Algorithm to increase n^2 time - java

Alright so I've got code that essentially loops through 30,000 lines of text, and for each line, it runs through 20,000,000 lines of text in another file to compare it with.
while(x.hasNextLine())
while(y.hasNextLine())
where x has 30,000 and y has 20,000,000 lines respectively. Obviously, this is taking forever. Now I know of better algorithms, but I'm trying to compare a String in one with a String in another, so it's a little more difficult. I split a string in x, and I split a string in y. If part 1 of x, and part 2 of y are equal, I increment and do some other stuff. Generally, x appears in y a couple hundred times or so.
So, any ideas? I tried removing the line in y after each pass, and then rewriting the file so each time it parses through less in the second loop, but obviously this didn't help when you're writing a >500MB file.

If I'm reading right, you're reading from disk the 20M line (500MB) file 30,000 times?
If the 30k strings are small enough to keep in memory, you could reverse the inner/outer bits of the loop, and only go through the 500MB file once. Assuming DiskIO is the bottleneck, this'll save a lot of time.

The kind of data that you're working with will really determine how you can speed it up.
For example:
If your strings have some structure to them, then you might consider arranging the 20000 set of strings into a kind of tree Data structure, where you only compare sections of one string to another, effectively reducing the total number of comparisons made to some subset of the 20k strings.
You could also take advantage of your CPU architecture by running on multiple threads at once.
Ie create a separate thread each time you run a compare vs the 20k strings.
Maybe if you post some examples of the strings you're using, it'll be easier to find optimisations, but otherwise be creative :)
Edit:
Also check out Multimap from the Guava package, provided by google. I remember using it for a small project of mine Yonks ago, that seems quite similar to what you're attempting. Maybe it'll help you out, since it provides a key/value data structure.

Related

Fastest way to process through million line files with timestamps

So I've got these huge text files that are filled with a single comma delimited record per line. I need a way to process the files line by line, removing lines that meet certain criteria. Some of the removals are easy, such as one of the fields is less than a certain length. The hardest criteria is that these lines all have timestamps. Many records are identical except for their timestamps and I have to remove all records but one that are identical and within 15 seconds of one another.
So I'm wondering if some others can come up with the best approach for this. I did come up with a small program in Java that accomplishes the task, using JodaTime for the timestamp stuff which makes it really easy. However, the initial way I coded the program was running into OutofMemory Heap Space errors. I refactored the code a bit and it seemed ok for the most part but I do still believe it has some memory issues as once in awhile the program just seems to get hung up. That and it just seems to take way too long. I'm not sure if this is a memory leak issue, a poor coding issue, or something else entirely. And yes I tried increasing the Heap Size significantly but still was having issues.
I will say that the program needs to be in either Perl or Java. I might be able to make a python script work too but I'm not overly familiar with python. As I said, the timestamp stuff is easiest (to me) in Java because of the JodaTime library. I'm not sure how I'd accomplish the timestamp stuff in Perl. But I'm up for learning and using whatever would work best.
I will also add the files being read in vary tremendously in size but some big ones are around 100Mb with something like 1.3 million records.
My code essentially reads in all the records and puts them into a Hashmap with the keys being a specific subset of the data from a record that similar records would share. So a subset of the record not including the timestamps which would be different. This way you'd end up with some number of records with identical data but that occurred at different times. (So completely identical minus the timestamps).
The value of each key then, is a Set of all records that have the same subset of data. Then I simply iterate through the Hashmap, taking each set and iterating through it. I take the first record and compare its times to all the rest to see if they're within 15 seconds. If so the record is removed. Once that set is finished it's written out to a file until all the records have been gone through. Hopefully that makes sense.
This works but clearly the way I'm doing it is too memory intensive. Anyone have any ideas on a better way to do it? Or, a way I can do this in Perl would actually be good because trying to insert the Java program into the current implementation has caused a number of other headaches. Though perhaps that's just because of my memory issues and poor coding.
Finally, I'm not asking someone to write the program for me. Pseudo code is fine. Though if you have ideas for Perl I could use more specifics. The main thing I'm not sure how to do in Perl is the time comparison stuff. I've looked a little into Perl libraries but haven't seen anything like JodaTime (though I haven't looked much). Any thoughts or suggestions are appreciated. Thank you.
Reading all the rows in is not ideal, because you need to store the whole lot in memory.
Instead you could read line by line, writing out the records that you want to keep as you go. You could keep a cache of the rows you've hit previously, bounded to be within 15 seconds of the current program. In very rough pseudo-code, for every line you'd read:
var line = ReadLine()
DiscardAnythingInCacheOlderThan(line.Date().Minus(15 seconds);
if (!cache.ContainsSomethingMatchingCriteria()) {
// it's a line we want to keep
WriteLine(line);
}
UpdateCache(line); // make sure we store this line so we don't write it out again.
As pointed out, this assumes that the lines are in time stamp order. If they aren't, then I'd just use UNIX sort to make it so they are, as that'll quite merrily handle extremely large files.
You might read the file and output just the line numbers to be deleted (to be sorted and used in a separate pass.) Your hash map could then contain just the minimum data needed plus the line number. This could save a lot of memory if the data needed is small compared to the line size.

