analysis that uses the actual filename sizes and tracks the per-page overhead, to see what the actual picture looks like for 22 bits to 24 bits. It'll take a while to run but that's still way faster than building a multi-gigabyte file blindly and then finding that you have wasted 70% of space or that searches take significantly more than 1.05 page reads on average.
Any B-tree based solution would be much more involved (read: complicated) but could not reduce the page read count per search below 1.000, for obvious reasons, and even that only on the assumption that a sufficient number of internal nodes can be kept cached in memory. If your system has such humongous amounts of RAM that data pages can be cached to a significant degree then the hashing solution will benefit just as much as one that is based on some kind of B-tree.
As much as I would like an excuse for building a screamingly fast hybrid radix/B+tree, the hashing solution delivers essentially the same performance for a tiny fraction of the effort. The only thing where B-treeish solutions can outdo hashing here is space efficiency, since it is trivial to construct an optimum tree for existing pre-sorted data.

The are plenty of Open Source key/value stores and full database engines - take a week off and start Googling. Even if you end up using none of them, you still need to study a representative cross section (architecture, design histories, key implementation details) to get enough of an overview over the subject matter so that you can make informed decisions and ask intelligent questions. For a brief overview, try to Google details on index file formats, both historic ones like IDX or NTX, and current ones used in various database engines.
If you want to roll your own then you might consider hitching yourself to the bandwagon of an existing format, like the dBASE variants Clipper and Visual FoxPro (my favourite). This gives you the ability to work your data with existing tools, including Total Commander plugins and whatnot. You don't need to support the full formats, just the single binary instance of the format that you choose for your project. Great for debugging, reindexing, ad hoc queries and so on. The format itself is dead simple and easy to generate even if you don't use any of the existing libraries. The index file formats aren't quite as trivial but still manageable.
If you want to roll your own from scratch then you've got quite a road ahead of you, since the basics of intra-node (intra-page) design and practice are poorly represented on the Internet and in literature. For example, some old DDJ issues contained articles about efficient key matching in connection with prefix truncation (a.k.a. 'prefix compression') and so on but I found nothing comparable out there on the 'net at the moment, except buried deeply in some research papers or source code repositories.
The single most important item here is the algorithm for searching prefix-truncated keys efficiently. Once you've got that, the rest more or less falls into place. I have found only one resource on the 'net, which is this DDJ (Dr Dobb's Journal) article:
Supercharging Sequential Searches by Walter Williams
A lot of tricks can also be gleaned from papers like
Efficient index compression in DB2 LUW
For more details and pretty much everything else you could do a lot worse than reading the following two books cover to cover (both of them!):
Goetz Graefe: Modern B-Tree Techniques (ISBN 1601984820)
Jim Gray: Transaction Processing. Concepts and Techniques (ISBN 1558601902)
An alternative to the latter might be
Philip E. Bernstein: Principles of Transaction Processing (ISBN 1558606238)
It covers a similar spectrum and it seems to be a bit more hands-on, but it does not seem to have quite the same depth. I cannot say for certain, though (I've ordered a copy but haven't got it yet).
These books give you a complete overview over all that's involved, and they are virtually free of fat - i.e. you need to know almost everything that's in there. They will answer gazillions of questions that you didn't know you had, or that you should have asked yourself. And they cover the whole ground - from B-tree (and B+tree) basics to detailed implementation issues like concurrency, locking, page replacement strategies and so forth. And they enable you to utilise the information that is scattered over the 'net, like articles, papers, implementation notes and source code.
Having said that, I'd recommend matching the node size to the architecture's RAM page size (4 KB or 8 KB), because then you can utilise the paging infrastructure of your OS instead of running afoul of it. And you're probably better off keeping index and blob data in separate files. Otherwise you couldn't put them on different volumes and the data would b0rken the caching of the index pages in subsystems that are not part of your program (hardware, OS and so forth).
I'd definitely go with a B+tree structure instead of watering down the index pages with data as in a normal B-tree. I'd also recommend using an indirection vector (Graefe has some interesting details there) in connection with length-prefixed keys. Treat the keys as raw bytes and keep all the collation/normalisation/upper-lower nonsense out of your core engine. Users can feed you UTF8 if they want - you don't want to have to care about that, trust me.
There is something to be said for using only suffix truncation in internal nodes (i.e. for distinguishing between 'John Smith' and 'Lucky Luke', 'K' or 'L' work just as well as the given keys) and only prefix truncation in leaves (i.e. instead of 'John Smith' and 'John Smythe' you store 'John Smith' and 7+'ythe').
It simplifies the implementation, and gives you most of the bang that could be got. I.e. shared prefixes tend to be very common at the leaf level (between neighbouring records in index order) but not so much in internal nodes, i.e. at higher index levels. Conversely, the leaves need to store the full keys anyway and so there's nothing to truncate and throw away there, but internal nodes only need to route traffic and you can fit a lot more truncated keys in a page than non-truncated ones.
Key matching against a page full of prefix-truncated keys is extremely efficient - on average you compare a lot less than one character per key - but it's still a linear scan, even with all the hopping forward based on skip counts. This limits effective page sizes somewhat, since binary search is more complicated in the face of truncated keys. Graefe has a lot of details on that. One workaround for enabling bigger node sizes (many thousands of keys instead of hundreds) is to lay out the node like a mini B-tree with two or three levels. It can make things lightning-fast (especially if you respect magic thresholds like 64-byte cache line size), but it also makes the code hugely more complicated.
I'd go with a simple lean and mean design (similar in scope to IDA's key/value store), or use an existing product/library, unless you are in search of a new hobby...

