multi-constrainted single machine scheduling using Dynamic Programming - dynamic-programming

Let a set of tasks are given to machine to find a profitable ordering of tasks. Each task has profit, start and finish time. Machine is constrained in energy, memory and execution time duration. In addition a schedule will have a set of compatible tasks (no overlapping). Is there any Dynamic Programming strategy to produce a profitable schedule by considering all the constraints or condition?
I can solve three constraints (energy, memory and execution time duration) by using constraints merging and surrogate relaxation. But I can not handle no overlapping or tasks compatibility with other constraints...
Anybody please suggest a way to merge all the constraints for Dynamic Programming....

Related

Does it make sense to write concurrent program if you have 1 hardware thread? [duplicate]

What is the difference between concurrency and parallelism?
Concurrency is when two or more tasks can start, run, and complete in overlapping time periods. It doesn't necessarily mean they'll ever both be running at the same instant. For example, multitasking on a single-core machine.
Parallelism is when tasks literally run at the same time, e.g., on a multicore processor.
Quoting Sun's Multithreaded Programming Guide:
Concurrency: A condition that exists when at least two threads are making progress. A more generalized form of parallelism that can include time-slicing as a form of virtual parallelism.
Parallelism: A condition that arises when at least two threads are executing simultaneously.
Why the Confusion Exists
Confusion exists because dictionary meanings of both these words are almost the same:
Concurrent: existing, happening, or done at the same time(dictionary.com)
Parallel: very similar and often happening at the same time(merriam webster).
Yet the way they are used in computer science and programming are quite different. Here is my interpretation:
Concurrency: Interruptability
Parallelism: Independentability
So what do I mean by above definitions?
I will clarify with a real world analogy. Let’s say you have to get done 2 very important tasks in one day:
Get a passport
Get a presentation done
Now, the problem is that task-1 requires you to go to an extremely bureaucratic government office that makes you wait for 4 hours in a line to get your passport. Meanwhile, task-2 is required by your office, and it is a critical task. Both must be finished on a specific day.
Case 1: Sequential Execution
Ordinarily, you will drive to passport office for 2 hours, wait in the line for 4 hours, get the task done, drive back two hours, go home, stay awake 5 more hours and get presentation done.
Case 2: Concurrent Execution
But you’re smart. You plan ahead. You carry a laptop with you, and while waiting in the line, you start working on your presentation. This way, once you get back at home, you just need to work 1 extra hour instead of 5.
In this case, both tasks are done by you, just in pieces. You interrupted the passport task while waiting in the line and worked on presentation. When your number was called, you interrupted presentation task and switched to passport task. The saving in time was essentially possible due to interruptability of both the tasks.
Concurrency, IMO, can be understood as the "isolation" property in ACID. Two database transactions are considered isolated if sub-transactions can be performed in each and any interleaved way and the final result is same as if the two tasks were done sequentially. Remember, that for both the passport and presentation tasks, you are the sole executioner.
Case 3: Parallel Execution
Now, since you are such a smart fella, you’re obviously a higher-up, and you have got an assistant. So, before you leave to start the passport task, you call him and tell him to prepare first draft of the presentation. You spend your entire day and finish passport task, come back and see your mails, and you find the presentation draft. He has done a pretty solid job and with some edits in 2 more hours, you finalize it.
Now since, your assistant is just as smart as you, he was able to work on it independently, without needing to constantly ask you for clarifications. Thus, due to the independentability of the tasks, they were performed at the same time by two different executioners.
Still with me? Alright...
Case 4: Concurrent But Not Parallel
Remember your passport task, where you have to wait in the line?
Since it is your passport, your assistant cannot wait in line for you. Thus, the passport task has interruptability (you can stop it while waiting in the line, and resume it later when your number is called), but no independentability (your assistant cannot wait in your stead).
Case 5: Parallel But Not Concurrent
Suppose the government office has a security check to enter the premises. Here, you must remove all electronic devices and submit them to the officers, and they only return your devices after you complete your task.
In this, case, the passport task is neither independentable nor interruptible. Even if you are waiting in the line, you cannot work on something else because you do not have necessary equipment.
Similarly, say the presentation is so highly mathematical in nature that you require 100% concentration for at least 5 hours. You cannot do it while waiting in line for passport task, even if you have your laptop with you.
In this case, the presentation task is independentable (either you or your assistant can put in 5 hours of focused effort), but not interruptible.