How to remove duplicate words using Java when words are more than 200 million?

I have a file (size = ~1.9 GB) which contains ~220,000,000 (~220 million) words / strings. They have duplication, almost 1 duplicate word every 100 words.
In my second program, I want to read the file. I am successful to read the file by lines using BufferedReader.
Now to remove duplicates, we can use Set (and it's implementations), but Set has problems, as described following in 3 different scenarios:
With default JVM size, Set can contain up to 0.7-0.8 million words, and then OutOfMemoryError.
With 512M JVM size, Set can contain up to 5-6 million words, and then OOM error.
With 1024M JVM size, Set can contain up to 12-13 million words, and then OOM error. Here after 10 million records addition into Set, operations become extremely slow. For example, addition of next ~4000 records, it took 60 seconds.
I have restrictions that I can't increase the JVM size further, and I want to remove duplicate words from the file.
Please let me know if you have any idea about any other ways/approaches to remove duplicate words using Java from such a gigantic file. Many Thanks :)
Addition of info to question: My words are basically alpha-numeric and they are IDs which are unique in our system. Hence they are not plain English words.
Use merge sort and remove the duplicates in a second pass. You could even remove the duplicates while merging (just keep the latest word added to output in RAM and compare the candidates to it as well).
Divide the huge file into 26 smaller files based on the first letter of the word. If any of the letter files are still too large, divide that letter file by using the second letter.
Process each of the letter files separately using a Set to remove duplicates.
You might be able to use a trie data structure to do the job in one pass. It has advantages that recommend it for this type of problem. Lookup and insert are quick. And its representation is relatively space efficient. You might be able to represent all of your words in RAM.
If you sort the items, duplicates will be easy to detect and remove, as the duplicates will bunch together.
There is code here you could use to mergesort the large file:
http://www.codeodor.com/index.cfm/2007/5/10/Sorting-really-BIG-files/1194
For large files I try not to read the data into memory but instead operate on a memory mapped file and let the OS page in/out memory as needed. If your set structures contain offsets into this memory mapped file instead of the actual strings it would consume significantly less memory.
Check out this article:
http://javarevisited.blogspot.com/2012/01/memorymapped-file-and-io-in-java.html
Question: Are these really WORDS, or are they something else -- phrases, part numbers, etc?
For WORDS in a common spoken language one would expect that after the first couple of thousand you'd have found most of the unique words, so all you really need to do is read a word in, check it against a dictionary, if found skip it, if not found add it to the dictionary and write it out.
In this case your dictionary is only a few thousand words large. And you don't need to retain the source file since you write out the unique words as soon as you find them (or you can simply dump the dictionary when you're done).
If you have the posibility to insert the words in a temporary table of a database (using batch inserts), then it would be a select distinct towards that table.
One classic way to solve this kind of problem is a Bloom filter. Basically you hash your word a number of times and for each hash result set some bits in a bit vector. If you're checking a word and all the bits from its hashes are set in the vector you've probably (you can set this probability arbitrarily low by increasing the number of hashes/bits in the vector) seen it before and it's a duplicate.
This was how early spell checkers worked. They knew if a word was in the dictionary, but they couldn't tell you what the correct spelling was because it only tell you if the current word is seen.
There are a number of open source implementations out there including java-bloomfilter
I'd tackle this in Java the same way as in every other language: Write a deduplication filter and pipe it as often as necessary.
This is what I mean (in pseudo code):
Input parameters: Offset, Size
Allocate searchable structure of size Size (=Set, but need not be one)
Read Offset (or EOF is encountered) elements from stdin and just copy them to stdout
Read Size elments from stdin (or EOF), store them in Set. If duplicate, drop, else write to stdout.
Read elements from stdin until EOF, if they are in Set then drop, else write to stdout
Now pipe as many instances as you need (If storage is no problem, maybe only as many as you have cores) with increasing Offsets and sane Size. This lets you use more cores, as I suspect the process is CPU bound. You can even use netcat and spread processing over more machines, if you are in a hurry.
Even in English, which has a huge number of words for a natural language, the upper estimates are only about 80000 words. Based on that, you could just use a HashSet and add all your words it (probably in all lower case to avoid case issues):
Set<String> words = new HashSet<String>();
while (read-next-word) {
words.add(word.toLowerCase());
}
If they are real words, this isn't going to cause memory problems, will will be pretty fast too!
To not have to worry to much about implementation you should use a database system, either plain old relational SQL or a No-SQL solution. Im pretty sure you could use e.g. Berkeley DB java edition and then do (pseudo code)
for(word : stream) {
if(!DB.exists(word)) {
DB.put(word)
outstream.add(word)
}
}
The problem is in essence easy, you need to store things on disk because there is not enough memory, then either use sorting O(N log N) (unecessary) or hashing O(N) to find the unique words.
If you want a solution that will very likely work but is not guaranteed to do so use a LRU type hash table. According to the empirical Zpif's law you should be OK.
A follow up question to some smart guy out there, what if I have 64-bit machine and set heap size to say 12GB, shouldn't virtual memory take care of the problem (although not in an optimal way) or is java not designed this way?
Quicksort would be a good option over Mergesort in this case because it needs less memory. This thread has a good explanation as to why.
Most performant solutions arise from omiting unecessary stuff. You look only for duplicates, so just do not store words itself, store hashes. But wait, you are not interested in hashes either, only if they awere seen already - do not store them. Treat hash as really large number, and use bitset to see whether you already seen this number.
So your problem boils down to really big sparse populated bitmap - with size depending on hash width. If your hash is up to 32 bit, you can use riak bitmap.
... gone thinking about really big bitmap for 128+ bit hashes %) (I'll be back )

