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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 bit-packing. That is, suppose you have 240…
Realz Slaw
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NP-hardness of covering with rectangular pieces (Google Hash Code 2015 Test Round)

The Google Hash Code 2015 Test Round (problem statement) asked about the following problem: input: a grid $M$ with some marked squares, a threshold $T \in \mathbb{N}$, a maximal area $A \in \mathbb{N}$ output: the largest possible total area of a…
a3nm
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Is page size always equal to frame size?

I'm learning about paging. My book says that the logical addresses generated by the CPU are in the form |p|d|(page number, page offset) and the physical addresses are in the form |f|d|(frame number, frame offset). It is also specifically mentioned…
Fuel
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Prove that the complement of $\{0^n1^n \mid n \geq{} 0\}$ is not regular using closure properties

I want to prove that the complement of $\{0^n1^n \mid n \geq{} 0\}$ is not regular using closure properties. I understand pumping lemma can be used to prove that $\{0^n1^n \mid n \geq{} 0\}$ is not a regular language. I also understand regular…
anthony34234
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Minimal Spanning Tree With Double Weight Parameters

Consider a graph $G(V,E)$. Each edge $e$ has two weights $A_e$ and $B_e$. Find a spanning tree that minimizes the product $\left(\sum_{e \in T}{A_e}\right)\left(\sum_{e \in T}{B_e}\right)$. The algorithm should run in polynomial time with respect to…
Strin
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What is the relationship between problems and languages?

I want to ask exactly what is the relationship between problems and languages. We know that the set of all languages uncountable. Is the set of problems also uncountable? Can every problem be defined by a language? Can a language solve more than…
Ravi Singh
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How do you determine the number of errors in the Welch-Berlekamp algorithm?

In the Welch-Berlekamp algorithm for decoding Reed-Solomon codes, one is given a list of points $(a_i, b_i)$ representing a message with $e$ errors on the $b_i$ in unknown locations (and $e$ is given to the algorithm). The output is a polynomial…
JeremyKun
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Data General MV/8000 virtues of "No mode bit"

I'm reading Tracy Kidder's "The Soul of a New Machine" where a team at Data General design a new machine (codenamed "Eagle", later named MV/8000). It is 32-bit extension of a previous architecture (the 16-bit Eclipse). One of the revolving themes…
Morty
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Good mathematical book on algorithms

I’m a sucker for mathematical elegance and rigour, and now am looking for such literature on algorithms and algorithm analysis. Now, it doesn’t matter much to me what algorithms are covered, but very much how they are presented and treated.¹ I most…
k.stm
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Edit distance of list with unique elements

Levenshtein-Distance edit distance between lists is a well studied problem. But I can't find much on possible improvements if it is known that no element does occurs more than once in each list. Let's also assume that the elements are…
user362178
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Good snapshottable data structure for an in-memory index

I'm designing an in-memory object database for a very specific use case. It is single writer, but must support efficient concurrent reads. Reads must be isolated. There is no query language, the database only supports: get object/-s by…
dm3
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How much bigger can an LR(1) automaton for a language be than the corresponding LR(0) automaton?

In an LR(0) parser, each state consists of a collection of LR(0) items, which are productions annotated with a position. In an LR(1) parser, each state consists of a collection of LR(1) items, which are productions annotated with a position and a…
templatetypedef
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Are there any known AM-complete problems/is AM-complete well defined?

I'm curious about whether there are any complete problems in the Arthur-Merlin complexity class. Graph Non-Isomorphism (GNI) seems to be the canonical example of a problem in AM, but it's probably not a complete one. I suppose I'm also wondering if…
Linear
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Why in a min priority queue (heap based) it is called "decrease-key" and not just "set-key"?

When you call decrease-key in a min priority queue, you are basically setting the key, you can accidentally put a higher key, right? so why isn't it called "set-key" or "update-key"? why (according to Wikipedia and other sources) a min priority…
Eran Medan
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Undecidable problems limit physical theories

Does the existence of undecidable problems immediately imply the non-predictability of physical systems? Let us consider the halting problem, first we construct a physical UTM, say using the usual circuit based construction. Then there can be no…
user2663116
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