Case 6: Concurrent and Parallel Execution
Now, say that in addition to assigning your assistant to the presentation, you also carry a laptop with you to passport task. While waiting in the line, you see that your assistant has created the first 10 slides in a shared deck. You send comments on his work with some corrections. Later, when you arrive back home, instead of 2 hours to finalize the draft, you just need 15 minutes.
This was possible because presentation task has independentability (either one of you can do it) and interruptability (you can stop it and resume it later). So you concurrently executed both tasks, and executed the presentation task in parallel.
Let’s say that, in addition to being overly bureaucratic, the government office is corrupt. Thus, you can show your identification, enter it, start waiting in line for your number to be called, bribe a guard and someone else to hold your position in the line, sneak out, come back before your number is called, and resume waiting yourself.
In this case, you can perform both the passport and presentation tasks concurrently and in parallel. You can sneak out, and your position is held by your assistant. Both of you can then work on the presentation, etc.
Back to Computer Science
In computing world, here are example scenarios typical of each of these cases:
Case 1: Interrupt processing.
Case 2: When there is only one processor, but all executing tasks have wait times due to I/O.
Case 3: Often seen when we are talking about map-reduce or hadoop clusters.
Case 4: I think Case 4 is rare. It’s uncommon for a task to be concurrent but not parallel. But it could happen. For example, suppose your task requires access to a special computational chip that can be accessed through only processor-1. Thus, even if processor-2 is free and processor-1 is performing some other task, the special computation task cannot proceed on processor-2.
Case 5: also rare, but not quite as rare as Case 4. A non-concurrent code can be a critical region protected by mutexes. Once it is started, it must execute to completion. However, two different critical regions can progress simultaneously on two different processors.
Case 6: IMO, most discussions about parallel or concurrent programming are basically talking about Case 6. This is a mix and match of both parallel and concurrent executions.
Concurrency and Go
If you see why Rob Pike is saying concurrency is better, you have to understand what the reason is. You have a really long task in which there are multiple waiting periods where you wait for some external operations like file read, network download. In his lecture, all he is saying is, “just break up this long sequential task so that you can do something useful while you wait.” That is why he talks about different organizations with various gophers.
Now the strength of Go comes from making this breaking really easy with go keyword and channels. Also, there is excellent underlying support in the runtime to schedule these goroutines.
But essentially, is concurrency better than parallelism?
Are apples better than oranges?
I like Rob Pike's talk: Concurrency is not Parallelism (it's better!)
(slides)
(talk)
Rob usually talks about Go and usually addresses the question of Concurrency vs Parallelism in a visual and intuitive explanation! Here is a short summary:
Task: Let's burn a pile of obsolete language manuals! One at a time!
Concurrency: There are many concurrently decompositions of the task! One example:
Parallelism: The previous configuration occurs in parallel if there are at least 2 gophers working at the same time or not.
To add onto what others have said:
Concurrency is like having a juggler juggle many balls. Regardless of how it seems, the juggler is only catching/throwing one ball per hand at a time. Parallelism is having multiple jugglers juggle balls simultaneously.
Say you have a program that has two threads. The program can run in two ways:
Concurrency Concurrency + parallelism
(Single-Core CPU) (Multi-Core CPU)
___ ___ ___
|th1| |th1|th2|
| | | |___|
|___|___ | |___
|th2| |___|th2|
___|___| ___|___|
|th1| |th1|
|___|___ | |___
|th2| | |th2|
In both cases we have concurrency from the mere fact that we have more than one thread running.
If we ran this program on a computer with a single CPU core, the OS would be switching between the two threads, allowing one thread to run at a time.
If we ran this program on a computer with a multi-core CPU then we would be able to run the two threads in parallel - side by side at the exact same time.
Concurrency: If two or more problems are solved by a single processor.
Parallelism: If one problem is solved by multiple processors.
Imagine learning a new programming language by watching a video tutorial. You need to pause the video, apply what been said in code then continue watching. That's concurrency.
Now you're a professional programmer. And you enjoy listening to calm music while coding. That's Parallelism.
As Andrew Gerrand said in GoLang Blog
Concurrency is about dealing with lots of things at once. Parallelism
is about doing lots of things at once.
Enjoy.
I will try to explain with an interesting and easy to understand example. :)
Assume that an organization organizes a chess tournament where 10 players (with equal chess playing skills) will challenge a professional champion chess player. And since chess is a 1:1 game thus organizers have to conduct 10 games in time efficient manner so that they can finish the whole event as quickly as possible.
