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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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1answer
23 views

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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0answers
65 views

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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0answers
12 views

Adjusting the loss function for Support Vector Machines for SVC in sklearn

I have the following problem. The minimization problem of the SVM that I want to solve is: $$ \min_{w, b} \frac{1}{2}w^{T}w + \sum^{m}_{i=1}C_{i}xi_{i} $$ Subject to: $$ y_{i}(w^{T}x_{i} - b) \geq 1 - ...
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1answer
92 views

How much type information do Hindley-Milner proof assistants need to remain sound?

A known benefit of the HM type system is that you can usually infer a term's most general type with no user-provided type annotations. For example, if my theory contains the standard axiom: $$\forall ...
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1answer
63 views

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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1answer
81 views

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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1answer
101 views

Required sample size to hit certain subset of a ground set

Suppose $X$ is a set of $n$ points in $\mathbb{R}^d$ and $N_1,\cdots,N_k$ are k disjoint (unknown)subsets of $X$. There is a probability distribution $\phi$ on $X$ defined as $\phi(p) = \frac{\lvert\...
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1answer
73 views

How to know if a problem is distributable?

I am new to the world of Parallel computing and that is why don't know exactly where I should look at or search to get the answer. Is there any theorem or just general theory determining which code ...
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1answer
29 views

Algorithm in logarithmic time that finds a number with the help of a subarray that is not in the array

The question is as follows. Given: A sorted array A of n integers where A[n − 1] − A[0] ≥ n. Asked: Give an algorithm and the invariant of the algorithm that finds a number between A[0] and A[n - 1] ...
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1answer
58 views

semantics of “destroy object” in HRU model

In the access control model HRU there is the primitive request destroy object o which is only defined if o is an object in the current protection state which is not a subject. I am interested in why ...
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1answer
160 views

Will a non-linear lower bound on some NP complete problem prove non-linear lower bound on 3SAT?

A problem $\Pi$ is $\mathsf{NP}$ complete if there is a polynomial time reduction from an $\mathsf{NP}$ complete problem $\Pi^\circ$ to $\Pi$ with polynomial blow up on number of variables and ...
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1answer
78 views

Find non-intersecting submatrices

I have a rectangular boolean matrix and I'd like to have an efficient algorithm to find non-intersecting submatrices. I'll to demonstrate that in the example below. The ideal case is when all ...
-1
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1answer
34 views

M/G/$\infty$ queue with mixture of deterministic service times

Hey guys I am studying queueing theory and I am trying to understand this problem. Consider an $M/GI/ \infty $ queue with the following service time distribution: the service time is $1/\mu_i$ with ...
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1answer
120 views

Combinatorial algorithm for load balancing

I have a problem that can be solved with linear programming, but I'm hoping there's a combinatorial algorithm for this (even approximation is fine). This is basically a load balancing problem using ...
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1answer
149 views

NP Hardness of Metric Steiner Tree

It is known that the metric steiner tree problem is NP hard (Garry and Johnson [1977]). I wanted to know if there is a simpler way of proving the same. Specifically, I am trying to find a polynomial ...
-1
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1answer
164 views

Representation suitable for reconstruction of a tree with bounded degree

I am dealing with reconstruction of molecular graphs for which unlabelled rooted trees with maximum degree 4 are fair approximations. In particular, I would like to encode a small tree (assume number ...
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1answer
2k views

Time complexity analysis of random forest and k-means?

I am working with random forest for a supervised classification problem, and I am using the k-means clustering algorithm to split the data at each node, where $n$ is the number of points, $K$ is ...
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1answer
181 views

Clustering without specifying the number of clusters apriori

Does anyone know of an algorithm that can perform the following tasks: Unsupervised clustering without specifying the number of clusters apriori. For example if all the buildings in wide geographical ...
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1answer
423 views

Canopy clustering: what should we do with samples in overlapping canopies?

