# All Questions

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### Reference request: recursively enumerated subset is generated by some formal grammar

Let $\Sigma$ be a finite set. Let $\Sigma^*$ be the set of finite strings in $\Sigma$. Is there a standard reference for the following fact: is $S\subset \Sigma^*$ is a recursively enumerated subset ...
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### Is time-slot matchmaking NP-hard?

I have the following problem, which I intuitively expect to be NP-hard but cannot see how to write a reduction for: Givens: There is a fixed set of time slots, e.g. {9-10, 10-11, 11-12, 12-1, etc.}. ...
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### Is the modular exponentiation or discrete logarithm known to be hard for a class above $TC^0$?

Modular exponentiation is applicable to cryptography and discrete logarithm problem hardness is a cryptographic assumption. Is the modular exponentiation or discrete logarithm known to be hard for a ...
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### No free lunch theorem and finite hypothesis classes

I have read the no free lunch theorem(NFLT) section 5.1 of Understanding machine learning by Shai Shalev-Shwartz. There is also this Corollary 4.6 which states any finite hypothesis class is PAC ...
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### Al-Mubaid's Similarity Measure for Ontological Concepts

Al-Mubaid et al. proposed a semantic similarity measure in their research paper [1]. They see ontologies as connected graphs but refer to clusters within ontology graphs without ever defining what ...
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### Continous work distribution algorithm with failover

Imagine there's a system where there's N workers and M units of work, for example, N ≤ 64, M = 256. Is there an algorithm that ...
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### Leader election algorithm in a grid

I have to write a leader election algorithm in an unoriented mesh (a grid a*b), with many initiators. Someone give me an indication to wake up each node and then make an election in the exterior ring ...
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### AVL-tree T: can T be a chain (linear BST) according to the definition?

AVL-tree T: can T be a chain (linear BST) according to the definition ? The definition of an AVL-tree is as follows: A binary search tree (BST) is called an AVL-tree if for every internal node $v$ ...
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### Efficient algorithm to create a directed dependency graph

I am looking for an efficient algorithm to create a graph like this: Initially the graph is filled with x then hs then ...
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### Why is the zero value ignored while deriving a ranking function for query terms in Probabilistic IR?

Take for instance equation 67 and 68 from this chapter: the value of $P(q|R=1,q)$ can become zero if the term is not present in the document, and as all probabilities are multiplied, the probability ...
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### Mapping input and output sequences using neural networks in high dimensional data

I have this huge dimensional data with 31200 features and only 6000 examples. I want to learn a neural network that can find the non linear relation between the input and outputs. However, I have ...
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### Which algorithm for a project about online machine learning?

I have a basic understanding of how machine learning works, but my knowledge isn't enough in order to develop a personal project I would like to start. I want to develop a system based on online ...
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### Randomized algorithm for finding Minimum feedback vertex set

Algorithm FVS(G, k): If k < 0, return ”NOT FOUND” If G is acyclic (i.e., a forest), return  While there exists a vertex 𝑢 of degree at most 2: If deg(u) = 1, remove u If deg(u) = 2, i.e. u's ...
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### does within the “range a and b” include a and b?

I have not found the answer to this doubt of mine elsewhere, hence posting it here. It may be a silly question but I just want to be sure :P would be great if someone could help me out with this ...
199 views

### Distinguish Graph from Tree using Adjacency Matrix

Given an adjacency matrix, is there a way to determine if the graph will be a tree or a graph (whether or not there is a cycle). For example, given the adjacency matrix: ...
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### Proving NP-complete problem

Suppose the following problem: Given an undirected graph G=(V,E), is it possible to choose a subset V' of vertex set V, such that deleting it removes all triangles (cycles of length 3), where |V'| is ...
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### Subset-Sum modulo small primes

I was thinking about the strategy of solving Subset-Sum (with a set of size n and integers having n bits each) by using Dynamic Programming (described here: http://en.wikipedia.org/wiki/...
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### Find sentences with similar relative meaning from a list of sentences against an example one

I want to be able to find sentences with the same meaning. I have a query sentence, and a long list of millions of other sentences. Sentences are words, or a special type of word called a symbol which ...
605 views

### Proving NP-hardness of scheduling problem (total weighted completion time)

Consider the problem $P \mid \mid \sum w_j C_j$. I want to prove that this problem is (strongly) NP-hard by reducing from $3$-Partition, but I am not really sure how to do this. Just to be precise, ...
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### Help find algorithm for array-based task

Given array if numbers a[1..n]. Pair of numbers (i, j) is interesting, if i < j и a[i] > 2a[j]. How to count number of interesting pairs in O(nlogn)? What is the solution? My solution is not ...
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### Polynomial-time reducibility of Primality and 3-SAT

Is 3-SAT $\leq_{p}$ Primality? And/or is Primality $\leq_{p}$ 3-SAT? I think the answer is no and yes, respectively, but I'm not sure. Any help would be appreciated. Thank you.