The more I use a Java HashMap, the more the performance drops - even with stable size

I want to scan through a huge corpus of text and count word frequencies (n-gram frequencies actually for those who are familiar with NLP/IR). I use a Java HashMap for this. So what happens is I process the text line by line. For each line, I extract the words, and for each word, I update the corresponding frequency in the hashmap.
The problem is that this process gets slower and slower. For example, it starts by processing around 100k lines / second - and the performance starts falling right away. After about 28 million lines , the performance has fallen to 16k lines / second - and of course keeps falling.
First thing that came to mind was that it was caused of too many entries in the hashmap, which caused every put and every get to be slower every time. So what I tried was to only keep the most (say 100k) frequent entries in the hashmap at anytime. This was done by using a second map that mapped frequencies to words (as in here: Automatically sorted by values map in Java )
This performed a lot faster in general. (although it started at 56 k lines / sec, by the time it reached 28 mil lines, the performance had only dropped to 36.5k lines / sec). However, this also kept falling, at a much slower rate - but the fact remains, that it kept falling.
Have you got any possible explanation of why does this happen when the hashmap's size remains the same? Do you think this has anything to do with the garbage collector? Meaning, that the fact that I keep putting, and removing object to/from hashmaps fragments up the memory or something? Or could it be a hashing function problem? Since I'm using strings, the hashing function is Java's default hashing function for strings.
Here is the part of my code that performs the aforementioned task:
http://pastebin.com/P8S6Sj86
NOTE: I am a Java newbie so any elaboration in your answers is more than welcome
I recommend using Java VisualVM to do some profiling. This comes with Java - go to the command line and type jvisualvm to run it. This makes it easy to see if memory churn is your problem, or if particular types of objects are being created hundreds of thousands of times.
If you break up your code into several methods, you'll also be able to tell which methods take too long to run.
I did notice that you are unnecessarily creating lots of objects in inner loops. This certainly won't help performance, although it may not be the main culprit.
For example:
float avg = new Float(sumItems) / new Float (freqMap.size());
should just be
float avg = (float)sumItems / freqMap.size();
Another piece of your code which also could be troublesome is:
System.out.println(numItems + " items counted");
Depending on your operating system or IDE, writing 100,000s of lines to the console requires significant time. Instead, just write an update of progress for each 1000 items.
Suggestion:
Try implementing a custom hashCode method for the object you're storing in your hashmap. Here are some links:
Java HashMap performance optimization / alternative
http://www.ibm.com/developerworks/java/library/j-jtp05273/index.html
http://www.javamex.com/tutorials/collections/hash_function_guidelines.shtml
Bad idea to use String key in HashMap?

