Inkeeping with my interests in algorithms (see here), I would like to know if there are (contrary to my previous question), algorithms and data structures that are mainstream in parallel programming. It is probably early to ask about mainstream parallel algos and ds, but some of the gurus here may have had good experiences/bad experiences with some of them.
EDIT: I am more interested in successful practical applications of algos and ds than in academic papers.
Thanks
Many of Google's whitepapers, especially but not exclusively ones linked from this page, describe successful practical applications of parallel distributed computing and/or their DS and algorithmic underpinnings. For example, this paper deals with modifying a DBMS's data structures to extract intra-transaction parallelism; this one (and some others) introduces the popular mapreduce architecture, since implemented e.g. in hadoop; this one is about highly parallelizable approximate matrix factoring suitable for use in "kernel methods" in machine learning; etc, etc...
Maybe, I totally miss the point, but there are a ton of mainstream parallel algos and data structures, e.g. matrix multiplication, FFT, PDE and linear equation solvers, integration and simulation (Monte-Carlo / random numbers), searching and sorting, and so on. Take a look at the Designing and Building Parallel Programs or Patterns for Parallel Programming. And then there is CUDA and the like. What are you after?
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One of the promises of side-effect free, referentially transparent functional programming is that such code can be extensively optimized.
To quote Wikipedia:
Immutability of data can, in many cases, lead to execution efficiency, by allowing the compiler to make assumptions that are unsafe in an imperative language, thus increasing opportunities for inline expansion.
I'd like to see examples where a functional language compiler outperforms an imperative one by producing a better optimized code.
Edit: I tried to give a specific scenario, but apparently it wasn't a good idea. So I'll try to explain it in a different way.
Programmers translate ideas (algorithms) into languages that machines can understand. At the same time, one of the most important aspects of the translation is that also humans can understand the resulting code. Unfortunately, in many cases there is a trade-off: A concise, readable code suffers from slow performance and needs to be manually optimized. This is error-prone, time consuming, and it makes the code less readable (up to totally unreadable).
The foundations of functional languages, such as immutability and referential transparency, allow compilers to perform extensive optimizations, which could replace manual optimization of code and free programmers from this trade-off. I'm looking for examples of ideas (algorithms) and their implementations, such that:
the (functional) implementation is close to the original idea and is easy to understand,
it is extensively optimized by the compiler of the language, and
it is hard (or impossible) to write similarly efficient code in an imperative language without manual optimizations that reduce its conciseness and readability.
I apologize if it is a bit vague, but I hope the idea is clear. I don't want to give unnecessary restrictions on the answers. I'm open to suggestions if someone knows how to express it better.
My interest isn't just theoretical. I'd like to use such examples (among other things) to motivate students to get interested in functional programming.
At first, I wasn't satisfied by a few examples suggested in the comments. On second thoughts I take my objections back, those are good examples. Please feel free to expand them to full answers so that people can comment and vote for them.
(One class of such examples will be most likely parallelized code, which can take advantage of multiple CPU cores. Often in functional languages this can be done easily without sacrificing code simplicity (like in Haskell by adding par or pseq in appropriate places). I' be interested in such examples too, but also in other, non-parallel ones.)
There are cases where the same algorithm will optimize better in a pure context. Specifically, stream fusion allows an algorithm that consists of a sequence of loops that may be of widely varying form: maps, filters, folds, unfolds, to be composed into a single loop.
The equivalent optimization in a conventional imperative setting, with mutable data in loops, would have to achieve a full effect analysis, which no one does.
So at least for the class of algorithms that are implemented as pipelines of ana- and catamorphisms on sequences, you can guarantee optimization results that are not possible in an imperative setting.
A very recent paper Haskell beats C using generalised stream fusion by Geoff Mainland, Simon Peyton Jones, Simon Marlow, Roman Leshchinskiy (submitted to ICFP 2013) describes such an example. Abstract (with the interesting part in bold):
Stream fusion [6] is a powerful technique for automatically transforming
high-level sequence-processing functions into efficient implementations.
It has been used to great effect in Haskell libraries
for manipulating byte arrays, Unicode text, and unboxed vectors.