Hopefully following scenarios will easily describe multiple ways of conducting these 10 games:
1) SERIAL - let's say that the professional plays with each person one by one i.e. starts and finishes the game with one person and then starts the next game with the next person and so on. In other words, they decided to conduct the games sequentially. So if one game takes 10 mins to complete then 10 games will take 100 mins, also assume that transition from one game to other takes 6 secs then for 10 games it will be 54 secs (approx. 1 min).
so the whole event will approximately complete in 101 mins (WORST APPROACH)
2) CONCURRENT - let's say that the professional plays his turn and moves on to the next player so all 10 players are playing simultaneously but the professional player is not with two person at a time, he plays his turn and moves on to the next person. Now assume a professional player takes 6 sec to play his turn and also transition time of a professional player b/w two players is 6 sec so the total transition time to get back to the first player will be 1min (10x6sec). Therefore, by the time he is back to the first person with whom the event was started, 2mins have passed (10xtime_per_turn_by_champion + 10xtransition_time=2mins)
Assuming that all player take 45sec to complete their turn so based on 10mins per game from SERIAL event the no. of rounds before a game finishes should 600/(45+6) = 11 rounds (approx)
So the whole event will approximately complete in 11xtime_per_turn_by_player_&_champion + 11xtransition_time_across_10_players = 11x51 + 11x60sec= 561 + 660 = 1221sec = 20.35mins (approximately)
SEE THE IMPROVEMENT from 101 mins to 20.35 mins (BETTER APPROACH)
3) PARALLEL - let's say organizers get some extra funds and thus decided to invite two professional champion players (both equally capable) and divided the set of same 10 players (challengers) into two groups of 5 each and assigned them to two champions i.e. one group each. Now the event is progressing in parallel in these two sets i.e. at least two players (one in each group) are playing against the two professional players in their respective group.
However within the group the professional player with take one player at a time (i.e. sequentially) so without any calculation you can easily deduce that whole event will approximately complete in 101/2=50.5mins to complete
SEE THE IMPROVEMENT from 101 mins to 50.5 mins (GOOD APPROACH)
4) CONCURRENT + PARALLEL - In the above scenario, let's say that the two champion players will play concurrently (read 2nd point) with the 5 players in their respective groups so now games across groups are running in parallel but within group, they are running concurrently.
So the games in one group will approximately complete in 11xtime_per_turn_by_player_&_champion + 11xtransition_time_across_5_players = 11x51 + 11x30 = 600 + 330 = 930sec = 15.5mins (approximately)
So the whole event (involving two such parallel running group) will approximately complete in 15.5mins
SEE THE IMPROVEMENT from 101 mins to 15.5 mins (BEST APPROACH)
NOTE: in the above scenario if you replace 10 players with 10 similar jobs and two professional players with two CPU cores then again the following ordering will remain true:
SERIAL > PARALLEL > CONCURRENT > CONCURRENT+PARALLEL
(NOTE: this order might change for other scenarios as this ordering highly depends on inter-dependency of jobs, communication needs between jobs and transition overhead between jobs)
Concurrent programming execution has 2 types : non-parallel concurrent programming and parallel concurrent programming (also known as parallelism).
The key difference is that to the human eye, threads in non-parallel concurrency appear to run at the same time but in reality they don't. In non - parallel concurrency threads rapidly switch and take turns to use the processor through time-slicing.
While in parallelism there are multiple processors available so, multiple threads can run on different processors at the same time.
Reference: Introduction to Concurrency in Programming Languages
Simple example:
Concurrent is: "Two queues accessing one ATM machine"
Parallel is: "Two queues and two ATM machines"
Parallelism is simultaneous execution of processes on a multiple cores per CPU or multiple CPUs (on a single motherboard).
Concurrency is when Parallelism is achieved on a single core/CPU by using scheduling algorithms that divides the CPU’s time (time-slice). Processes are interleaved.
Units:
1 or many cores in a single CPU (pretty much all modern day processors)
1 or many CPUs on a motherboard (think old school servers)
1 application is 1 program (think Chrome browser)
1 program can have 1 or many processes (think each Chrome browser tab is a process)
1 process can have 1 or many threads from 1 program (Chrome tab playing Youtube video in 1 thread, another thread spawned for comments
section, another for users login info)
Thus, 1 program can have 1 or many threads of execution
1 process is thread(s)+allocated memory resources by OS (heap, registers, stack, class memory)
They solve different problems. Concurrency solves the problem of having scarce CPU resources and many tasks. So, you create threads or independent paths of execution through code in order to share time on the scarce resource. Up until recently, concurrency has dominated the discussion because of CPU availability.
