Can someone please explain the difference between the LZSS and the LZ77 algorithm. I've been looking online for a couple of hours but I couldn't find the difference. I found the LZ77 algorithm and I understood its implementation.
But, how does LZSS differ from LZ77? Let's say if we have an string "abracadabra" how is LZSS gonna compress it differently from LZ77? Is there a C pseudo-code that I could follow?
Thank you for your time!
Unfortunately, both terms LZ77 and LZSS tend to be used very loosely, so they do not really imply very specific algorithms. When people say that they compressed their data using an LZ77 algorithm, they usually mean that they implemented a dictionary based compression scheme, where a fixed-size window into the recently decompressed data serves as the dictionary and some words/phrases during the compression are replaced by references to previously seen words/phrases within the window.
Let us consider the input data in the form of the word
abracadabra
and assume that window can be as large as the input data. Then we can represent "abracadabra" as
abracad(-7,4)
Here we assume that letters are copied as is, and that the meaning of two numbers in brackets is "go 7 positions back from where we are now and copy 4 symbols from there", which reproduces "abra".
This is the basic idea of any LZ77 compressor. Now, the devil is in the detail. Note that the original word "abracadabra" contains 11 letters, so assuming ASCII representation the word, it is 11 bytes long. Our new representation contains 13 symbols, so if we assume the same ASCII representation, we just expanded the original message, instead of compressing it. One can prove that this can sometimes happen to any compressor, no matter how good it actually is.
So, the compression efficiency depends on the format in which you store the information about uncompressed letters and back references. The original paper where the LZ77 algorithm was first described (Ziv, J. & Lempel, A. (1977) A universal algorithm for sequential data compression. IEEE Transactions on information theory, 23(3), 337-343) uses the format that can be loosely described here as
(0,0,a)(0,0,b)(0,0,r)(0,1,c)(0,1,d)(0,3,a)
So, the compressed data is the sequence of groups of three items: the absolute (not relative!) position in the buffer to copy from, the length of the dictionary match (0 means no match was found) and the letter that follows the match. Since most letters did not match anything in the dictionary, you can see that this is not a particularly efficient format for anything but very compressible data.
This inefficiency may well be the reason why the original form of LZ77 has not been used in any practical compressors.
SS in the "LZSS" refers to a paper that was trying to generalize the ideas of dictionary compression with the sliding window (Storer, J. A. & Szymanski, T. G. (1982). Data compression via textual substitution. Journal of the ACM, 29(4), 928-951). The paper itself looks at several variations of dictionary compression schemes with windows, so once again, you will not find an explicit "algorithm" in it. However, the term LZSS is used by most people to describe the dictionary compression scheme with flag bits, e.g. describing "abracadabra" as
|0a|0b|0r|0a|0c|0a|0d|1-7,4|
where I added vertical lines purely for clarity. In this case numbers 0 and 1 are actually prefix bits, not bytes. Prefix bit 0 says "copy the next byte into the output as is". Prefix bit 1 says "next follows the information for copying a match". Nothing else is really specific, term LZSS is used to say something specific about the use of these prefix signal bits. Hopefully you can see how this can be done compactly, in fact much more efficiently than the format described in LZ77 paper.
Related
As it becomes ever easier to use computers in general and get into programming in particular, an increasing fraction of beginners seem to lack certain fundamental understanding that was once taken for granted in programming circles. Meanwhile as technology advances, the details of that understanding have grown more complex (I personally was programming before Unicode existed, let alone, say, JSON or XML). So, for the sake of having a solid reference, it seems apropos to ask:
What exactly is in a file, anyway? What do we mean when we say that we "open" and "read" a file - what are we getting out of it? I know the term "data", but just giving a name to something is not a real explanation.