Storing enormously large arrays

I have a problem. I work in Java, Eclipse. My program calculates some mathematical physics, and I need to draw animation (Java SWT package) of the process (some hydrodynamics). The problem is 2D, so each iteration returns two dimensional array of numbers. One iteration takes rather long time and time needed for iteration changes from one iteration to another, so showing pictures dynamically as program works seems like a bad idea. In this case my idea was to store a three dimensional array, where third index represents time, and building an animation when calculations are over. But in this case, as I want accuracuy from my program, I need a lot of iterations, so program easily reaches maximal array size. So the question is: how do I avoid creating such an enormous array or how to avoid limitations on array size? I thought about creating a special file to store data and then reading from it, but I'm not sure about this. Do you have any ideas?

When I was working on a procedural architecture generation system at university for my dissertation I created small, extremely easily read and parsed binary files for calculated data. This meant that the data could be read in within an acceptable amount of time, despite being quite a large amount of data...
I would suggest doing the same for your animations... It might be of value storing maybe five seconds of animation per file and then caching each of these as they are about to be required...
Also, how large are your arrays, you could increase the amount of memory your JVM is able to allocate if it's not maximum array size, but maximum memory limitations you're hitting.
I hope this helps and isn't just my ramblings...

PageRank implementation for Research

After reading theory of PageRank algorithm from this site I would like to play with it.
I am trying to implement this in Java. I mean I would like to play with PageRank in detail (like giving different weights and so on). For this I need to build hyperlink matrix. If I have 1 million nodes then my hyperlink matrix will be 1 million x 1 million size, which causes this exception:
Exception in thread "main" java.lang.OutOfMemoryError: Java heap space
at WebGraph.main(WebGraph.java:6)
How can I implement PageRank in Java, is there any way of storing hyperlink matrix?

That is a great article to learn about pagerank. I implemented a Perl version from it here to use with Textrank. However, if you want to just learn about pagerank and how the various aspects discussed in the article affect the results (dampening factor, direct or undirected graph, etc.), I would recommend running experiments in R or Octave. If you want to learn how to implement it efficiently, then programming it up from scratch, as you are doing, is best.
Most web graphs (or networks) are very sparse, which means most of the entries in the matrix representation of the graph are zero. A common data structure used to represent a sparse matrix is a hash-map, where the zero values are not stored. For example, if the matrix was
1, 0, 0
0, 0, 2,
0, 3, 0
a two dimension hash-map would store only the values for hm(0,0)=1, hm(1,2)=2, and hm(2,1)=3. So in a 1,000,000 by 1,000,000 matrix of a web graph, I would expect only a few million values to be non-zero. If each row averages only 5 non-zero values, a hash-map will use about 5*(8+8+8)10^6 bytes ~ 115mb to store it (8 for the left int index, 8 for the right int index, and 8 for the double value). The square matrix will use 810^6*10^6 ~ 7 terabytes.
Implementing an efficient sparse matrix-vector multiply in Java is not trivial, and there are some already implemented if you don't want to devote time to that aspect of the algorithm. The sparse-matrix multiply is the most difficult aspect to implement of the pagerank algorithm, so after that it gets easier (and more interesting).

Python networkx module has a nice implementation of pagerank. It uses scipy/numpy for the matrix implementation. The below two questions on stackoverflow should be enough to get you started.
How do weighted edges affect PageRank in networkx?
Networkx: Differences between pagerank, pagerank_numpy, and pagerank_scipy?

A few suggestions:
Use python, not Java: python is an excellent prototyping language, and has available sparse matrices (in scipy) as well as many other goodies. As others have noted, it also has a pagerank implementation.
Store your data not all in memory: any type of lightweight database would be fine, for instance sqlite, hibernate, ...
Work on tiles of the data: if there is a big matrix NxN, break it up into small tiles MxM where M is a fraction of N, that fit in memory. Combined with sparse matrices this allows you to work with really big N (hundreds of millions to billions, depending on how sparse the data is).