Parallelism solves the problem of finding enough tasks and appropriate tasks (ones that can be split apart correctly) and distributing them over plentiful CPU resources. Parallelism has always been around of course, but it's coming to the forefront because multi-core processors are so cheap.
concurency:
multiple execution flows with the potential to share resources
Ex:
two threads competing for a I/O port.
paralelism:
splitting a problem in multiple similar chunks.
Ex:
parsing a big file by running two processes on every half of the file.
Concurrency => When multiple tasks are performed in overlapping time periods with shared resources (potentially maximizing the resources utilization).
Parallel => when single task is divided into multiple simple independent sub-tasks which can be performed simultaneously.
Concurrency vs Parallelism
Rob Pike in 'Concurrency Is Not Parallelism'
Concurrency is about dealing with lots of things at once.
Parallelism is about doing lots of things at once.
[Concurrency theory]
Concurrency - handles several tasks at once
Parallelism - handles several thread at once
My vision of concurrency and parallelism
[Sync vs Async]
[Swift Concurrency]
If at all you want to explain this to a 9-year-old.
Think of it as servicing queues where server can only serve the 1st job in a queue.
1 server , 1 job queue (with 5 jobs) -> no concurrency, no parallelism (Only one job is being serviced to completion, the next job in the queue has to wait till the serviced job is done and there is no other server to service it)
1 server, 2 or more different queues (with 5 jobs per queue) -> concurrency (since server is sharing time with all the 1st jobs in queues, equally or weighted) , still no parallelism since at any instant, there is one and only job being serviced.
2 or more servers , one Queue -> parallelism ( 2 jobs done at the same instant) but no concurrency ( server is not sharing time, the 3rd job has to wait till one of the server completes.)
2 or more servers, 2 or more different queues -> concurrency and parallelism
In other words, concurrency is sharing time to complete a job, it MAY take up the same time to complete its job but at least it gets started early. Important thing is , jobs can be sliced into smaller jobs, which allows interleaving.
Parallelism is achieved with just more CPUs , servers, people etc that run in parallel.
Keep in mind, if the resources are shared, pure parallelism cannot be achieved, but this is where concurrency would have it's best practical use, taking up another job that doesn't need that resource.
I really like Paul Butcher's answer to this question (he's the writer of Seven Concurrency Models in Seven Weeks):
Although they’re often confused, parallelism and concurrency are
different things. Concurrency is an aspect of the problem domain—your
code needs to handle multiple simultaneous (or near simultaneous)
events. Parallelism, by contrast, is an aspect of the solution
domain—you want to make your program run faster by processing
different portions of the problem in parallel. Some approaches are
applicable to concurrency, some to parallelism, and some to both.
Understand which you’re faced with and choose the right tool for the
job.
In electronics serial and parallel represent a type of static topology, determining the actual behaviour of the circuit. When there is no concurrency, parallelism is deterministic.
In order to describe dynamic, time-related phenomena, we use the terms sequential and concurrent. For example, a certain outcome may be obtained via a certain sequence of tasks (eg. a recipe). When we are talking with someone, we are producing a sequence of words. However, in reality, many other processes occur in the same moment, and thus, concur to the actual result of a certain action. If a lot of people is talking at the same time, concurrent talks may interfere with our sequence, but the outcomes of this interference are not known in advance. Concurrency introduces indeterminacy.
The serial/parallel and sequential/concurrent characterization are orthogonal. An example of this is in digital communication. In a serial adapter, a digital message is temporally (i.e. sequentially) distributed along the same communication line (eg. one wire). In a parallel adapter, this is divided also on parallel communication lines (eg. many wires), and then reconstructed on the receiving end.
Let us image a game, with 9 children. If we dispose them as a chain, give a message at the first and receive it at the end, we would have a serial communication. More words compose the message, consisting in a sequence of communication unities.
I like ice-cream so much. > X > X > X > X > X > X > X > X > X > ....
This is a sequential process reproduced on a serial infrastructure.
Now, let us image to divide the children in groups of 3. We divide the phrase in three parts, give the first to the child of the line at our left, the second to the center line's child, etc.
I like ice-cream so much. > I like > X > X > X > .... > ....
> ice-cream > X > X > X > ....
> so much > X > X > X > ....
This is a sequential process reproduced on a parallel infrastructure (still partially serialized although).
In both cases, supposing there is a perfect communication between the children, the result is determined in advance.
If there are other persons that talk to the first child at the same time as you, then we will have concurrent processes. We do no know which process will be considered by the infrastructure, so the final outcome is non-determined in advance.
