I'm doing some administration work for an aviation transport company. They build aircraft containers and such here. One of the things they want me to code is a order optimization script that the guys on the floor can use to get the most out of the given material. To give a simple overview: say we order a certain amount beams that are 10 meters per unit. We need beam chunks of 5x 6m, 10x 3.5m, 4x 3m, which are acquired by cutting the 10m in smaller parts. What would be the minimum amount of 10m beams we need to order?
There are some parallels with the multiprocessor job scheduling problem (one beam is a processor, each chunk a job), although that focusses on minimizing the time required to perform all jobs instead of minimizing the amount of processors needed to perform all jobs within a pre-set time. The multiprocessor job scheduling problem is in NP-complete, but I wonder if my variation of the problem is too. Does anybody know similar problems and methods for solving them?
This problem is exactly: http://en.wikipedia.org/wiki/Cutting_stock_problem (more generally http://en.wikipedia.org/wiki/Bin_packing_problem). You can use any old ILP solver. I like http://lpsolve.sourceforge.net/5.5/, its quite friendly to use.
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If I have a large custom task graph fed into Dask, and a list of times that each task will take (e.g. in the simplest case, each task might take the same number of CPU seconds/minutes), is there a way to calculate how "parallelizable" the problem is from the structure of the graph, without actually running the tasks? The assumption would be that the time to calculate scheduling priorities etc is negligible compared to the time of each task.
I'm thinking of a metric either that plots the number of parallel processes being used over time (assuming an infinite number of available cores), or perhaps the number of hours that the whole graph would take, given a fixed number of CPU cores.
If not, this seems like a nice thing to be able to provide for the task scheduler, especially if individual tasks are expected to take many minutes or hours. However, I guess it might be hard to calculate analytically, depending on the algorithm(s) underlying task allocation in Dask.
I have a computation bound application. I have executed it on multi-nodes ( 4nodes, 8nodes) I'm wondering if communication between the nodes could have any effect on the run time? If so, how would it be possible? because as far as I found, computation bound application just depends on the computing capability of system.
Also, can I consider CPU amount of my system as computing capability?
Any help would be appreciated.
Updated:
In order to see if the application is memory-bound or compute-bound, I've run the application over 1 nodes using different number of cores. For that application (NPB-LU), the run time decreased linearly by increasing the number of cores. So I found this application could be compute-bound (I didn't have another option to figure it out).
Then, I have predicted the run time of the application with a model which considers the latency(in my case it's message-time) in different connection levels like inter-socket, inter-node. There are some difference in the predicted time which achieved by different latency connection levels although the application seemed to be computation-bound.
n:grid size, p:number of cores, m(total Mops/s), f(Mop/s/core)
Imagine you have horse that is drinking water, let's say 1 liter per minute.
In order to give the water to the horse you have a water well where you can take the water from. Imagine you can pump up to 1.5 liters per minute.
Having this situation your water consumption is horse-bounded.
Then it turns out that you have two horses drinking the same amount of water: 1 liter each per minute. Then your water consumption is no longer horse-bounded but well-bounded.
Your application behavior can change depending of the environment. In order to determine what is happening to your application I recommend you to profile your app. You have a lot of alternatives such as gprof, perf, PAPI and many others to better observe what is your application behaviour.
Then you can determine experimentally very intersting metrics like Instructions per Clock cycle, which can give you a better understanding of the behaviour of your app.
I'm studying task-based parallel computing and got interested in a variation of the old project management problem -- the critical path of an activity-on-vertex (AOV) project network, which can be calculated using the topological sorting algorithm if there's no deadlock cycle. The total time of those activities on a critical path gives the minimum completion time of the project.
But this is assuming we always have enough workers simultaneously finishing the activities with no dependence on each other. If the number of workers (processors/cores) available is finite, certain activities can wait not because some activities they depend on have not yet been finished, but simply because all workers are now busy doing other activities. This is a simplified model for today's multi-core parallel computing. If there's only one worker who has to do all the activities, the project completion time is the total time of all activities. We are back to single-core serial computing that way.