How to store millions of Double during a calculation?

My engine is executing 1,000,000 of simulations on X deals. During each simulation, for each deal, a specific condition may be verified. In this case, I store the value (which is a double) into an array. Each deal will have its own list of values (i.e. these values are indenpendant from one deal to another deal).
At the end of all the simulations, for each deal, I run an algorithm on his List<Double> to get some outputs. Unfortunately, this algorithm requires the complete list of these values, and thus, I am not able to modify my algorithm to calculate the outputs "on the fly", i.e. during the simulations.
In "normal" conditions (i.e. X is low, and the condition is verified less than 10% of the time), the calculation ends correctly, even if this may be enhanced.
My problem occurs when I have many deals (for example X = 30) and almost all of my simulations verify my specific condition (let say 90% of simulations). So just to store the values, I need about 900,000 * 30 * 64bits of memory (about 216Mb). One of my future requirements is to be able to run 5,000,000 of simulations...
So I can't continue with my current way of storing the values. For the moment, I used a "simple" structure of Map<String, List<Double>>, where the key is the ID of the element, and List<Double> the list of values.
So my question is how can I enhance this specific part of my application in order to reduce the memory usage during the simulations?
Also another important note is that for the final calculation, my List<Double> (or whatever structure I will be using) must be ordered. So if the solution to my previous question also provide a structure that order the new inserted element (such as a SortedMap), it will be really great!
I am using Java 1.6.
Edit 1
My engine is executing some financial calculations indeed, and in my case, all deals are related. This means that I cannot run my calculations on the first deal, get the output, clean the List<Double>, and then move to the second deal, and so on.
Of course, as a temporary solution, we will increase the memory allocated to the engine, but it's not the solution I am expecting ;)
Edit 2
Regarding the algorithm itself. I can't give the exact algorithm here, but here are some hints:
We must work on a sorted List<Double>. I will then calculate an index (which is calculated against a given parameter and the size of the List itself). Then, I finally return the index-th value of this List.
public static double algo(double input, List<Double> sortedList) {
if (someSpecificCases) {
return 0;
}
// Calculate the index value, using input and also size of the sortedList...
double index = ...;
// Specific case where I return the first item of my list.
if (index == 1) {
return sortedList.get(0);
}
// Specific case where I return the last item of my list.
if (index == sortedList.size()) {
return sortedList.get(sortedList.size() - 1);
}
// Here, I need the index-th value of my list...
double val = sortedList.get((int) index);
double finalValue = someBasicCalculations(val);
return finalValue;
}
I hope it will help to have such information now...
Edit 3
Currently, I will not consider any hardware modification (too long and complicated here :( ). The solution of increasing the memory will be done, but it's just a quick fix.
I was thinking of a solution that use a temporary file: Until a certain threshold (for example 100,000), my List<Double> stores new values in memory. When the size of List<Double> reaches this threshold, I append this list in the temporary file (one file per deal).
Something like that:
public void addNewValue(double v) {
if (list.size() == 100000) {
appendListInFile();
list.clear();
}
list.add(v);
}
At the end of the whole calculation, for each deal, I will reconstruct the complete List<Double> from what I have in memory and also in the temporary file. Then, I run my algorithm. I clean the values for this deal, and move to the second deal (I can do that now, as all the simulations are now finished).
What do you think of such solution? Do you think it is acceptable?
Of course I will lose some time to read and write my values in an external file, but I think this can be acceptable, no?
Your problem is algorithmic and you are looking for a "reduction in strength" optimization.
Unfortunately, you've been too coy in the the problem description and say "Unfortunately, this algorithm requires the complete list of these values..." which is dubious. The simulation run has already passed a predicate which in itself tells you something about the sets that pass through the sieve.
I expect the data that meets the criteria has a low information content and therefore is amenable to substantial compression.
Without further information, we really can't help you more.
You mentioned that the "engine" is not connected to a database, but have you considered using a database to store the lists of elements? Possibly an embedded DB such as SQLite?
If you used int or even short instead of string for the key field of your Map, that might save some memory.
If you need a collection object that guarantees order, then consider a Queue or a Stack instead of your List that you are currently using.
Possibly think of a way to run deals sequentially, as Dommer and Alan have already suggested.
I hope that was of some help!
EDIT:
Your comment about only having 30 keys is a good point.
In that case, since you have to calculate all your deals at the same time, then have you considered serializing your Lists to disk (i.e. XML)?
Or even just writing a text file to disk for each List, then after the deals are calculated, loading one file/List at a time to verify that List of conditions?
Of course the disadvantage is slow file IO, but, this would reduced your server's memory requirement.
Can you get away with using floats instead of doubles? That would save you 100Mb.
