Questions tagged [data-compression]

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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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87 views

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 ...
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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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1answer
31 views

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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22 views

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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1answer
57 views

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 ...
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40 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. $w_{i\to j}$ ...
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2answers
26 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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1answer
37 views

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 ...
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2answers
67 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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1answer
56 views

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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37 views

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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3answers
118 views

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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1answer
38 views

Adaptive arithmetic coding confusion

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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1answer
25 views

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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How do you work out the Huffman code for an extension?

I have worked out the following: v = 1101 0010 1101 0101 0100 1000 P(0) = 0.54 P(1) = 0.46 A = {0,1} I have also worked out question (c) to be: H(A^2) = 1.991 and H(A^3) = 2.9859 I am having ...
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176 views

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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1answer
41 views

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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1answer
30 views

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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1answer
43 views

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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1answer
94 views

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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1answer
33 views

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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2answers
68 views

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 ...
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1answer
61 views

How a Data Compression Software Reads a File as pure Binary File and makes Output?

I have an hybrid compression technique I want to implement, my implementation is (so far): I can encode a string into a encoded compressed string. These are binary strings. For example, I read texts ...
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1answer
26 views

Find an infinite set of strings that are compressable better than in $O(\log n)$ space

The task is to find an infinite set of strings $a_1,a_2\ldots$, where $|a_{i+1}|>|a_i|$ and to find a compression algorithm $f$ for these strings, such that $|f(a_i)|=o(\log_2 |a_i|)$ with $i\to\...
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Is arithmetic coding restricted to powers of $2$ in denominator equivalent to Huffman coding?

With restriction to $\frac{k}{2^n}$ as line segment ends, does arithmetic coding degrade to Huffman coding? As far as I can tell, each symbol will be encoded with an integer amount of bits, which is ...
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365 views

Advantages/Disadvantages of adaptive contexual arithmetic coding

What are the advantages and drawbacks of considering ever longer block lengths or context lengths, if one was to work with estimated probabilities(measuring on the fly: aka "adaptive") rather than ...
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1answer
76 views

How many “compressible” strings are there?

Let's say that a string of length $N$ is "compressible" iff its Kolmogorov complexity is less than $N$. To keep it simple, we can assume binary strings for this. It is easy to see that almost all ...
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How can i compare lossy image compression techniques?

I need to find which lossy image compression technique is the best. I chose to test JPEG, WebP and BPG. Which criteria can I choose for comparison apart from quality and speed of compression and how ...
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3answers
120 views

Is it possible to have high compression but low predictability?

Can you have a process that generates a binary sequence with high compression rate (low entropy) but impossible to predict next symbol? 'impossible to predict' - sequence cannot be predicted ...
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1answer
29 views

Proof high-entropy sequences are hard to compress

When comparing random-variable sequences generated from probability distributions, what's a formal proof that a distribution with higher entropy produces a sequence that's "harder" to compress? In ...
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1answer
55 views

Is a complete code always optimal?

According to wikipedia, Kraft's inequality holds with equality when a code is complete. Huffman encoding produces a complete code that is optimal. Are all complete codes optimal and vice versa?
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Can data be compressed through this hash function technique?

I'd like to know if this data compression scheme would work or not, and why: Suppose we have a file. If we treat the bits that make up the file as the binary representation of a number n, we have n (...
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60 views

Modifying the JPEG compression to use custom block patterns

recently, while watching a video about machine learning, I had an idea about creating an image compression algorithm, that works similar to JPEG, but is based on arbitrary bitmaps as blocks. I should ...
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Implementing binary arithmetic encoder

I have set integers that are normally distributed, and I'm trying to implement binary arithmetic encoding, as suggested in this post: Compressing normally distributed data I'm running into trouble ...
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1answer
53 views

How to find optimal token set for compression?

By token I mean the smallest element of source data, that the compression algorithm works on. It may be a bit (like in DMC), a letter (like in Huffman or PPM), a word, or variable-length string (like ...
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52 views

is there a (FLAC like) loseless compression coding format for EEG data? [closed]

EEG and Audio data are very similar, both are numerical samples in continuous sequence have a sample rate need and can have multiple channels channels for multi-channel audio channels for each ...
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1answer
135 views

Run Length Encoding Compression With Nested Level

I am studying about some compression methods, and I'm very interested in RLE Algorithms. But are there any Nested-Level RLE methods, such as: ABABABCABABABC --> 3(AB)C3AB(C) --> 2(3(AB)C) ? It's ...
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Is entropy a good indicator of the quality of a lossy compression?

Say I want to quantitively evaluate the effectiveness of several color-to-grayscale conversion algorithms, which can be considered as lossy compression. Would entropy be a good indicator? To ...
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1answer
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Question is about a paper “A Block-sorting Lossless Data Compression Algorithm” by M. Burrows and D.J. Wheeler

In the paper A Block-sorting Lossless Data Compression Algorithm by M. Burrows and D.J. Wheeler Link. On page number 5. please describe this line If the original string $S$ is of the form $Z^p$ for ...
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An interesting compression algorithm idea

I stumbled on this paper about compressing images using a kind of odd, but interesting idea. It seems pretty easy to implement and I was wondering if there is something wrong with it that I haven't ...
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1answer
50 views

Coding for data compression with large target's symbol set (where the target symbol set is larger than the source symbol set)

For data compression, every codding that I've seen is binary. It means we convert a language with $N$ symbol size to a language with $M=2$ symbol size. For example, in Huffman coding, the goal is to ...
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734 views

How does a predictive coding aid in lossless compression?

I'm working on this lab where we need to apply a lossless predictive coding to an image before compressing it (with Huffman, or some other lossless compression algorithm). From the example seen ...
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1answer
62 views

Is it possible to achieve greater than perfect compression using machine learning and big data?

Imagine Google wanted to make their chrome browser faster. Let "database" be all the machines which serve content from Google's servers, including Search and Google cloud services. Google begins using ...

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