# Questions tagged [data-compression]

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7answers
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### Can PRNGs be used to magically compress stuff?

This idea occurred to me as a kid learning to program and on first encountering PRNG's. I still don't know how realistic it is, but now there's stack exchange. Here's a 14 year-old's scheme for an ...
5answers
6k views

### Is there a known maximum for how much a string of 0's and 1's can be compressed?

A long time ago I read a newspaper article where a professor of some sort said that in the future we will be able to compress data to just two bits (or something like that). This is of course not ...
6answers
8k views

### Do lossless compression algorithms reduce entropy?

According to Wikipedia: Shannon's entropy measures the information contained in a message as opposed to the portion of the message that is determined (or predictable). Examples of the latter ...
5answers
7k views

### Enumerate all non-isomorphic graphs of a certain size

I'd like to enumerate all undirected graphs of size $n$, but I only need one instance of each isomorphism class. In other words, I want to enumerate all non-isomorphic (undirected) graphs on $n$ ...
6answers
19k views

### Efficient compression of simple binary data

I have a file containing ordered binary numbers from $0$ to $2^n - 1$: 0000000000 0000000001 0000000010 0000000011 0000000100 ... 1111111111 7z did not compress ...
11answers
10k views

### Is von Neumann's randomness in sin quote no longer applicable?

Some chap said the following: Anyone who attempts to generate random numbers by deterministic means is, of course, living in a state of sin. That's always taken to mean that you can't generate ...
5answers
6k views

### Data compression using prime numbers

I have recently stumbled upon the following interesting article which claims to efficiently compress random data sets by always more than 50%, regardless of the type and format of the data. Basically ...
3answers
2k views

### Approximating the Kolmogorov complexity

I've studied something about the Kolmogorov Complexity, read some articles and books from Vitanyi and Li and used the concept of Normalized Compression Distance to verify the stilometry of authors (...
1answer
999 views

### Compression of domain names

I am curious as to how one might very compactly compress the domain of an arbitrary IDN hostname (as defined by RFC5890) and suspect this could become an interesting challenge. A Unicode host or ...
7answers
9k views

### Why are these (lossless) compression methods of many similar png images ineffective?

I just came across the following thing: I put multiple identical copies of a png image into a folder and then tried to compress that folder with the following methods: ...
4answers
2k views

### Compressing two integers disregarding order

Comparing an ordered pair (x,y) to an unordered pair {x, y} (set), then information theoretically, the difference is only one bit, as whether x comes first or y requires exactly a single bit to ...
7answers
3k views

### Can random suitless $52$ playing card data be compressed to approach, match, or even beat entropy encoding storage? If so, how?

I have real data I am using for a simulated card game. I am only interested in the ranks of the cards, not the suits. However it is a standard $52$ card deck so there are only $4$ of each rank ...
4answers
6k views

### Can data be compressed to size smaller than Shannon data compression limit?

I was reading about data compression algorithms and the theoretical limit for data compression. Recently I encountered a compression method called "Combinatorial Entropy Encoding", the main idea of ...
1answer
455 views

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4answers
5k views

### Are there any compression algorithms based on PI?

What we know is that π is infinite and quite likely it contains every possible finite string of digits (disjunctive sequence). I've seen recently some prototype of πfs which assume that every file ...
2answers
2k views

### Is there a generalization of Huffman Coding to Arithmetic coding?

In trying to understand the relationships between Huffman Coding, Arithmetic Coding, and Range Coding, I began to think of the shortcomings of Huffman coding to be related to the problem of fractional ...
4answers
7k views

1answer
1k views

### How to calculate Huffman code length without generating the actual huffman code?

Given a vector of elements, how can I calculate the length of the Huffman codewords without generating the Huffman code itself? Using Matlab, I was able to compute the Huffman code and and get the ...
1answer
5k views

### Does there exist a data compression algorithm that uses a large dataset distributed with the encoder/decoder?

If my goal were to compress say 10,000 images and I could include a dictionary or some sort of common database that the compressed data for each image would reference, could I use a large dictionary ...
0answers
131 views

### What is the intuition behind the Geometric Burrows-Wheeler Transform?

What is the intuition behind the Geometric Burrows-Wheeler Transform? And how can I use a GBWT with blocking factor $d$ to match a given pattern $P$ of length $|P| = m$ with $m \ge d$ $m < d$ ...
0answers
128 views

### Evaluating sums of subsets

Let $X=\{x_1,...,x_N\}$ be a set of real numbers. We consider $M$ sums over its subsets, e.g. $N=9$, $M=3$  \begin{align*} s_1&=x_1+x_2+x_3+x_9,\\ s_2&=x_1+x_2+x_4+x_9,\\ s_3&=x_1+x_2+...
0answers
244 views

### Average redundancy in Huffman or Hu-Tucker codes on random symbol probabilities

Huffman and Hu-Tucker codes are well-known compression schemes, which both come close to the entropy lower bound. It is known that if $L_1$ and $L_2$ are the lengths of a Huffman resp. Hu-Tucker code, ...
0answers
327 views

### LZ-type compression with a limited recursion depth

I would like to begin by apologizing. I am not a computer scientist, so my use of terminology will be off. I came across an interesting problem, which I believe to be pretty hard and would love to get ...
5answers
218 views

### How can I explain lossless compression to a misguided audio engineer?

I have recently been involved in a discussion with someone who doesn't accept that lossless compression is possible, even in principle. This person considers himself to be technically literate, and an ...