More importantly, how do we make sense of data? If I try simply reading some data from a file and outputting it to the console, why does it often look like garbage? Why do some other files appear to have some text scattered among that garbage, while yet others seem to be mostly or completely text? Why isn't it sufficient to ask the program to read, say, an image file, in order to display the image? Again, I know the term "format", but this doesn't explain the concept. If we say, for example, that we make sense of data according to its format, then that only raises two more questions - how do we determine the format, and how does it actually help?
Related: What exactly causes binary file "gibberish"?.
Data, bits and bytes
Everyone who has had to buy hardware, or arrange a network connection, should have some familiarity with the concept of a "bit" and of a "byte". They're used to measure the capacity of storage devices and transfer rates. In short, they measure data: the amount of data that can be stored on a disk, or the amount of data transferred along a cable (or via a wireless connection) per second.
Data is essentially information - a record of some kind of knowledge. The bit is the fundamental unit of information, representing the smallest possible amount of knowledge: the answer to a yes-or-no question, a choice between two options, a record of a decision between two alternatives. (There would need to be at least two possibilities; with only one, there was no answering, choice or decision necessary, and thus nothing is learned by seeing that single possibility arise.)
A byte is simply a grouping of bits in a standard size. Almost everyone nowadays defines a byte to mean 8 bits, mainly because all contemporary consumer hardware is designed around that concept. In some very specific technical contexts (such as certain C or C++ language standard documents), "byte" may have a broader meaning, and octet is used to be precise about 8-bit groupings. We will stick with "byte" here, because we don't need to worry about ancient hardware or idiosyncratic compiler implementations for now.
Data storage devices - both permanent ones like HDDs and SSDs, and temporary ones like RAM - use a huge amount of individual components (depending on the device) to represent data, each of which can conceptually be in either of two states (we commonly use "on or off", "1 or 0" etc. as metaphors). Because there's a decision to be made between those two states, the component thus represents one bit of data. The data isn't a physical thing - it's not the component itself. It's the state of that component: the answer to the question "which of the two possible ways is this component configured right now?".
How data is made useful
It's clear to see how we can use a bit to represent a number, if there are only two possible numbers we are interested in. Suppose those numbers are 0 and 1; then we can ask, "is the number 1?", and according to the bit that tells us the answer to that question, we know which number is represented.
It turns out that in fact this is all we need in order to represent all kinds of numbers. For example, if we need to represent a number from {0, 1, 2, 3}, we can use two bits: one that tells us whether the represented number is in {0, 1} or {2, 3}, and one that tells us whether it's in {0, 2} or {1, 3}. If we can answer those two questions, we can identify the number. This technique generalizes, using base two arithmetic, to represent any integer: essentially, each bit corresponds to a value from the geometric sequence 1, 2, 4, 8, 16..., and then we just add up (implicitly) the values that were chosen by the bits. By tweaking this convention slightly, we can represent negative integers as well. If we let some bits correspond to binary fractions as well (1/2, 1/4, 1/8...), we can approximate real numbers (including the rationals) as closely as we want, depending on how many bits we use for the fractional part. Alternately, we can just use separate groups of bits to represent the numerator and denominator of a rational number - or, for that matter, the real and imaginary parts of a complex number.
Furthermore, once we can represent numbers, we can represent all kinds of answers to questions. For example, we can agree on a sequence of symbols that are used in text; and then, implicitly, a number represents the symbol at that position in the sequence. So we can use some amount of bits to represent a symbol; and by representing individual symbols repeatedly, we can represent text.
Similarly, we can represent the height of a sound wave at a given instant in time; by repeating this process a few tens of thousands of times per second, we can represent sound audible to humans.
Similarly, having studied how the human eye works, we find that we can analyze colours as combinations of three intensity values (i.e., numbers) representing "components" of the colour. By describing colours at many points a small distance apart (like with the sound wave, but in a two-dimensional grid), we can represent images. By considering images across time (a few tens of times per second), we can represent animations.
And so on, and so on.
Choosing an interpretation
There's a problem, here, though. All of this simply talks about possibilities for what data could represent. How do we know what it does represent?