Is there an efficient algorithm that gives the minimum completion time of an AOV network given a finite number of workers available? How should we wisely choose which activities to do first when the doable activities is more than the number of workers so as to minimize the idling time of workers later on? The minimum time should be somewhere in between the critical path time (infinite workers) and the total time of all activities (one worker). It should also be greater than equal to the total time divided by the number of workers (no idling). Is there an algorithm to get that minimum time?
I found a C++ conference video called "work stealing" that almost answers my question. At 18:40, the problem is said on the slide to be NP-hard if activities cannot be paused, further divided, or transferred from worker to worker. Such restrictions make decisions of which workers to finish which jobs (activities) too hard to make. Work stealing is therefore introduced to avoid making such difficult decisions beforehand. Instead, it makes such decions no longer crucial so long as certain apparent greedy rules are followed. The whole project will be always finished as soon as possible under the constraint of either the critical path or the no-idling time of the finite number of workers or both. The video then goes on talking about how to make the procedure of "work stealing" between different workers (processors) more efficient by making the implementation distributed and cache-friendly, etc.
According to the video, future C++ shared-memory parallel coding will be task-based rather than loop-based. To solve a problem, the programmer defines a bunch of tasks to finish and their dependence relations to respect, and then the coding language will automatically schedule the tasks on multiple cores at run time in a flexible way. This "event-driven"-like way of implementing a flexible code by a distributed task queuing system will become very useful in parallel computing.
When an optimization problem is NP-hard, the best way to solve it is to find ways to avoid it.
Let's say I have a data with 25 blocks and the replication factor is 1. The mapper requires about 5 mins to read and process a single block of the data. Then how can I calculate the time for one worker node? The what about 15 nodes? Will the time be changed if we change the replication factor to 3?
I really need a help.
First of all I would advice reading some scientific papers regarding the issue (Google Scholar is a good starting point).
Now a bit of discussion. From my latest experiments I have concluded that processing time has very strong relation with amount of data you want to process (makes sense). On our cluster, on average it takes around 7-8 seconds for Mapper to read a block of 128MBytes. Now there are several factors which you need to consider in order to predict the overall execution time:
How much data the Mapper produces, which will determine moreless the time Hadoop requires to execute Shuffling
What Reducer is doing? Does it do some iterative processing? (might be slow!)
What is the configuration of the resources? (how many Mappers and Reducers are allowed to run on the same machine)
Finally are there other jobs running simultaneously? (this might be slowing down the jobs significantly, since your Reducer slots can be occupied waiting for data instead of doing useful things).
So already for one machine you are seeing the complexity of the task of predicting the time of job execution. Basically during my study I was able to conclude that in average one machine is capable of processing from 20-50 MBytes/second (the rate is calculated according to the following formula: total input size/total job running time). The processing rate includes the staging time (when your application is starting and uploading required files to the cluster for example). The processing rate is different for different use cases and greatly influenced by the input size and more importantly the amount of data produced by Mappers (once again this values are for our infrastructure and on different machine configuration you will be seeing completely different execution times).
When you start scaling your experiments, you would see in average improved performance, but once again from my study I could conclude that it is not linear and you would need to fit by yourself, for your own infrastructure the model with respective variables which would approximate the job execution time.
Just to give you an idea, I will share some part of the results. The rate when executing determine use case on 1 node was ~46MBytes/second, for 2 nodes it was ~73MBytes/second and for 3 nodes it was ~85MBytes/second (in my case the replication factor was equal to the number of nodes).
The problem is complex requires time, patience and some analytical skills to solve it. Have fun!
I parallelized a simulation engine in 12 threads to run it on a cluster of 12 nodes(each node running one thread). Since chances of availability of 12 systems is generally less, I also tweaked it for 6 threads(to run on 6 nodes), 4 threads(to run on 4 nodes), 3 threads(to run on 3 nodes), and 2 threads(to run on 2 nodes). I have noticed that more the number of nodes/threads, more is the speedup. But obviously, the more nodes I use, the more expensive(in terms of cost and power) the execution becomes.