I'm going to offer an answer that conflicts a bit with some of the popular answers here. In my opinion, concurrency is a general term that includes parallelism. Concurrency applies to any situation where distinct tasks or units of work overlap in time. Parallelism applies more specifically to situations where distinct units of work are evaluated/executed at the same physical time. The raison d'etre of parallelism is speeding up software that can benefit from multiple physical compute resources. The other major concept that fits under concurrency is interactivity. Interactivity applies when the overlapping of tasks is observable from the outside world. The raison d'etre of interactivity is making software that is responsive to real-world entities like users, network peers, hardware peripherals, etc.
Parallelism and interactivity are almost entirely independent dimension of concurrency. For a particular project developers might care about either, both or neither. They tend to get conflated, not least because the abomination that is threads gives a reasonably convenient primitive to do both.
A little more detail about parallelism:
Parallelism exists at very small scales (e.g. instruction-level parallelism in processors), medium scales (e.g. multicore processors) and large scales (e.g. high-performance computing clusters). Pressure on software developers to expose more thread-level parallelism has increased in recent years, because of the growth of multicore processors. Parallelism is intimately connected to the notion of dependence. Dependences limit the extent to which parallelism can be achieved; two tasks cannot be executed in parallel if one depends on the other (Ignoring speculation).
There are lots of patterns and frameworks that programmers use to express parallelism: pipelines, task pools, aggregate operations on data structures ("parallel arrays").
A little more detail about interactivity:
The most basic and common way to do interactivity is with events (i.e. an event loop and handlers/callbacks). For simple tasks events are great. Trying to do more complex tasks with events gets into stack ripping (a.k.a. callback hell; a.k.a. control inversion). When you get fed up with events you can try more exotic things like generators, coroutines (a.k.a. Async/Await), or cooperative threads.
For the love of reliable software, please don't use threads if what you're going for is interactivity.
Curmudgeonliness
I dislike Rob Pike's "concurrency is not parallelism; it's better" slogan. Concurrency is neither better nor worse than parallelism. Concurrency includes interactivity which cannot be compared in a better/worse sort of way with parallelism. It's like saying "control flow is better than data".
From the book Linux System Programming by Robert Love:
Concurrency, Parallelism, and Races
Threads create two related but distinct phenomena: concurrency and
parallelism. Both are bittersweet, touching on the costs of threading
as well as its benefits. Concurrency is the ability of two or more
threads to execute in overlapping time periods. Parallelism is
the ability to execute two or more threads simultaneously.
Concurrency can occur without parallelism: for example, multitasking
on a single processor system. Parallelism (sometimes emphasized as
true parallelism) is a specific form of concurrency requiring multiple processors (or a single processor capable of multiple engines
of execution, such as a GPU). With concurrency, multiple threads make
forward progress, but not necessarily simultaneously. With
parallelism, threads literally execute in parallel, allowing
multithreaded programs to utilize multiple processors.
Concurrency is a programming pattern, a way of approaching problems.
Parallelism is a hardware feature, achievable through concurrency.
Both are useful.
This explanation is consistent with the accepted answer. Actually the concepts are far simpler than we think. Don't think them as magic. Concurrency is about a period of time, while Parallelism is about exactly at the same time, simultaneously.
Concurrency is the generalized form of parallelism. For example parallel program can also be called concurrent but reverse is not true.
Concurrent execution is possible on single processor (multiple threads, managed by scheduler or thread-pool)
Parallel execution is not possible on single processor but on multiple processors. (One process per processor)
Distributed computing is also a related topic and it can also be called concurrent computing but reverse is not true, like parallelism.
For details read this research paper
Concepts of Concurrent Programming
I really liked this graphical representation from another answer - I think it answers the question much better than a lot of the above answers
Parallelism vs Concurrency
When two threads are running in parallel, they are both running at the same time. For example, if we have two threads, A and B, then their parallel execution would look like this:
CPU 1: A ------------------------->
CPU 2: B ------------------------->
When two threads are running concurrently, their execution overlaps. Overlapping can happen in one of two ways: either the threads are executing at the same time (i.e. in parallel, as above), or their executions are being interleaved on the processor, like so:
CPU 1: A -----------> B ----------> A -----------> B ---------->
So, for our purposes, parallelism can be thought of as a special case of concurrency
Source: Another answer here
Hope that helps.
"Concurrency" is when there are multiple things in progress.
"Parallelism" is when concurrent things are progressing at the same time.
Examples of concurrency without parallelism:
Multiple threads on a single core.
Multiple messages in a Win32 message queue.