Plainly, the raw data stored by a computer doesn't inherently represent anything specific. Because it's all in the same regular, sequence-of-bits form, nothing stops us from taking any arbitrary chunk of data and interpreting it by any of the schemes described above.
It just... isn't likely to appear like anything meaningful, that way.
However, the choice of interpretations is a choice... which means it can be encoded and recorded in this raw-data form. We say that such data is metadata: data that tells us about the meaning of other data. This could take many forms: the names of our files and the folder structure (telling us how those files relate to each other, and how the user intends to keep track of them); extensions on file names, special data at the beginning of files or other notes made within the file system (telling us what type of file it is, corresponding to a file format - keep reading); documentation (something that humans can read in order to understand how another file is intended to work); and computer programs (data which tells the computer what steps to take, in order to present the file's contents to the user).
What is a (file) format?
Quite simply, a format is the set of rules that describes a way to interpret some data (typically, the contents of a file). When we say that a file is "in" a particular format, we mean that it a) has a valid interpretation according to that format (not every possible chunk of data will meet the requirements, in general) and b) is intended to be interpreted that way.
Put another way: a format is the meaning represented by some metadata.
A format can be a subset or refinement of some other format. For example, JSON documents are also text documents, using UTF-8 encoding. The JSON format adds additional meaning to the text that was represented, by describing how specific text sequences are used to represent structured data. A programming language can also be thought of as this kind of format: it gives additional meaning to text, by explaining how that text can be translated into instructions a computer can follow. (A computer's "machine code" is also a kind of format, that gets interpreted directly by the hardware rather than by a program.)
(Recall: we established that a computer program can be a kind of metadata, and that a programming language can be a kind of format, and that metadata represents a format. To close the loop: of course, one can have a computer program that implements a programming language - that's what a compiler is.)
A format can also involve multiple steps, explained by separate standards. For example, Unicode is the de facto standard text format, but it only describes how abstract numbers correspond to text symbols. It doesn't directly say how to convert the bits into numbers (and this does need to be specified; "treat each byte as a number from 0..255" a) would still be making a choice of many possible ways to do it; b) isn't really sufficient, because there are a lot more possible text symbols than that). To represent text, we also need an encoding, i.e. the rest of the rules for the data format, specifically to convert bits to numbers. UTF-8 is one such encoding, and has become dominant.
What actually happens when we read the file?
Raw data is transferred from the file on disk, into the program's memory.
That's it.
Some languages offer convenience functionality, for the common case of treating the data like text. This might mean doing some light processing on the data (because operating systems disagree about which text symbols, in what order represent "the end of a line"), and loading the data into the language's built-in "string" data structure, using some kind of encoding. (Yes, even if the encoding is "each byte represents a number from 0 to 255 inclusive, which represents the corresponding Unicode code point", that is an encoding - even if it doesn't represent all text and thus isn't a proper Unicode encoding - and it is being used even if the programmer did nothing to specify it; there is no such thing as "plain text", and ignoring this can have all kinds of strange consequences.)
But fundamentally, the reading is really just a transfer of data. Text conversion is often treated as special because, for a long time, programmers were sloppy about treating text properly as an interpretation of data; for decades there was an interpretation of data as text - one byte per text symbol (incidentally, "character" does not mean the same thing as a Unicode code point) - so well established that everyone started forgetting they were actually using it. Programmers forgot about this even though it only actually specifies what half the possible values of a byte mean and leaves the other half up to a local interpretation, and even though that scheme is still woefully inadequate for many world languages, such that programmers in many other countries came up with their own solutions. The solution - the Unicode standard, mentioned several times above - had its first release in 1991, but there are still a few programmers today blithely ignoring it.
But enough ranting.
How does interpreting a file work?
In order to display an image, render a web page, play sound or anything else from a file, we need to:
Have data that is actually intended to represent the corresponding thing;
Know the format that is used by the data to represent the thing;
Load the data (read the file, or read data from a network connection, or create the data by some other process);
Process the data according to the format.
