Tagged Questions

Theoretical questions in Parallel Computing

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1answer
69 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 ...
1
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0answers
29 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
29 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
90 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
24 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 ...
4
votes
2answers
114 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
112 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 ...
0
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0answers
20 views

What's the official name for time-driven parallel informed sorting methods?

If you have a set $\Delta = \{A,B,C,D,E,...\}$ and you want to sort $\Delta$ based on a certain quality of the elements $\in \Delta$, then you can use a certain classification or ranking algorithm $R$ ...
2
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1answer
141 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 ...
2
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0answers
34 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
34 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
2
votes
1answer
122 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 ...
3
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0answers
70 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 ...
-1
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1answer
180 views

Differences between Quantum Computing and Parallelism [closed]

What are the differences between Quantum Computing and Parallelism? thanks in advance
3
votes
0answers
176 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 ...
0
votes
1answer
66 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 ...
0
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0answers
27 views

synchronization problem in complex networks

What is the time and communication complexity of synchronizing clocks on a random graph of N vertices, whose degrees are distributed according to a power-law?
1
vote
1answer
85 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
233 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
64 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
61 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 ...
12
votes
1answer
469 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 ...
12
votes
2answers
498 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
144 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 ...
1
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0answers
162 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
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1answer
201 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
119 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 ...
2
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0answers
106 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(or safety) of concurrent objects ranging from simple shared variable to concurrent data structures like ...
1
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3answers
431 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 ...
5
votes
1answer
127 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
118 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 ...
6
votes
2answers
220 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 ...
2
votes
1answer
76 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
196 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 ...
3
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1answer
190 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
votes
1answer
129 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 ...
3
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5answers
370 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
vote
1answer
184 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
vote
1answer
615 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 ...
7
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0answers
120 views

Reference request: reducing rank computations to characteristic polynomials over arbitrary rings

Question. I'm looking into certain algorithms for linear algebra which lie in NC2. Does anyone know of alternative references for the proof of the proposition just below, relating rank of matrices ...
3
votes
3answers
592 views

parallelizable fast matrix in-place transposition

what is the current state of the art in fast and parallel matrix in-place transposition? I would be very happy, if I could be given some pseudocode for this problem. As far as I could find papers, ...
17
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1answer
593 views

Is solving systems of equations modulo $k$ in $\mathsf{coMod}_k\mathsf L$ for $k$ composite?

I'm interested in the complexity of solving linear equations modulo k, for arbitrary k (and with a special interest in prime powers), specifically: Problem. For a given system of $m$ linear ...
1
vote
1answer
156 views

Most optimal parallel method for calculating the integral of a 2D function

I posted already this question to SO but got no answer so I try it now here: In some crunching number program, I have a function which can be just 1 or 0 in three dimensions. I do not know in advance ...
1
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0answers
115 views

Optimal parallel algorithm for finding roots of a function [closed]

In some problem I need to find the zeroes (multiple real solutions) of some functions in 1D and 2D. I wonder which is the best parallel algorithm for this, which can provide the highest accuracy and ...
1
vote
0answers
192 views

Algorithm for permuting elements using constant work space

I'm searching for an algorithm to do the following: A 1->3 B 2->6 C 4->5 D 5->2 E 6->4 F 3->7 G 8->9 H 10->11 Elements A-H are stored on ...
10
votes
3answers
303 views

Introductory notes on parallelization, in particular patterns of problems and algorithms

I am looking for online available Lecture notes or other resources that give a good introduction into parallel programming, just like parallel analog of basic classes in computer science. My focus is ...
2
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0answers
294 views

Recursive parallel topological sorting in linear time

While doing some research on topological sorting I came across a paper Parallel Topological Sorting Algorithm, TADA, A. and MIGITA, M. and NAKAMURA, R. which claims a recursive divide-and-conquer ...
11
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0answers
239 views

Parallel algorithms for reachability in directed planar graphs

Chong, Han and Lam showed that undirected st-connectivity can be solved on the EREW PRAM in $O({\log}n)$ time with $O(m+n)$ processors. What is the best known parallel algorithm for st-connectivity ...
3
votes
1answer
304 views

Parallel sorting: introduction and state of research

there seem to exist papers on parallel sorting, but I have not found a good introduction into this topic. So, do you know a good summary or introduction into parallel sorting algorithms? In ...
6
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3answers
267 views

Best algorithm for calculating lists of neighbours

Given a collection of thousands of points in 3D, I need to get the list of neighbours for each particle that fall inside some cutoff value (in terms of euclidean distance), and if possible, sorted ...