However, some operations, like vector append, still do not perform
well within the standard stream fusion framework. Others,
like SIMD computation using the SSE and AVX instructions available
on modern x86 chips, do not seem to fit in the framework at
all.
In this paper we introduce generalized stream fusion, which
solves these issues. The key insight is to bundle together multiple
stream representations, each tuned for a particular class of stream
consumer. We also describe a stream representation suited for efficient
computation with SSE instructions. Our ideas are implemented
in modified versions of the GHC compiler and vector library.
Benchmarks show that high-level Haskell code written using
our compiler and libraries can produce code that is faster than both
compiler- and hand-vectorized C.
This is just a note, not an answer: the gcc has a pure attribute suggesting it can take account of purity; the obvious reasons are remarked on in the manual here.
I would think that 'static single assignment' imposes a form of purity -- see the links at http://lambda-the-ultimate.org/node/2860 or the wikipedia article.
make and various build systems perform better for large projects by assuming that various build steps are referentially transparent; as such, they only need to rerun steps that have had their inputs change.
For small to medium sized changes, this can be a lot faster than building from scratch.
libsvm and liblinear are both software libraries that implement Support Vector Machines. What's the difference? And how do the differences make liblinear faster than libsvm?
In practice the complexity of the SMO algorithm (that works both for kernel and linear SVM) as implemented in libsvm is O(n^2) or O(n^3) whereas liblinear is O(n) but does not support kernel SVMs. n is the number of samples in the training dataset.
Hence for medium to large scale forget about kernels and use liblinear (or maybe have a look at approximate kernel SVM solvers such as LaSVM).
Edit: in practice libsvm becomes painfully slow at 10k samples.
SVM is support vector machine, which is basically a linear classifier, but using many kernel transforms to turn a non-linear problem into a linear problem beforehand.
From the link above, it seems like liblinear is very much the same thing, without those kernel transforms. So, as they say, in cases where the kernel transforms are not needed (they mention document classification), it will be faster.
From : http://www.csie.ntu.edu.tw/~cjlin/papers/liblinear.pdf
It supports L2-regularized logistic regression (LR), L2-loss and L1-loss linear support vector machines (SVMs) (Boser et al., 1992). It inherits many features of the popular SVM library LIBSVM
And you might also see some useful information here from one of the creators: http://agbs.kyb.tuebingen.mpg.de/km/bb/showthread.php?tid=710
The main idea, I would say, is that liblinear is optimized to deal with linear classification (i.e. no kernels necessary), whereas linear classification is only one of the many capabilities of libsvm, so logically it may not match up to liblinear in terms of classification accuracy. Obviously, I'm making some broad generalizations here, and the exact details on the differences are probably covered in the paper I linked above as well as with the corresponding user's guide to libsvm from the libsvm website.
I am planning to write a bunch of programs on computationally intensive algorithms. The programs would serve as an indicator of different compiler/hardware performance.
I would want to pick up some common set of algorithms which are used in different fields, like Bioinformatics, Gaming, Image Processing, et al. The reason I want to do this would be to learn the algorithms and have a personal mini benchmark suit that would be small | useful | easy to maintain.
Any advice on algorithm selection would be tremendously helpful.
Benchmarks are not worthy of your attention!
The very best guide is to processor performance is: http://www.agner.org/optimize/
And then someone will chuck it in a box with 3GB of RAM defeating dual-channel hopes and your beautifully tuned benchmark will give widely different results again.
If you have a piece of performance critical code and you are sure you've picked the winning algorithm you can't then go use a generic benchmark to determine the best compiler. You have to actually compile your specific piece of code with each compiler and benchmark them with that. And the results you gain, whilst useful for you, will not extrapolate to others.
Case in point: people who make compression software - like zip and 7zip and the high-end stuff like PPMs and context-mixing and things - are very careful about performance and benchmark their programs. They hang out on www.encode.ru
And the situation is this: for engineers developing the same basic algorithm - say LZ or entropy coding like arithmetic-coding and huffman - the engineers all find very different compilers are better.
That is to say, two engineers solving the same problem with the same high-level algorithm will each benchmark their implementation and have results recommending different compilers...