This happens for even the simplest cases, and it can involve multiple programs. For example, a simple command-line program that inputs text from the user (from the "standard input stream") and outputs text back (to the "standard output stream"), generally, is not actually causing the text to appear on screen, or figuring out what keys were pressed on the keyboard. Instead: the operating system interprets signals from the keyboard, in order to create readable data; after the program writes out its response to the input, another program (the terminal) will translate the text into pixel colour values (getting help from the operating system to choose images from a font); then the operating system will arrange to send the appropriate data to the monitor (according to the terminal window's position etc.).
this idea had been flowing in my head for 3 years and i am having problems to apply it
i wanted to create a compression algorithm that cuts the file size in half
e.g. 8 mb to 4 mb
and with some searching and experience in programming i understood the following.
let's take a .txt file with letters (a,b,c,d)
using the IO.File.ReadAllBytes function , it gives the following array of bytes : ( 97 | 98 | 99 | 100 ) , which according to this : https://en.wikipedia.org/wiki/ASCII#ASCII_control_code_chart is the decimal value of the letter.
what i thought about was : how to mathematically cut this 4-membered-array to only 2-membered-array by combining each 2 members into a single member but you can't simply mathematically combine two numbers and simply reverse them back as you have many possibilities,e.g.
80 | 90 : 90+80=170 but there is no way to know that 170 was the result of 80+90 not like 100+70 or 110+60.
and even if you could overcome that , you would be limited by the maximum value of bytes (255 bytes) in a single member of the array.
i understand that most of the compression algorithms use the binary compression and they were successful,but imagine cutting a file size in half , i would like to hear your ideas on this.
Best Regards.
It's impossible to make a compression algorithm that makes every file shorter. The proof is called the "counting argument", and it's easy:
There are 256^L possible files of length L.
Lets say there are N(L) possible files with length < L.
If you do the math, you find that 256^L = 255*N(L)+1
So. You obviously cannot compress every file of length L, because there just aren't enough shorter files to hold them uniquely. If you made a compressor that always shortened a file of length L, then MANY files would have to compress to the same shorter file, and of course you could only get one of them back on decompression.
In fact, there are more than 255 times as many files of length L as there are shorter files, so you can't even compress most files of length L. Only a small proportion can actually get shorter.
This is explained pretty well (again) in the comp.compression FAQ:
http://www.faqs.org/faqs/compression-faq/part1/section-8.html
EDIT: So maybe you're now wondering what this compression stuff is all about...
Well, the vast majority of those "all possible files of length L" are random garbage. Lossless data compression works by assigning shorter representations (the output files) to the files we actually use.
For example, Huffman encoding works character by character and uses fewer bits to write the most common characters. "e" occurs in text more often than "q", for example, so it might spend only 3 bits to write "e"s, but 7 bits to write "q"s. bytes that hardly ever occur, like character 131 may be written with 9 or 10 bits -- longer than the 8-bit bytes they came from. On average you can compress simple English text by almost half this way.
LZ and similar compressors (like PKZIP, etc) remember all the strings that occur in the file, and assign shorter encodings to strings that have already occurred, and longer encodings to strings that have not yet been seen. This works even better since it takes into account more information about the context of every character encoded. On average, it will take fewer bits to write "boy" than "boe", because "boy" occurs more often, even though "e" is more common than "y".
Since it's all about predicting the characteristics of the files you actually use, it's a bit of a black art, and different kinds of compressors work better or worse on different kinds of data -- that's why there are so many different algorithms.
I bet somebody has solved this before, but my searches have come up empty.
I want to pack a list of words into a buffer, keeping track of the starting position and length of each word. The trick is that I'd like to pack the buffer efficiently by eliminating the redundancy.
Example: doll dollhouse house
These can be packed into the buffer simply as dollhouse, remembering that doll is four letters starting at position 0, dollhouse is nine letters at 0, and house is five letters at 3.