Multiple SqlDataReaders on a MARS connection.
Multiple JavaScript promises in a browser tab.
Note, however, that the difference between concurrency and parallelism is often a matter of perspective. The above examples are non-parallel from the perspective of (observable effects of) executing your code. But there is instruction-level parallelism even within a single core. There are pieces of hardware doing things in parallel with CPU and then interrupting the CPU when done. GPU could be drawing to screen while you window procedure or event handler is being executed. The DBMS could be traversing B-Trees for the next query while you are still fetching the results of the previous one. Browser could be doing layout or networking while your Promise.resolve() is being executed. Etc, etc...
So there you go. The world is as messy as always ;)
The simplest and most elegant way of understanding the two in my opinion is this. Concurrency allows interleaving of execution and so can give the illusion of parallelism. This means that a concurrent system can run your Youtube video alongside you writing up a document in Word, for example. The underlying OS, being a concurrent system, enables those tasks to interleave their execution. Because computers execute instructions so quickly, this gives the appearance of doing two things at once.
Parallelism is when such things really are in parallel. In the example above, you might find the video processing code is being executed on a single core, and the Word application is running on another. Note that this means that a concurrent program can also be in parallel! Structuring your application with threads and processes enables your program to exploit the underlying hardware and potentially be done in parallel.
Why not have everything be parallel then? One reason is because concurrency is a way of structuring programs and is a design decision to facilitate separation of concerns, whereas parallelism is often used in the name of performance. Another is that some things fundamentally cannot fully be done in parallel. An example of this would be adding two things to the back of a queue - you cannot insert both at the same time. Something must go first and the other behind it, or else you mess up the queue. Although we can interleave such execution (and so we get a concurrent queue), you cannot have it parallel.
Hope this helps!
"Concurrent" is doing things -- anything -- at the same time. They could be different things, or the same thing. Despite the accepted answer, which is lacking, it's not about "appearing to be at the same time." It's really at the same time. You need multiple CPU cores, either using shared memory within one host, or distributed memory on different hosts, to run concurrent code. Pipelines of 3 distinct tasks that are concurrently running at the same time are an example: Task-level-2 has to wait for units completed by task-level-1, and task-level-3 has to wait for units of work completed by task-level-2. Another example is concurrency of 1-producer with 1-consumer; or many-producers and 1-consumer; readers and writers; et al.
"Parallel" is doing the same things at the same time. It is concurrent, but furthermore it is the same behavior happening at the same time, and most typically on different data. Matrix algebra can often be parallelized, because you have the same operation running repeatedly: For example the column sums of a matrix can all be computed at the same time using the same behavior (sum) but on different columns. It is a common strategy to partition (split up) the columns among available processor cores, so that you have close to the same quantity of work (number of columns) being handled by each processor core. Another way to split up the work is bag-of-tasks where the workers who finish their work go back to a manager who hands out the work and get more work dynamically until everything is done. Ticketing algorithm is another.
Not just numerical code can be parallelized. Files too often can be processed in parallel. In a natural language processing application, for each of the millions of document files, you may need to count the number of tokens in the document. This is parallel, because you are counting tokens, which is the same behavior, for every file.
In other words, parallelism is when same behavior is being performed concurrently. Concurrently means at the same time, but not necessarily the same behavior. Parallel is a particular kind of concurrency where the same thing is happening at the same time.
Terms for example will include atomic instructions, critical sections, mutual exclusion, spin-waiting, semaphores, monitors, barriers, message-passing, map-reduce, heart-beat, ring, ticketing algorithms, threads, MPI, OpenMP.
Gregory Andrews' work is a top textbook on it: Multithreaded, Parallel, and Distributed Programming.
Concurrency can involve tasks run simultaneously or not (they can indeed be run in separate processors/cores but they can as well be run in "ticks"). What is important is that concurrency always refer to doing a piece of one greater task. So basically it's a part of some computations. You have to be smart about what you can do simultaneously and what not to and how to synchronize.
Parallelism means that you're just doing some things simultaneously. They don't need to be a part of solving one problem. Your threads can, for instance, solve a single problem each. Of course synchronization stuff also applies but from different perspective.
Parallelism:
Having multiple threads do similar task which are independent of each other in terms of data and resource that they require to do so. Eg: Google crawler can spawn thousands of threads and each thread can do it's task independently.
Concurrency:
Concurrency comes into picture when you have shared data, shared resource among the threads. In a transactional system this means you have to synchronize the critical section of the code using some techniques like Locks, semaphores, etc.
