# Questions tagged [data-compression]

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### Can more compression be achieved when data is sorted (in ascending or descending order)?

Let's say I have a file which is exactly 1 MB in size. Contents of file are : 0001001000... upto 128 bytes (128 bytes per line in file). If I sort it in ascending or descending order (using notepad+...
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### Compress set of mostly known bitstrings

Let's say there is a sender sending messages with commands to a recipient. The sender knows a set of commands but doesn't know anything about the recipient. A command is simply an opaque uniform ...
52 views

### What is the entropy of an unordered list?

I'm trying to compress unordered lists of a few thousand integers for transmission over HTTP, and Claude Shannon is disappointing me with his mathematical ambiguity :) Each integer is 6-digits, so ...
55 views

### Why XML dumps from Wikipedia are so compressed?

Few years ago I downloaded an XML dump of one of Wikipedia's fandom sites. It was the XML datadump of Marvel Fandom. The XML was zipped , size was 900 MB (approx). But when I unzipped it , it was ...
56 views

### Is every binary sequence the output of some meaningful-text-input algorithm?

Here is the problem: Let's say we have a random binary sequence, just an arbitrary sequence of zeroes and ones (of some arbitrary length of digits). Can we find an algorithm that would decode/...
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### Asymptotically Optimal Universal Code In Other Bases

Universal codes are fairly well studied, and many asymptotically optimal universal codes exist for binary data (see https://en.wikipedia.org/wiki/Universal_code_(data_compression) especially https://...
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### Is this a general compression algorithm?

I'm aware that an algorithm that compresses every input doesn't exist (by the pigeonhole principle), however I tend to think about the problem sometimes and I came up with a (flawed, but why?) idea: ...
40 views

### Compression algorithm using key value mapping

Would it be possible to do better than standard compression if you fed a bunch of zipped files through a machine learning algorithm that kept track of the most common bit sequences and produced a ...
58 views

### How to find the compression method used on an unknown sequence of bytes? [closed]

I have a sequence of bytes: https://drive.google.com/file/d/17sfchPgsySi2ilIxLuBb1q-UUqq5lO87 What the data is, is unknown (see NOTE below). I'm pretty sure this data is compressed in some way, due to ...
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### Is defragmentation a kind of minification, a kind of compression or perhaps both?

As far as I understand defragmentation: Removes spaces between objects by putting objects nearer one to the other reorganizes objects for better performance The first action feels to me as some kind ...
41 views

### How does data compression relate to the ordinary meaning of “compression”?

When I think about "compressing" outside computers I can think about a compressed car which has become a metal rectangle. It doesn't have less redundancy because it has everything it had ...
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### Online algorithm for compressing multiple SETS?

Algorithms like LZW and others compress data sequences. What I'm looking is an algorithm that compress multiple Sets. if possible online algorithm. For example : ...
871 views

### Why does the Huffman coding algorithm produce a valid tree?

I am not asking about the Huffman Code, but the most widely described algorithm for generating one, also described on the english wikipedia: https://en.wikipedia.org/wiki/Huffman_coding#Compression ...
45 views

### File compression using prime numbers

My theory take a file examplesize:(3GB) convert said file to a number divide that number by a large prime number example:(2^82,589,932 · (2^82,589,933-1))[2018 Dec 07] get the quotient and the ...
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### How Data Compression relates to Estimating Distribution?

I recently read this paper Mahoney, 1999. And encountered this line, optimal compression of a probabilistic language L with unknown distribution (such as English) using an estimated distribution M (...
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### Compressing a bit string when I know how many 1s and 0s there are

Say I have a 256 bit bit-string, and I know that there are 16 ones and 240 zeros. I know that this bit string can be compressed, because there are only 256 choose 16...
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### LZW with dictionary clearing

How does LZW decompress data with dictionary clearing/flushing? I understand that a space is reserved in the dictionary that represents a clear code (usually 256), but how is this code actually used ...
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### Can you give me insight into the time and space complexity of those pairing functions?

I am looking for a pairing function with linear time complexity. I found one in Steven Pigeon's thesis (p 115, §5.3.6.3) described in English on MathOverflow that works by bit interleaving. another ...
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### What is the simplest algorithm to compress a string?

I need to compress a string in my application but I am very limited in the operations I can perform. In particular, I cannot store data in any file and I cannot query any database. Also, I cannot call ...
18 views

### Efficiently compressing and decompressing an array of combinations

I'm wondering if there exists a way to efficiently compress an array containing combinations ${n}\choose{k}$, so that it can be easily decompressed minimizing the data read from that array. An example ...
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### Prime factorization for compressing streams of random numbers

We covered compression/encoding/decoding of data streams very briefly last lecture and I had an odd idea: Let's say I have a stream of random 8-Bit numbers. Now the probabilty to encounter each number ...
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### How many strings of length |w| are unrelated?

For sufficiently large |w|, how many of the 2^|w| strings of length |w| are entirely unrelated? A way to define this: two strings are unrelated if their joint Kolomogorov complexity is practically ...
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### Can you build a solver from a verifier?