I want to publish these results in a journal so I want to know if there are any laws/theorems which will help me to decide the optimum number of nodes on which I should run this program?
Thanks,
Akshey
How have you parallelised your program and what is inside each of your nodes ?
For instance, on one of my clusters I have several hundred nodes each containing 4 dual-core Xeons. If I were to run an OpenMP program on this cluster I would place a single execution on one node and start up no more than 8 threads, one for each processor core. My clusters are managed by Grid Engine and used for batch jobs, so there is no contention while a job is running. In general there is no point in asking for more than one node on which to run an OpenMP job since the shared-memory approach doesn't work on distributed-memory hardware. And there's not much to be gained by asking for fewer than 8 threads on an 8-core node, I have enough hardware available not to have to share it.
If you have used a distributed-memory programming approach, such as MPI, then you are probably working with a number of processes (rather than threads) and may well be executing these processes on cores on different nodes, and be paying the costs in terms of communications traffic.
As #Blank has already pointed out the most efficient way to run a program, if by efficiency one means 'minimising total cpu-hours', is to run the program on 1 core. Only. However, for jobs of mine which can take, say, a week on 256 cores, waiting 128 weeks for one core to finish its work is not appealing.
If you are not already familiar with the following terms, Google around for them or head for Wikipedia:
Amdahl's Law
Gustafson's Law
weak scaling
strong scaling
parallel speedup
parallel efficiency
scalability.
"if there are any laws/theorems which will help me to decide the optimum number of nodes on which I should run this program?"
There's no such general laws, because every problem has slightly different characteristics.
You can make a mathematical model of the performance of your problem on different number of nodes, knowing how much computational work has to be done, and how much communications has to be done, and how long each takes. (The communications times can be estimated by the amount of commuincations, and typical latency/bandwidth numbers for your nodes' type of interconnect). This can guide you as to good choices.
These models can be valuable for understanding what is going on, but to actually determine the right number of nodes to run on for your code for some given problem size, there's really no substitute for running a scaling test - running the problem on various numbers of nodes and actually seeing how it performs. The numbers you want to see are:
Time to completion as a function of number of processors: T(P)
Speedup as a function of number of processors: S(P) = T(1)/T(P)
Parallel efficiency: E(P) = S(P)/P
How do you choose the "right" number of nodes? It depends on how many jobs you have to run, and what's an acceptable use of computational resources.
So for instance, in plotting your timing results you might find that you have a minimum time to completion T(P) at some number of processors -- say, 32. So that might seem like the "best" choice. But when you look at the efficiency numbers, it might become clear that the efficiency started dropping precipitously long before that; and you only got (say) a 20% decrease in run time over running at 16 processors - that is, for 2x the amount of computational resources, you only got a 1.25x increase in speed. That's usually going to be a bad trade, and you'd prefer to run at fewer processors - particularly if you have a lot of these simulations to run. (If you have 2 simulations to run, for instance, in this case you could get them done in 1.25 time units insetad of 2 time units by running the two simulations each on 16 processors simultaneously rather than running them one at a time on 32 processors).
On the other hand, sometimes you only have a couple runs to do and time really is of the essence, even if you're using resources somewhat inefficiently. Financial modelling can be like this -- they need the predictions for tomorrow's markets now, and they have the money to throw at computational resources even if they're not used 100% efficiently.
Some of these concepts are discussed in the "Introduction to Parallel Performance" section of any parallel programming tutorials; here's our example, https://support.scinet.utoronto.ca/wiki/index.php/Introduction_To_Performance
Increasing the number of nodes leads to diminishing returns. Two nodes is not twice as fast as one node; four nodes even less so than two. As such, the optimal number of nodes is always one; it is with a single node that you get most work done per node.