What I've come up with so far is:
Sort the words longest to shortest: (dollhouse, house, doll)
Scan the buffer to see if the string already exists as a substring, if so note the location.
If it doesn't already exist, add it to the end of the buffer.
Since long words often contain shorter words, this works pretty well, but it should be possible to do significantly better. For example, if I extend the word list to include ragdoll, then my algorithm comes up with dollhouseragdoll which is less efficient than ragdollhouse.
This is a preprocessing step, so I'm not terribly worried about speed. O(n^2) is fine. On the other hand, my actual list has tens of thousands of words, so O(n!) is probably out of the question.
As a side note, this storage scheme is used for the data in the `name' table of a TrueType font, cf. http://www.microsoft.com/typography/otspec/name.htm
This is the shortest superstring problem: find the shortest string that contains a set of given strings as substrings. According to this IEEE paper (which you may not have access to unfortunately), solving this problem exactly is NP-complete. However, heuristic solutions are available.
As a first step, you should find all strings that are substrings of other strings and delete them (of course you still need to record their positions relative to the containing strings somehow). These fully-contained strings can be found efficiently using a generalised suffix tree.
Then, by repeatedly merging the two strings having longest overlap, you are guaranteed to produce a solution whose length is not worse than 4 times the minimum possible length. It should be possible to find overlap sizes quickly by using two radix trees as suggested by a comment by Zifre on Konrad Rudolph's answer. Or, you might be able to use the generalised suffix tree somehow.
I'm sorry I can't dig up a decent link for you -- there doesn't seem to be a Wikipedia page, or any publicly accessible information on this particular problem. It is briefly mentioned here, though no suggested solutions are provided.
I think you can use a Radix Tree. It costs some memory because of pointers to leafs and parents, but it is easy to match up strings (O(k) (where k is the longest string size).
My first thought here is: use a data structure to determine common prefixes and suffixes of your strings. Then sort the words under consideration of these prefixes and postfixes. This would result in your desired ragdollhouse.
Looks similar to the Knapsack problem, which is NP-complete, so there is not a "definitive" algorithm.
I did a lab back in college where we tasked with implementing a simple compression program.
What we did was sequentially apply these techniques to text:
BWT (Burrows-Wheeler transform): helps reorder letters into sequences of identical letters (hint* there are mathematical substitutions for getting the letters instead of actually doing the rotations)
MTF (Move to front transform): Rewrites the sequence of letters as a sequence of indices of a dynamic list.
Huffman encoding: A form of entropy encoding that constructs a variable-length code table in which shorter codes are given to frequently encountered symbols and longer codes are given to infrequently encountered symbols
Here, I found the assignment page.
To get back your original text, you do (1) Huffman decoding, (2) inverse MTF, and then (3) inverse BWT. There are several good resources on all of this on the Interwebs.
Refine step 3.
Look through current list and see whether any word in the list starts with a suffix of the current word. (You might want to keep the suffix longer than some length - longer than 1, for example).
If yes, then add the distinct prefix to this word as a prefix to the existing word, and adjust all existing references appropriately (slow!)
If no, add word to end of list as in current step 3.
This would give you 'ragdollhouse' as the stored data in your example. It is not clear whether it would always work optimally (if you also had 'barbiedoll' and 'dollar' in the word list, for example).
I would not reinvent this wheel yet another time. There has already gone an enormous amount of manpower into compression algorithms, why not take one of the already available ones?
Here are a few good choices:
gzip for fast compression / decompression speed
bzip2 for a bit bitter compression but much slower decompression
LZMA for very high compression ratio and fast decompression (faster than bzip2 but slower than gzip)
lzop for very fast compression / decompression
If you use Java, gzip is already integrated.
It's not clear what do you want to do.
Do you want a data structure that lets to you store in a memory-conscious manner the strings while letting operations like search possible in a reasonable amount of time?
Do you just want an array of words, compressed?
In the first case, you can go for a patricia trie or a String B-Tree.