Given code to just an NP-verifier, where the certificate/witness is required to be of size polynomial in the instance, for a language L, can you, from that data alone, construct code for a solver, or ...
45 views

### How do I compress data vectors in broadcast messages?

Let us model a wireless broadcast network as an undirected graph $G(V,E)$ where there is an edge between every pair of nodes ${i,j}\in V$ if they are in transmission range of each other. $w_{i\to j}$ ...
29 views

### Compression algorithm for statistical data with a desired outcome size

I did some basic research on regular lossy and lossless compression algorithms but somehow I couldn't really figure the right direction for the information I need. My basic problem is that I would ...
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### Arithmetic Encoding vs Adaptive Arithmetic Encoding

I am working on a personal project and I am having some conceptual level questions on arithmetic encoding. Let's take a scenario where I have an array of sensors and the data collected is transmitted ...
83 views

### Is Prediction the same as Compression?

Just came across this transcript that states: The principle is that prediction is the same thing as compression. And what that means is that whenever you have a prediction algorithm, you can also get ...
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### Is arithmetic coding slightly more efficient than rANS?

I'm extending a framework for lossy compression of multidimensional floating-point data. At some point in the pipeline, sequences of symbols from a non-uniform distribution are losslessly compressed ...
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### Clustering data for compression with PCA

If I have datapoints in a high dimensional space and want to find a (linear) subspace onto which a data-set projects well, I can use PCA and then discard less important dimensions of the new basis to ...
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### How can 4 GB of data can expand into 40 GB of data, when I install Windows on a Computer

Say I start with an iso with about 4GB of data and use this, to install windows on a computer. After installation, the operating system will take up about 40GB of disk space. Where does all this &...
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### Mathematical limits on lossless data compression

Let's say Bob wants to send a particular binary sequence to Alice. Imagine that Bob and Alice both have powerful machines but slow Internet connections. Bob could just send the sequence directly but ...
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### Design of a synchronized clock

I was living in a country where Internet wasn't that fast so the younger me had the following idea for compressing data Let say 2 parties want to send data to each other, we know that data can be ...
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### Can a 600 MB text file with digits of the square root of 2 be compressed to 600 KB?

I have a simple script to calculate gaps in a sequence of digits of the square root of 2 (or any other multi-precision constant). As input, I generated files with the bigfloat module in Python: ...
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I'm confused about the point of adaptive arithmetic coding. I understand that static arithmetic coding involves using preset probabilities of symbols that remain static during the whole process. I ...
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### Significance of model in arithmetic coding

I am trying to understand the concept of arithmetic coding, i understand how the range is subdivided after each character is read from the string. But i am unable to understand why using a more ...
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### How does value decompression work for Facebook's Gorilla in the case where count of leading zeroes is not stored

I am referring to this paper: http://www.vldb.org/pvldb/vol8/p1816-teller.pdf My question is regarding section 4.1.2 where it says: When XOR is non-zero, calculate the number of leading and ...
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### Source code or detailed explanation of "WKS" virtual memory compression algorithm?

I've been trying to find information on various program data virtual memory compression algorithms that are in the "WK" family of algorithms. So far, I've been successful with the "WKdm" compression ...
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### Is the source file size smaller than the executable file size?

Wondering if compilation increases file size in general, is the source file size smaller than the executable file size?
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### How would I make sure my compressed string has the smallest length possible?

I'm trying to make a function that takes a string and compresses the repeating blocks. The code I'm using is implemented in such a way that a single character like 'a' would be converted to '1(a)' ...
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### Data compression - Entropy

Let's say I have an alphabet $$\Sigma = \{A, B, C, D, E\}$$ with probabilities $$P(A) = P(B) = P(C) = 0.25 \text{ and } P(D)=P(E) = 0.125.$$ I know that the entropy then is: H(\Sigma) = 3 \cdot 0....
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### on-the-fly decompress a flat-file database

I'm facing the following problem. I have a flat-file database (e.g. CSV). Since it's relatively large to store in memory, I'd like to compress it. Given a key, I need to return the uncompressed text (...
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### Alternatives to multiplication/division/modulo for encoding choices?

The obvious way to encode, with minimum entropy, choosing s out of n (equiprobable) choices when x is already encoded is to identify s with a number [0, n) and set x = n * x + s, decoded with s = x % ...
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### Applying SVD compression to integral point images

Suppose that we have an $m\times n$ matrix $A$ of rank $n$, whose entries are 8-bit unsigned integers obtained from a grayscale image. Now we want to apply SVD to $A$ and to use the first $k$ singular ...
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### Space-efficient data structure for analytical querying of multiple branching evolutions of a dataset

Problem Description I have a data state space: a set of data sets, each of which can be modelled as a collection of arbitrary key-value pairs. These data sets are each a branch of evolution of a ...
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### Data Compression :Compress a Compressed File

Suppose we have file A that has been compressed by the the method B and the output-file is C, now if I am not wrong We can not compress C more by method B, but there might another method=algorithm D ...