Explanation from this source was helpful for me:
Concurrency is related to how an application handles multiple tasks it
works on. An application may process one task at at time
(sequentially) or work on multiple tasks at the same time
(concurrently).
Parallelism on the other hand, is related to how an application
handles each individual task. An application may process the task
serially from start to end, or split the task up into subtasks which
can be completed in parallel.
As you can see, an application can be concurrent, but not parallel.
This means that it processes more than one task at the same time, but
the tasks are not broken down into subtasks.
An application can also be parallel but not concurrent. This means
that the application only works on one task at a time, and this task
is broken down into subtasks which can be processed in parallel.
Additionally, an application can be neither concurrent nor parallel.
This means that it works on only one task at a time, and the task is
never broken down into subtasks for parallel execution.
Finally, an application can also be both concurrent and parallel, in
that it both works on multiple tasks at the same time, and also breaks
each task down into subtasks for parallel execution. However, some of
the benefits of concurrency and parallelism may be lost in this
scenario, as the CPUs in the computer are already kept reasonably busy
with either concurrency or parallelism alone. Combining it may lead to
only a small performance gain or even performance loss.
Concurrent programming regards operations that appear to overlap and is primarily concerned with the complexity that arises due to non-deterministic control flow. The quantitative costs associated with concurrent programs are typically both throughput and latency. Concurrent programs are often IO bound but not always, e.g. concurrent garbage collectors are entirely on-CPU. The pedagogical example of a concurrent program is a web crawler. This program initiates requests for web pages and accepts the responses concurrently as the results of the downloads become available, accumulating a set of pages that have already been visited. Control flow is non-deterministic because the responses are not necessarily received in the same order each time the program is run. This characteristic can make it very hard to debug concurrent programs. Some applications are fundamentally concurrent, e.g. web servers must handle client connections concurrently. Erlang is perhaps the most promising upcoming language for highly concurrent programming.
Parallel programming concerns operations that are overlapped for the specific goal of improving throughput. The difficulties of concurrent programming are evaded by making control flow deterministic. Typically, programs spawn sets of child tasks that run in parallel and the parent task only continues once every subtask has finished. This makes parallel programs much easier to debug. The hard part of parallel programming is performance optimization with respect to issues such as granularity and communication. The latter is still an issue in the context of multicores because there is a considerable cost associated with transferring data from one cache to another. Dense matrix-matrix multiply is a pedagogical example of parallel programming and it can be solved efficiently by using Straasen's divide-and-conquer algorithm and attacking the sub-problems in parallel. Cilk is perhaps the most promising language for high-performance parallel programming on shared-memory computers (including multicores).
Copied from my answer: https://stackoverflow.com/a/3982782

Set priority of PPL thread groups

I have a scenario where some functions need to complete as quickly as possible and be given computation resources at the expense of other tasks (i.e. they are high-priority). Specifically, graphics rendering, and any tasks that are spawned for rendering should run as quickly as possible but do not consume the full CPU capacity. Simultaneously, I want to fill empty cycles of the CPU with other work that is not as time-critical and make sure not to steal cycles from the rendering tasks.
The basic idea is fairly simple, but I cannot figure out how to do what I want through PPL. I have found how to set the default scheduler to different priorities, but I don't want to globally change the priority. Rather, I want to have two distinct scheduling policies that I can add tasks to at any time.
The ideal situation is if I could create two task_group instances with different priorities and add tasks to the relevant group as needed, but I don't see how to do that. I linked the most relevant documentation I found, which does what I want, but uses agents in a way that leaves me unsure how to do the simple action of just adding a task. I would also rather not add the complexity of agents and message passing if I can use the basic facilities in PPL.
https://msdn.microsoft.com/en-us/library/dd984038.aspx
It is also important that I can ensure that any sub-tasks spawned from a thread inherit the priority of the parent. Specifically, I call parallel_for from both high and low priority tasks and the parallel_for blocks should keep the same priority.
The task constructor (and create_task function) can take a task_options parameter with a custom scheduler.
https://msdn.microsoft.com/en-us/library/dn237306.aspx

statisics for randomized task on multiple cores

Consider the time for completing a task on a processor core is a distribution with mean m and standard deviation s. If the same task runs on n cores, what is the mean and standard deviation of the time it takes to complete the task? (the task is finished when one of the cores finishes the task)
This is more of a statistics question, than anything else. Without information on the distribution function of the time t a single task needs to complete, I could only give you a hint: You need to calculate the distribution function of the minimum of t for n of your tasks, as seen here. Using that you can then calculate the mean and the standard deviation.
