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Theoretical questions in Parallel Computing

5
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1answer
145 views

Confusion about a formal definition of PRAM consistency

I am reading the paper "Consistency in Non-Transactional Distributed Storage Systems" by Paolo Viotti and Marko Vukolić. The authors provide a comprehensive survey of various consistency semantics ...
2
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0answers
107 views

BQNC and Abelian Hidden Subgroup Problem

We know integer factorization is in $BPP^{BQNC}$ from Cleve and Watrous. Is Abelian Hidden Subgroup Problem also in $BPP^{BQNC}$? If not what is it that makes integer factorization special? In ...
2
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0answers
174 views

Primality in $NC$ hierarchy?

AKS primality testing solves whether a given integer is prime in $P$. AKS algorithm is following: Input: integer n > 1. Check if $n$ is a perfect power: if $n = a^b$ for integers $a > 1$ and $b &...
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0answers
81 views

Fixed dimension Integer programming minus LLL in fixed parameter $NC$?

If you remove LLL part then is remaining part of a. Lenstra algorithm b. Barvinok algorithm in $O(f(n)(\log(mL))^c)$ time on $O(g(n)(mL)^c)$ processors with fixed $c>0$ in fixed $n$...
9
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0answers
93 views

Problems in $\mathsf{NC^{2}}$ that are not known to be in $\mathsf{AC^{1}}$ or $\mathsf{DET}$

Do we know of any problems in $\mathsf{NC^{2}}$ that are not known to be in $\mathsf{AC^{1}}$ or $\mathsf{DET}$? Context: based on Josh's answer to this question, it could be possible that all ...
6
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1answer
177 views

Cases of Linear programming known to be in $NC$?

Linear programming is $P$-complete. However are there special situations where we know an $NC$ algorithm?
8
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1answer
171 views

Rank-robustness of the parallel complexity of linear algebra problems

It is known that most computational problems related to linear algebra can be computed in $NC^2$ - i.e. for an $n\times n$ matrix $A$, over the reals or a finite field, we can compute the rank of $A$, ...
2
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0answers
82 views

On analogies between parallel complexity and polynomial time hierarchy structure?

Is it known $\mathsf{RNC=NC\iff P=RP}$ or $\mathsf{BPNC=NC\iff P=BPP}$? Are there any analogies (such as collapse results, problems which suggest analogies such as gcd(in NC) and factoring (in P), ...
9
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1answer
286 views

Problems in NC not known to lie in NC2

Are there interesting problems that are in $\mathsf{NC}$ but not known to be in $\mathsf{NC^{2}}$? In the paper 'A Taxonomy of Problems With Fast Parallel Algorithms', Cook mentions that MIS was known ...
3
votes
1answer
145 views

Does such model exists?

I have a problem on distributed graph, with the following model: 1. There is a Global Graph $G=(V,E)$ 2. There are $k$ computers. 3. Each computer $1 \leq i \leq k$ knows ALL the nodes of the graph,...
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222 views

Modern distributed computing book

Lynch's Distributed Algorithms book is a classic but it is from 1996 and rather out of date. Are there any recent distributed computing books that can be used as textbooks for a graduate distributed ...
11
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1answer
230 views

To what extent, computational ability for hard tasks helps in solving easy tasks

In short, the question is: to what extent, computational ability for hard tasks really helps you in solving easy tasks. (There could be various ways to make this question interesting and non-trivial, ...
1
vote
1answer
88 views

Is multiprocessing possible on a Turing Machine? [closed]

I recently created a parallel implementation of the Merge Sort, in which the sorting of several groups was accomplished by different processes, and was wondering if this was theoretically possible on ...
-2
votes
1answer
190 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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0answers
52 views

NC algorithm for rank of skinny matrix

Suppose I want to find the rank of an $m \times n$ matrix $A$ over $GF(2)$, where $m \ll n$. The algorithms for rank in the literature seem to be focused on the case when $m = n$, giving a time ...
3
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0answers
43 views

Limits of parallel computing with local connections?