Just to clarify, do you need ALL of the information in memory at once? It sounds like you are doing financial simulations (maybe credit risk?). Say you are running 30 deals, do you need to store all of the values in memory? Or can you run the first deal (~900,000 * 64bits), then discard the list of double (serialize it to disk or something) and then proceed with the next? I thought this might be okay as you say the deals are independent of one another.
Apologies if this sounds patronising; I'm just trying to get a proper idea of the problem.
The flippant answer is to get a bunch more memory. Sun JVM's can (almost happily) handle multi gigabyte heaps and if it's a batch job then longer GC pauses might not be a massive issue.
You may decide that this not a sane solution, the first thing to attempt would be to write a custom list like collection but have it store primitive doubles instead of the object wrapper Double objects. This will help save the per object overhead you pay for each Double object wrapper. I think the Apache common collections project had primitive collection implementations, these might be a starting point.
Another level would be to maintain the list of doubles in a nio Buffer off heap. This has the advantage that the space being used for the data is actually not considered in the GC runs and could in theory could lead you down the road of managing the data structure in a memory mapped file.
From your description, it appears you will not be able to easily improve your memory usage. The size of a double is fixed, and if you need to retain all results until your final processing, you will not be able to reduce the size of that data.
If you need to reduce your memory usage, but can accept a longer run time, you could replace the Map<String, List<Double>> with a List<Double> and only process a single deal at a time.
If you have to have all the values from all the deals, your only option is to increase your available memory. Your calculation of the memory usage is based on just the size of a value and the number of values. Without a way to decrease the number of values you need, no data structure will be able to help you, you just need to increase your available memory.
From what you tell us it sounds like you need 10^6 x 30 processors (ie number of simulations multiplied by number of deals) each with a few K RAM. Perhaps, though, you don't have that many processors -- do you have 30 each of which has sufficient memory for the simulations for one deal ?
Seriously: parallelise your program and buy an 8-core computer with 32GB RAM (or 16-core w 64GB or ...). You are going to have to do this sooner or later, might as well do it now.
There was a theory that I read awhile ago where you would write the data to disk and only read/write a chunk what you. Of course this describes virtual memory, but the difference here is that the programmer controls the flow and location rathan than the OS. The advantage there is that the OS is only allocated so much virtual memory to use, where you have access to the whole HD.
Or an easier option is just to increase your swap/paged memory, which I think would be silly but would help in your case.
After a quick google it seems like this function might help you if you are running on Windows:
http://msdn.microsoft.com/en-us/library/aa366537(VS.85).aspx
You say you need access to all the values, but you cannot possibly operate on all of them at once? Can you serialize the data such that you can store it in a single file. Each record set apart either by some delimiter, key value, or simply the byte count. Keep a byte counter either way. Let that be a "circular file" composed of a left file and a right file operating like opposing stacks. As data is popped(read) off the left file it is processed and pushed(write) into the right file. If your next operation requires a previously processed value reverse the direction of the file transfer. Think of your algorithm as residing at the read/write head of your hard drive. You have access as you would with a list just using different methods and at much reduced speed. The speed hit will be significant but if you can optimize your sequence of serialization so that the most likely accessed data is at the top of the file in order of use and possibly put the left and right files on different physical drives and your page file on a 3rd drive you will benefit from increased hard disk performance due to sequential and simultaneous reads and writes. Of course its a bit harder than it sounds. Each change of direction requires finalizing both files. Logically something like,
if (current data flow if left to right) {send EOF to right_file; left_file = left_file - right_file;} Practically you would want to leave all data in place where it physically resides on the drive and just manipulate the beginning and ending addresses for the files in the master file table. Literally operating like a pair of hard disk stacks. This will be a much slower, more complicated process than simply adding more memory, but very much more efficient than separate files and all that overhead for 1 file per record * millions of records. Or just put all your data into a database. FWIW, this idea just came to me. I've never actually done it or even heard of it done. But I imagine someone must have thought of it before me. If not please let me know. I could really use the credit on my resume.
One solution would be to format the doubles as strings and then add them in a (fast) Key Value store which is ordering by-design.
Then you would only have to read sequentially from the store.
Here is a store that 'naturally' sorts entries as they are inserted.
And they boast that they are doing it at the rate of 100 million entries per second (searching is almost twice as fast):
http://forum.gwan.com/index.php?p=/discussion/comment/897/#Comment_897
With an API of only 3 calls, it should be easy to test.
A fourth call will provide range-based searches.