For the second case, you can just adopt some index compression techinique, like that:
If you have something like:
aaa
aaab
aasd
abaco
abad
You can compress like that:
0aaa
3b
2sd
1baco
2ad
The number is the length of the largest common prefix with the preceding string.
You can tweak that schema, for ex. planning a "restart" of the common prefix after just K words, for a fast reconstruction
I'm working on a personal project, a file compression program, and am having trouble with my symbol dictionary. I need to store previously encountered byte strings into a structure in such a way that I can quickly check for their existence and retrieve them. I've been operating under the assumption that a hash table would be best suited for this purpose so my question will be pertaining to hash functions. However, if someone can suggest a better alternative to a hash table, I'm all ears.
All right. So the problem is that I can't come up with a good hashing key for these byte strings. Everything I think of either has a very uneven distribution, or is takes too long. Here is a list of the situation I'm working with:
All byte strings will be at least
two bytes in length.
The hash table will have a maximum size of 3839, and it is very likely it will fill.
Testing has shown that, with any given byte, the highest order bit is significantly less likely to be set, as compared to the lower seven bits.
Otherwise, bytes in the string can be any value from 0 - 255 (I'm working with raw byte-data of any format).
I'm working with the C language in a UNIX environment. I'd prefer to stick with standard libraries, but it doesn't need to be portable to other OSs. (I.E. unistd.h is fine).
Security is of NO concern.
Speed is of a HIGH concern.
The size isn't of intense concern, as it will NOT be written to file. However, considering the potential size of the byte strings being stored, memory space could become an issue during the compression.
A trie is better suited to this kind of thing because it lets you store your symbols as a tree and quickly parse it to match values (or reject them).
And as a bonus, you don't need a hash at all. You're storing/retrieving/comparing the entire sequence at once, while still only holding a minimal amount of memory.
Edit: And as an additional bonus, with only a second parse, you can look up sequences that are "close" to your current sequence, so you can get rid of a sequence and use the previous one for both of them, with some internal notation to hold the differences. That will help you compress files better because:
smaller dictionary means smaller files, you have to write the dictionary to your file
smaller number of items can free up space to hold other, more rare sequences if you add a population cap and you hit it with a large file.
I am designing a binary file format from scratch, and I would like to include some magic bytes at the beginning so that it can be identified easily. How do I go about choosing which bytes? I am not aware of any central registry of magic numbers, so is it just a matter of picking something fairly random that isn't already identified by, say, the file command on a nearby UNIX box?
Stay away from super-short magic numbers. Just because you're designing a binary format doesn't mean you can't use a text string for identifier. Follow that by an EOF char, and as an added bonus people who cat or type your binary file won't get a mangled terminal.
There is no universally correct way. Best practices can be suggested, but these often situational. For example, if you're checking the integrity of volatile memory, which has an undefined initial state when power is applied, it may be beneficial to incorporate many 0s or 1s in a sequence (i.e. FFF0 00FF F000) which can stand out against random noise.
If the file is mostly binary, a popular choice is using a text encoding like ASCII which stands out among the binary data in a hex editor. For example, GIF uses GIF89a, FLAC uses fLaC. On the other hand, a plain text identifier may be falsely detected in a random text file, so invalid/control characters might be incorporated.
In general, it does not matter that much what they are, even a bunch of NULL bytes can be used for file detection. But ideally you want the longest unique identifier you can afford, and at minimum 4 bytes long. Any identifier under 4 bytes will show up more often in random data. The longer it is, the less likely it will ever be detected as a false positive. Some known examples are as long as 40 bytes. In a way, it's like a password.
Also, it doesn't have to be at offset 0. The file signature has conventionally been at offset zero, since it made sense to store it first if it will be processed first.
That said, a single file signature should not be the only line of defense. The actual parsing process itself should be able to verify integrity and weed out invalid files even if the signature matches. This can be done with additional file signatures, using length-sensitive data, value/range checking, and especially, hash/checksum values.