There are successes with an increasing numbers of individual computational units in GPUs or as processor cores. Given someone made the effort to build a huge array of processors which - however - can ...
3
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0answers
131 views

Algorithm (parallel and serial) for Gram-Schmidt

Suppose we are given $m$ vectors $v_1, \dots, v_m$ in $n$-dimensional space $\mathbf R^n$ (or perhaps they are specified up to $b$ bits of precision). I would like to find an orthonormal basis for the ...
2
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0answers
45 views

Lower bounds in PRAM model for evaluation of straight-line code

Miller, Ramachandran and Kaltofen showed that any straight line program can be executed in parallel time O(log n) using M(n) processors where M(n) is the number of processors for multiplying nxn ...
5
votes
2answers
178 views

Is there a mathematical analysis/proof available for correctness of solutions to inter process communication problems?

I've been going over some material related to IPC recently from Tanenbaum's "Modern Operating Systems" and revisited semaphore after many years. There is a lot of code and pseudo code based ...
5
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0answers
139 views

Evidence of non P-hard problems that require polynomial space?

It is admitted that a $\mathsf{P}$-complete problem requires polynomial space and thus cannot be efficiently parallelized. One purpose of these problems is that they can be used to 'defeat' an (...
3
votes
1answer
251 views

Parallel (NC) replacements for Gaussian elimination?

Suppose one has an matrix $A$ with $c$ columns and $r$ rows with entries in the binary field $GF(2)$. One wants to determine its rank, and a basis for its null-space. These can be computed easily ...
2
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0answers
90 views

Are the sets of executions of data-race free programs equal, when run on causal memory and on sequentially consistent memory respectively?

In the paper "Causal Memory: Definitions, Implementations, and Programming (Distributed Computing [DC] 1995)", the authors present a formal definition of causal memory, an abstraction of distributed ...
3
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0answers
46 views

Best complexity bound for parallel matrix-vector product?

I'm looking for the best known complexity (and a bound for the number of processors invoved) to do the calculation of a $(n,n)$ matrix-vector product. Thank you
3
votes
1answer
141 views

paradox-driven computers?

Has any research been done on paradox-driven computers? An example of what I mean by "paradox-driven": Given a computer which can send information back through time, an algorithm to instantly break ...
4
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0answers
164 views

Randomized Parallel Algorithm for Maximal Independent Set

There are a couple of randomized parallel algorithms for the maximal independent set problem, e.g. A Simple Parallel Algorithm for the Maximal Independent Set Problem, A fast and simple randomized ...
0
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1answer
1k views

Differences between Quantum Computing and Parallelism [closed]

What are the differences between Quantum Computing and Parallelism? thanks in advance
3
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0answers
1k views

DAG partitioning for parallel computing

Consider a set of processes ($P=\{p_1, p_2,\dots, p_n \}$) and their data dependencies. Each process $p_i$ has an execution runtime which is denoted by $d_i$. We are interested to parallelize these ...
2
votes
2answers
110 views

Multiple independent random number streams

Having multiple streams of pseudo-random numbers known to be independent and with a uniform distribution I want to do Monte Carlo simulations in parallel. In other words, one thread will have a full-...
1
vote
1answer
120 views

Calculation of Recursive Spawning

I'm reading the book Introduction to Algorithms (Cormel et al., 2009) on the chapter about multithreaded algorithms, and I'm confused about the following: We must also account for the overhead of ...
1
vote
2answers
469 views

Task Multithreading analysis for a Divide and Conquer algorithm

Suppose an algorithm that receive an input array of $n$ elements and it performs a task over each element. All tasks are independent and take $O(k)$ each (being $k$ a variable). Since all tasks are ...
1
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1answer
136 views

Should the Schedule of ``High-level Operations'' Respect the Linearizability of ``Low-level Operations'' in Proof of Simulation Algorithm?

Backgroud I am reading Chapter 10 ``Fault-Tolerant Simulations of Read/Write Objects'' of the Book Distributed Computing (by Hagit Attiya & Jennifer Welch). Specifically, in section 10.2.3, it ...
0
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0answers
126 views

Multiple k-selection using GPU

What I am trying to achieve is multiple k-selections (different but small datasets) running in parallel on a GPU. Basically, my aim is to select kth smallest element from an array of floats such that ...
13
votes
1answer
661 views

Is there a quantum NC algorithm for computing GCD?