As Dan W suggested, try to increase the heap size. If you run your Java application from the command line, just add the switch -Xmx with the desired heap size. Let's assume you compiled your Java code into a runnable JAR file called pagerank.jar, and you want to set your heap size to 512 MB, you would issue the following command:
java -jar -Xmx512m pagerank.jar
EDIT:
But that only works if you don't have that many "pages" ... A 1 Million x 1 Million array is too big to fit into your RAM (1 trillion times * 64 bit double value = 7.27595761 terabytes). You should change your algorithm to load chunks of data from the disk, manipulate it, and store it back to disk.
You could use a graph database like Neo4j for that purpose.

You don't have to store the whole 1000000x1000000 matrix, because most matrix entries will be zero. Instead, you can (for example) store a list of nonzero entries for each row, and write your matrix functions to use it directly, without expanding it into a full matrix.
This kind of compressed representation is called a sparse matrix format, and most matrix libraries have an option to build and work with sparse matrices.
One disadvantage with sparse matrices is that multiplying two of them will result in a matrix which is much less sparse. However, the PageRank algorithm is designed so that you don't need to do that: the hyperlink matrix is constant, and only the score vector is updated.

PageRank is performed by Google using the 'Pregel' BSP (really just keywords) framework.
I remembered Apache Giraph (another Pregel), which includes a version of PageRank in its benchmark package.
Here's a video about Giraph: it's an introduction, and it specifically talks about handling PageRank.
If that doesn't work:
In Java there is an implementation of Pregel called GoldenOrb.
Pseudo code for the PageRank algorithm is here (on a different implementation of Pregel).
You'll have to read around BSP, and PageRank to handle the size of data you have.

Because the matrix is sparse you can implement dimensionality reduction like svd,pca,mds or Lsi that includes svd. There is a library to implement this kind of processes which is called Jama. You can find it here

plotting high dimensional data in java

I have thousands of data points and each data point has 50 dimensions. I would like to see the sparseness of data using java. Is there any java package/methods to plot such high dimensional data.

What you need to look for is multidimensional scaling. It basically reduces the dimensionality of the data space, trying to maintain the distances.
So you take a MDS package, reduce your data to 2D (or 3D) and plot them using 2D/3d graphics library (swing, jogl).
It might work or not, depending on the number of the data points and the space they're in. For 50 dimensions you might be out of luck, but it really depends.
A quick google for java implementation got me this
There's a package in R too, so you can use that.

Smart buffering in an environment with limited amount of memory Java

Dear StackOverflowers,
I am in the process of writing an application that sorts a huge amount of integers from a binary file. I need to do it as quickly as possible and the main performance issue is the disk access time, since I make a multitude of reads it slows down the algorithm quite significantly.
The standard way of doing this would be to fill ~50% of the available memory with a buffered object of some sort (BufferedInputStream etc) then transfer the integers from the buffered object into an array of integers (which takes up the rest of free space) and sort the integers in the array. Save the sorted block back to disk, repeat the procedure until the whole file is split into sorted blocks and then merge the blocks together.
The strategy for sorting the blocks utilises only 50% of the memory available since the data is essentially duplicated (50% for the cache and 50% for the array while they store the same data).
I am hoping that I can optimise this phase of the algorithm (sorting the blocks) by writing my own buffered class that allows caching data straight into an int array, so that the array could take up all of the free space not just 50% of it, this would reduce the number of disk accesses in this phase by a factor of 2. The thing is I am not sure where to start.
EDIT:
Essentially I would like to find a way to fill up an array of integers by executing only one read on the file. Another constraint is the array has to use most of the free memory.
If any of the statements I made are wrong or at least seem to be please correct me,
any help appreciated,
Regards

when you say limited, how limited... <1mb <10mb <64mb?
It makes a difference since you won't actually get much benefit if any from having large BufferedInputStreams in most cases the default value of 8192 (JDK 1.6) is enough and increasing doesn't ussually make that much difference.
Using a smaller BufferedInputStream should leave you with nearly all of the heap to create and sort each chunk before writing them to disk.

You might want to look into the Java NIO libraries, specifically File Channels and Int Buffers.

You dont give many hints. But two things come to my mind. First, if you have many integers, but not that much distinctive values, bucket sort could be the solution.
Secondly, one word (ok term), screams in my head when I hear that: external tape sorting. In early computer days (i.e. stone age) data relied on tapes, and it was very hard to sort data spread over multiple tapes. It is very similar to your situation. And indeed merge sort was the most often used sorting that days, and as far as I remember, Knuths TAOCP had a nice chapter about it. There might be some good hints about the size of caches, buffers and similar.