In canopy clustering http://www.kamalnigam.com/papers/canopy-kdd00.pdf, if a sample falls in an overlap of 2 canopies, how do we choose its cluster?
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0answers
46 views

3-hitting set iterative compression

I have a question which i tried to solve without success. I need to prove that if 3-Hitting Set can be solved in time $2^kn^{O(1)}$,then 4-Hitting Set can be solved in time $3^kn^{O(1)}$. There is a ...
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1answer
54 views

Finding a greedy ordering criteria

I've been thinking through a problem, and I won't go into all the details here but I'm stumped on a particular subproblem: Consider this following definition of a task: $T_k = (a_k, b_k)$. $a_k$ is ...
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votes
1answer
77 views

Forming ordered pairs using monads and doing without the Kuratowski encoding of ordered pairs

Suppose we have a set $S$ of constants of the Simply-Typed Lambda Calculus (STLC) various types, and the operation of union $\cup$ which takes two constants and forms their union. For example, $S$ ...
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1answer
159 views

Complexity class on quantum computation and classic ones

Does the complexity speedup in superpolynomial by quantum computation mean it is possible to find new algorithm on classic Turing Machine which can speedup in classic Turing Machine in ...
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1answer
67 views

Assign each biclique to a distinct left

Given a minimum biclique edge cover, is it always possible to assign each biclique to a distinct left node (which it contains)? ie one such assignment for this graph (from wikipedia): http://upload....
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1answer
196 views

What are some natural problems that we can quickly find a solution to using massive parallelism but not a canonical solution?

For many problems, more than one output is acceptable. For instance, the problem of finding an assignment that satisfies a boolean formula. If randomness buys us something then it could be that it ...
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1answer
254 views

Problem in embedding

I want to embed PPTL(a kind of logic) in Coq. Because of its complex semantics, I just embed its systax. ...
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1answer
133 views

How to check if an algorithm in a distributed system worked within restraints?

I want to design a system in which a program is sent along with data and then it answers with the result. Is redundancy a must in this situation to check for correctness of the processed data? What is ...
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votes
1answer
283 views

Find all items which are subsets of an item

I have a problem that I think should have been studied. I am looking for algorithms for it. Each item is a set of key-value pairs. Let $x$ be an item and $F$ be a set of items. Each key and each ...
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0answers
68 views

Important derandomization in smallest $NC$

Are there problems in $RNC^1$, $coRNC^1$ and $ZPNC^1$ which are not known to be in $NC^1$?
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0answers
31 views

What kind of procedure is used to calculate the thread

my question would be how can I see which method is used to distribute the computing time to the following threads. ...
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1answer
176 views

Can we map this problem to subset-sum?

Let there be $n$ set of ordered pairs $s_1=\{(c_1,f_1),(c_1,f_2) ...(c_1,f_m)\}$, $s_2=\{(c_2,f_1),(c_2,f_2) ...(c_2,f_m)\}$, $s_3=\{(c_3,f_1),(c_3,f_2) ...(c_3,f_m)\}$, .... $s_n=\{(c_n,f_1)(c_n,f_2) ...
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1answer
155 views

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 ...
-3
votes
1answer
292 views

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 ...
-3
votes
1answer
224 views

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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votes
1answer
7k views

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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votes
1answer
71 views

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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1answer
553 views

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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1answer
225 views

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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0answers
26 views

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 ...
-4
votes
1answer
35 views

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 ...
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votes
1answer
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: ...
-4
votes
1answer
63 views

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 ...
-4
votes
1answer
1k views

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/...
-4
votes
1answer
2k views

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 ...
-4
votes
1answer
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, ...
-5
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1answer
23 views

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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votes
1answer
26 views

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.
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1answer
241 views

Some questions (still) unresolved about braids?

I was looking for interesting questions pertaining to braid theory. I don't know if the following are considered important, but I'd like to ask: (1) in relation with the following link, is it true ...
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votes
1answer
332 views

Attacking TSP via small nonintersecting circuits

Consider the problem of finding smaller "non-intersecting" circuits or paths in graphs embedded in the euclidean plane (visiting all vertices) in the sense of geometric intersections of edges plotted ...

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