From the comments on one of my questions on MathOverflow I get the feeling that the question regarding GCD being in $\mathsf{NC}$ vs. $\mathsf{P}$ is akin to the question regarding Integer ...
17
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2answers
714 views

Status on circuit lower bounds for polylog-bounded depth circuits

Bounded depth circuit complexity is one of the main areas of research within circuit complexity theory. This topic has origins in results like "the parity function is not in $AC^{0}$" and "the mod $p$ ...
1
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2answers
178 views

Classic parallel clustering algorithms

I'm starting a research about parallel clustering. I see a ton of articles on this topic, so that I don't know where to start. I'd like to get familiar with classic methods of parallelizing clustering....
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0answers
205 views

Big-Theta extension of Brent's Theorem?

Is there an extension or translation of Brent's theorem into asymptotics aside from big-$O$? Brent's Theorem: source Running time of a parallel algorithm with $p$ processors (say, $f(n,p)$), $W(n)$ ...
10
votes
1answer
224 views

Is deterministic pseudorandomness possibly stronger than randomness in parallel?

Let the class BPNC (the combination of $\mathsf{BPP}$ and $\mathsf{NC}$) be log depth parallel algorithms with bounded error probability and access to a random source (I'm not sure if this has a ...
0
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0answers
145 views

Sequential Consistency, cannot find a sufficient explanation

I am having a hard time understanding the SC memory model properly. The sentence "the result of any execution is the same as if the operations of all the processors were executed in some sequential ...
4
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0answers
125 views

What are the parts of consistency model playing in hardware, operating system, and programming language?

In multiprocessor programming, consistency model is the key concept to express the correctness of concurrent objects ranging from simple read/write shared variable to concurrent data structures like ...
1
vote
3answers
662 views

Does mathematical model for conccurent computations exist?

Turing machines can represent any computation. Can they also represent concurrent computations? Eg. multiple computations that can happen at the same time? If yes, how are the concurrent computations ...
6
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1answer
130 views

Can we do joins in NC?

Suppose we want to join two relations on a predicate. Is this in NC? I realize that a proof of it not being in NC would amount to a proof that $P\not=NC$, so I'd accept evidence of it being an open ...
5
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0answers
132 views

What is the relationship between $\mathsf{L}$ reductions and $\mathsf{NC}$ reductions?

The $\mathsf{P}$-complete problems can be considered "inherently sequential". $\mathsf{P}$-completeness may be defined using either $\mathsf{NC}$ reductions or $\mathsf{L}$ reductions. Since $\mathsf{...
7
votes
2answers
233 views

Are there [good/optimal] parallel comparison sorts?

Comparing each pair of elements and sorting according to [[number less than] minus [number greater than]] is a parallel comparison sorting algorithm with a depth of $1$ comparison and $O\left(n^2\...
2
votes
1answer
83 views

Lower bounds on batched query search

I am not much in the field of databases. But the problem I m facing is the following: given a database $D$, we receive a batch of distinct queries $Q = \{q_1, ..., q _k\}$, where each $q_i$ is a ...
3
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0answers
218 views

$NC^i \subseteq DSPACE[\log^i{n}]$?

The containment $NC^1 \subseteq DSPACE[\log{n}]$ is simple and well-known (assuming a reasonable notion of uniformity for $NC^1$) and follows by: start with an $O(\log{n})$-depth polynomial sized ...
4
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1answer
212 views

Is conversion of PRAM to parameter number of processors trivial

In section 2 of chapter 4 of Kumar the idea of scaling down is discussed. It is mentioned that the naive method (emulating by assignment) can scale the complexity of the problem more then just "...
2
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1answer
138 views

Parallel algorithms to find the optimum of polynomials

Are there any non-trivial parallel algorithms to find the optimum (local or global) of polynomials? By trivial, I mean something which is an obvious application of a serial algorithm. For example, one ...
4
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5answers
400 views

Advantages and specific applications of massively parallel programming thesis idea

I'm nearly graduated in computer science engineering and my thesis should discuss the massively parallel computational model of CUDA and its advantages/applications. I'm searching for an application ...
1
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1answer
199 views

How is the iteration space of a nested for-loop containing two sequential nested loops represented?

In a general for loop of the form: for (i = 0, i <= n, i++) { for (j = i, j <= n, j++) ... for (k = i, k <= n, k++) ... } What ...
1
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1answer
820 views

What do people mean by capabilities and capacities?

Someone made a casual remark to me about the terminology of capabilities and capacities, in the context of threads, processors and runtime systems, particularly their theoretical modelling. For ...