Questions tagged [dc.parallel-comp]
Theoretical questions in Parallel Computing
105
questions
0
votes
0
answers
26
views
Linear modular equalities with $0/1$ solution
Let $Ax\equiv b\bmod q$ be a $n\times n$ modular linear system known to have $0/1$ solution where $q$ is a large prime. We can solve in $NC^2$ for general linear systems using determinant and matrix ...
- 12.7k
3
votes
1
answer
246
views
Is modular square roots modulo primes in $NC$?
Assume modulus is prime. Is modular square roots then in $NC$?
If not then, are there special primes or prime powers or numbers related to these (such as $2^k\pm i$ where $i\in\{-1,0,+1\}$) where it ...
- 12.7k
2
votes
0
answers
71
views
Parallel complexity of fixed dimension fixed constraints integer programming
Papadimitriou in https://lara.epfl.ch/w/_media/papadimitriou81complexityintegerprogramming.pdf shows ILP is fixed parameter tractable in number of constraints and Lenstra in https://people.csail.mit....
- 12.7k
0
votes
0
answers
86
views
Boolean vs algebraic circuits difference
Valiant, Skyum, Berkowitz and Rackoff in https://epubs.siam.org/doi/10.1137/0212043 showed that $VP=VNC^2$, namely, that arithmetic circuits can be parallelized.
What is the central reason such a ...
- 12.7k
0
votes
0
answers
58
views
Polynomial GCD exact complexity in terms of degree and number of variables
https://en.wikipedia.org/wiki/Polynomial_greatest_common_divisor#Proof_that_GCD_exists_for_multivariate_polynomials states multivariate polynomial GCDs may be defined over $\mathbb F_p[x_1,x_2,\dots,...
- 12.7k
5
votes
1
answer
160
views
$AC^0$[subexp] vs. NC
My question is about the possibility of trading size for depth in circuits.
Under what conditions is it true (or, plausible) that $AC^0[2^{n^\delta}] \subseteq NC^i$ for some constants $\delta < 1, ...
- 187
1
vote
0
answers
70
views
Some examples of tools to demonstrate problem is in $NC$ [closed]
Unlike the class $P$ or $NP$ the class $NC$ does not have any complete problems. To show a problem is in $NC$ one needs to marshal efforts to directly show the problem is in $NC$ since there are no ...
- 12.7k
5
votes
1
answer
146
views
Is black box parallel quantum speedup ever nontrivial?
Grover's algorithm is not parallelizable, in that $p$ quantum processors searching over $n$ elements can't do better than $O(\sqrt{n/p})$ queries.
Are there any oracle problems where quantum ...
- 3,243
3
votes
1
answer
138
views
Embarrassingly Parallel: Formal Definition & Citation
I've been unable to find a good answer for this question: Formally, what makes a problem embarrassingly parallel? Intuitively, it would seem to me that an embarrassingly parallel problem is one where:
...
- 233
1
vote
0
answers
233
views
Fast algorithms for evaluating functions with high Kolmogorov complexity
Motivation:
I am motivated by a concrete example that occurs in neuroscience, dendritic computation, which may be approximated by functions computable on binary trees [1]. To be more precise, I ...
- 301
5
votes
1
answer
236
views
Qubit gates in google supremacy
The gates in quantum supremacy experiment are nearest-neighbor and have spatial locality. Would this additional information help bolster IBM's argument to perhaps simulate quantum supremacy experiment ...
- 539
1
vote
0
answers
80
views
Space complexity of global minimum cut
Are there any non-trivial bounds on the space complexity of global minimum cut? The problem is known to be in $\mathsf{RNC}$. Is anything known about containment in either $\mathsf{L}$ or $\mathsf{NL}$...
- 429
1
vote
0
answers
101
views
Parallel building time of a k-d tree on n points with n processors
Given a point set with $n$ points to build a k-d tree on. We have $n$ processors available. What is the time-optimal building time for the k-d tree?
A straight forward parallelization would be as ...
- 111
5
votes
1
answer
152
views
Problems which will be in $NC$ if fixed dimension Linear Integer Programming in $NC$
We know if fixed dimension linear integer programming is in $NC$ then integer $GCD$ is in $NC$. Is this the only non-trivial implication of fixed dimension linear integer programming in $NC$?
- 12.7k
1
vote
0
answers
72
views
Complexity class of approximating perfect match count
We know we can approximate perfect matching count of bipartite and approximate volume of convex bodies in randomized polynomial time.
Is there any evidence these approximations could be in Nick's ...
- 12.7k
5
votes
1
answer
233
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 ...
- 2,329
3
votes
0
answers
1k
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 $BPP^{BQNC}$?
In particular is Discrete Logarithm in $BQNC$ or at least in $BPP^{...
- 12.7k
3
votes
0
answers
261
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 &...
- 12.7k
1
vote
0
answers
146
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 $n$ dimension, $m$ ...
- 12.7k
10
votes
0
answers
172
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 ...
- 429
6
votes
1
answer
229
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?
- 12.7k
7
votes
1
answer
185
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 $A$, ...
- 1,224
2
votes
0
answers
104
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), ...
- 12.7k
14
votes
1
answer
627
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 ...
- 429
3
votes
1
answer
165
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,...
- 31
5
votes
1
answer
697
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 ...
- 4,001
11
votes
1
answer
277
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, ...
- 6,003
1
vote
1
answer
171
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 ...
- 123
-2
votes
1
answer
203
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 ...
- 121
1
vote
0
answers
58
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 ...
- 3,488
3
votes
0
answers
59
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 ...
- 147
3
votes
0
answers
179
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 ...
- 3,488
2
votes
0
answers
51
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 ...
- 21
5
votes
2
answers
197
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 ...
- 161
5
votes
0
answers
152
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 (...
- 314
4
votes
1
answer
458
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 ...
- 3,488
2
votes
0
answers
105
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 ...
- 2,329
3
votes
0
answers
53
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
- 131
4
votes
1
answer
155
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 ...
- 169
4
votes
0
answers
183
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 ...
- 1,338
2
votes
1
answer
2k
views
Differences between Quantum Computing and Parallelism [closed]
What are the differences between Quantum Computing and Parallelism?
thanks in advance
- 89
3
votes
0
answers
2k
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 ...
- 251
2
votes
2
answers
193
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-...
- 21
1
vote
1
answer
185
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 ...
- 113
1
vote
2
answers
548
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 ...
- 168
1
vote
1
answer
185
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 ...
- 2,329
0
votes
0
answers
210
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 ...
- 1
15
votes
1
answer
855
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 ...
- 12.7k
18
votes
2
answers
1k
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 $p$ ...
- 279
1
vote
2
answers
187
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....
- 111