(I have seen the same thing repeat itself repeatedly in competition programming e.g. Al Zimmermann's Programming Contests which is an equally performance-attentive community.)
(The newer GCC 4.x series is very good all round, but that's just my data-point, others still favour ICC)
(Platform benchmarks for IO-related tasks is altogether another thing; people don't appreciate how differently Linux, Windows and FreeBSD (and the rest) perform when under stress. And benchmarks there - on the same workload, same machine, different machines or different core counts - would be very generally informative. There aren't enough benchmarks like that about sadly.)
There was some work done at Berkeley about this a few years ago. The identified 13 common application paterns for parallel programming, the "13 Dwarves". The include things like linear algebra, n-body models, FFTs etc
http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-183.html
See page 10 onwards.
There are some sample .NET implementations here:
http://paralleldwarfs.codeplex.com/
The typical one is Fast Fourier Transform, perhaps you can also do something like the Lucas–Lehmer primality test.
I remember a guy who tested computational performance of machines, compiler versions by inverting Hilbert matrices.
For image processing, median filtering (used for removing noise, bad pixels) is always too slow. It might make a good test, given a large enough image say 1000x1000.
We know there are like a thousand of classifiers, recently I was told that, some people say adaboost is like the out of the shell one.
Are There better algorithms (with
that voting idea)
What is the state of the art in
the classifiers.Do you have an example?
First, adaboost is a meta-algorithm which is used in conjunction with (on top of) your favorite classifier. Second, classifiers which work well in one problem domain often don't work well in another. See the No Free Lunch wikipedia page. So, there is not going to be AN answer to your question. Still, it might be interesting to know what people are using in practice.
Weka and Mahout aren't algorithms... they're machine learning libraries. They include implementations of a wide range of algorithms. So, your best bet is to pick a library and try a few different algorithms to see which one works best for your particular problem (where "works best" is going to be a function of training cost, classification cost, and classification accuracy).
If it were me, I'd start with naive Bayes, k-nearest neighbors, and support vector machines. They represent well-established, well-understood methods with very different tradeoffs. Naive Bayes is cheap, but not especially accurate. K-NN is cheap during training but (can be) expensive during classification, and while it's usually very accurate it can be susceptible to overtraining. SVMs are expensive to train and have lots of meta-parameters to tweak, but they are cheap to apply and generally at least as accurate as k-NN.
If you tell us more about the problem you're trying to solve, we may be able to give more focused advice. But if you're just looking for the One True Algorithm, there isn't one -- the No Free Lunch theorem guarantees that.
Apache Mahout (open source, java) seems to pick up a lot of steam.
Weka is a very popular and stable Machine Learning library. It has been around for quite a while and written in Java.
Hastie et al. (2013, The Elements of Statistical Learning) conclude that the Gradient Boosting Machine is the best "off-the-shelf" Method. Independent of the Problem you have.
Definition (see page 352):
An “off-the-shelf” method is one that
can be directly applied to the data without requiring a great deal of timeconsuming data preprocessing or careful tuning of the learning procedure.
And a bit older meaning:
In fact, Breiman (NIPS Workshop, 1996) referred to AdaBoost with trees as the “best off-the-shelf classifier in the world” (see also Breiman (1998)).
How to implement efficient sorting algorithms for multiple processors in Scala? Here's the link for radix algorithm in GPU:
radix algorithm in GPU
Use scala.actors.Futures. It isn't a good solution, because you are talking about parallel computation, not concurrent computation, and Futures is aimed at the latter, not the former.
Things like parallel arrays that are coming with Java 7 and a later (not 2.8) version of Scala are more appropriate for parallel algorithms.
Just explaining, a parallel algorithm is one which does the same computation on multiple processing units. It is easy to see that each of which runs the same code. A concurrent computation is one in which each processing unit is running a potentially different code.
Also related, in parallel algorithms, the code being run doesn't change, only the data. In concurrent computation you have code changing constantly.
By the way, though that is not what you are asking, let me state that there's a library for Scala to run OpenCL code (ie, run computation on GPU). It's called ScalaCL.