PS: Is this homework?
EDIT:
Whether - and how much - it's worth to use multiple cores, depends on several things:
What you need to do. If you have to run the same program with different inputs, launching multiple instances makes a lot of sense. It might not cut down the overall time down to 1/n and each experiment will still need at least as much time as before, but the time needed for the whole series will be signigicantly less.
If on the other hand, you are hoping to run the same task with e.g. a different seed and keep the one that converges the fastest, you will probably gain far less, as estimated by the first part of my answer.
How well you have parallelized your tasks. n completely independent tasks is the ideal scenario. n threads with multiple synchronization points etc are not going to be near as efficient.
How well your hardware can handle multiple tasks. For example if each of these tasks needs a lot of memory, it will probably be faster to use a single core only, than forcing the system to use the swap space/pagefile/whatever your OS calls it by running multiple instances at once.

Check number of idle cores when creating .Net 4.0 Parallel Task

My question might sound a bit naive but I'm pretty new with multi-threaded programming.
I'm writing an application which processes incoming external data. For each data that arrives a new task is created in the following way:
System.Threading.Tasks.Task.Factory.StartNew(() => methodToActivate(data));
The items of data arrive very fast (each second, half second, etc...), so many tasks are created. Handling each task might take around a minute. When testing it I saw that the number of threads is increasing all the time. How can I limit the number of tasks created, so the number of actual working threads is stable and efficient. My computer is only dual core.
Thanks!
One of your issues is that the default scheduler sees tasks that last for a minute and makes the assumption that they are blocked on another tasks that have yet to be executed. To try and unblock things it schedules more pending tasks, hence the thread growth. There are a couple of things you can do here:
Make your tasks shorter (probably not an option).
Write a scheduler that deals with this scenario and doesn't add more threads.
Use SetMaxThreads to prevent
unbounded thread pool growth.
See the section on Thread Injection here:
http://msdn.microsoft.com/en-us/library/ff963549.aspx
You should look into using the producer/consumer pattern with a BlockingCollection<T> around a ConcurrentQueue<T> where you set the BoundedCapacity to something that makes sense given the characteristics of your workload. You can make your BoundedCapacity configurable and then tweak as you run through some profiling sessions to find the sweet spot.
While it's true that the TPL will take care of queueing up the tasks you create, creating too many tasks does not come without penalties. Also, what's the point in producing more work than you can consume? You want to produce enough work that the consumers will never be starved, but you don't want to get to far ahead of yourself because that's just wasting resources and potentially stealing those very same resources from your consumers.
You can create a custom TaskScheduler for the Task Parallel library and then schedule tasks on that by passing an instance of it to the TaskFactory constructor.
Here's one example of how to do that: Task Scheduler with a maximum degree of parallelism.

Is Work Stealing always the most appropriate user-level thread scheduling algorithm?

I've been investigating different scheduling algorithms for a thread pool I am implementing. Due to the nature of the problem I am solving I can assume that the tasks being run in parallel are independent and do not spawn any new tasks. The tasks can be of varying sizes.
I went immediately for the most popular scheduling algorithm "work stealing" using lock-free deques for the local job queues, and I am relatively happy with this approach. However I'm wondering whether there are any common cases where work-stealing is not the best approach.
For this particular problem I have a good estimate of the size of each individual task. Work-stealing does not make use of this information and I'm wondering if there is any scheduler which will give better load-balancing than work-stealing with this information (obviously with the same efficiency).
NB. This question ties up with a previous question.
I'd distribute the tasks upfront. With the information of their estimated running time you can distribute them into individual queues, for each thread one.
Distributing the tasks is basically the knapsack problem, each queue should take the same amount of time.
You should add some logic to modify the queues while they run. For example a re-distribution should occur after the estimated running time differs by a certain amount from the real running time.
It is true that work-stealing scheduler does not use that information, but it is because it does not depend on it to provide the theoretical limits it does (for example, the memory it uses, the expected total communication among workers and also the expected time to execute a fully strict computation as you can read here: http://supertech.csail.mit.edu/papers/steal.pdf)
One interesting paper (that I hope you can access: http://dl.acm.org/citation.cfm?id=2442538) actually uses bounded execution times to provide formal proofs (that try to be as close to the original work-stealing bounds as possible).
And yes, there are cases in which work-stealing does not perform optimally (for example, unbalanced tree searches and other particular cases). But for those cases, optimizations have been made (for example by allowing the steal of half of the victim's deque, instead of taking only one task: http://dl.acm.org/citation.cfm?id=571876).

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