Avoid an "out of memory error" in Java(eclipse), when using large data structure?

OK, so I am writing a program that unfortunately needs to use a huge data structure to complete its work, but it is failing with a "out of memory error" during its initialization. While I understand entirely what that means and why it is a problem, I am having trouble overcoming it, since my program needs to use this large structure and I don't know any other way to store it.
The program first indexes a large corpus of text files that I provide. This works fine.
Then it uses this index to initialize a large 2D array. This array will have n² entries, where "n" is the number of unique words in the corpus of text. For the relatively small chunk I am testing it o n(about 60 files) it needs to make approximately 30,000x30,000 entries. This will probably be bigger once I run it on my full intended corpus too.
It consistently fails every time, after it indexes, while it is initializing the data structure(to be worked on later).
Things I have done include:
revamp my code to use a primitive int[] instead of a TreeMap
eliminate redundant structures, etc...
Also, I have run the program with-Xmx2g to max out my allocated memory
I am fairly confident this is not going to be a simple line of code solution, but is most likely going to require a very new approach. I am looking for what that approach is, any ideas?
Thanks,
B.
It sounds like (making some assumptions about what you're using your array for) most of the entries will be 0. If so, you might consider using a sparse matrix representation.
If you really have that many entries (your current array is somewhere over 3 gigabytes already, even assuming no overhead), then you'll have to use some kind of on-disk storage, or a lazy-load/unload system.
There are several causes of out of memory issues.
Firstly, the simplest case is you simply need more heap. You're using 512M max heap when your program could operate correctly with 2G. Increase is with -Xmx2048m as a JVM option and you're fine. Also be aware than 64 bit VMs will use up to twice the memory of 32 bit VMs depending on the makeup of that data.
If your problem isn't that simple then you can look at optimization. Replacing objects with primitives and so on. This might be an option. I can't really say based on what you've posted.
Ultimately however you come to a cross roads where you have to make a choice between virtulization and partitioning.
Virtualizing in this context simply means some form of pretending there is more memory than there is. Operating systems use this with virtual address spaces and using hard disk space as extra memory. This could mean only keeping some of the data structure in memory at a time and persisting the rest to secondary storage (eg file or database).
Partitioning is splitting your data across multiple servers (either real or virtual). For example, if you were keeping track of stock trades on the NASDAQ you could put stock codes starting with "A" on server1, "B" on server2, etc. You need to find a reasonable approach to slice your data such that you reduce or eliminate the need for cross-communication because that cross-communication is what limits your scalability.
So simple case, if what you're storing is 30K words and 30K x 30K combinations of words you could divide it up into four server:
A-M x A-M
A-M x N-Z
N-Z x A-M
N-Z x N-Z
That's just one idea. Again it's hard toc omment without knowing specifics.
This is a common problem dealing with large datasets. You can optimize as much as you want, but the memory will never be enough (probably), and as soon as the dataset grows a little more you are still smoked. The most scalable solution is simply to keep less in memory, work on chunks, and persist the structure on disk (database/file).
If you don't need a full 32 bits (size of integer) for each value in your 2D array, perhaps a smaller type such as a byte would do the trick? Also you should give it as much heap space as possible - 2GB is still relatively small for a modern system. RAM is cheap, especially if you're expecting to be doing a lot of processing in-memory.

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