Ensure that a list of dependent tasks dont have cycles - algorithm

I want to make a CRUD app (SQL or document DB) for tasks: create them one at a time. Tasks may depend on one or more other tasks. Ideally this must be a directed acyclic graph.
How do I enforce that, when I create a new task (or modify the 'depends on'), there are no cycles? Its slow to load all the tasks to memory to traverse for cycles. Is there a better way to enforce them?
A simple way is to ensure that a task can depend only on previously created tasks. But this breaks in case we create task A, then we create task B which A depends on.

In the worst case, you'll definitely need to work with the whole graph - consider when there's a path from the new task through all the other tasks back to itself - you wouldn't be able to know this without processing the whole graph.
If you're primarily adding one task at a time, or modifying one relationship at a time, and the graph is fairly sparse (there aren't too many edges), one solution I can think of is to do a depth-first-search from the new task (perhaps in reverse, if that would have a smaller branching factor). If you get back to that task, you know there's a cycle. This would presumably result in only loading the required vertices one by one, which could be either a lot slower, or a lot faster, depending on how the data is stored (thus how long a single load would take), how many vertices need to be loaded in relation to the total number of vertices, and perhaps a few other factors.
If you make many changes at the same time, you're probably better off running a complete cycle detection algorithm on the graph.

Related

How is Monte Carlo Tree Search implemented in practice

I understand, to a certain degree, how the algorithm works. What I don't fully understand is how the algorithm is actually implemented in practice.
I'm interested in understanding what optimal approaches would be for a fairly complex game (maybe chess). i.e. recursive approach? async? concurrent? parallel? distributed? data structures and/or database(s)?
-- What type of limits would we expect to see on a single machine? (could we run concurrently across many cores... gpu maybe?)
-- If each branch results in a completely new game being played, (this could reach the millions) how do we keep the overall system stable? & how can we reuse branches already played?
recursive approach? async? concurrent? parallel? distributed? data structures and/or database(s)
In MCTS, there's not much of a point in a recursive implementation (which is common in other tree search algorithms like the minimax-based ones), because you always go "through" a game in sequences from current game state (root node) till game states you choose to evaluate (terminal game states, unless you choose to go with a non-standard implementation using a depth limit on the play-out phase and a heuristic evaluation function). The much more obvious implementation using while loops is just fine.
If it's your first time implementing the algorithm, I'd recommend just going for a single-threaded implementation first. It is a relatively easy algorithm to parallelize though, there are multiple papers on that. You can simply run multiple simulations (where simulation = selection + expansion + playout + backpropagation) in parallel. You can try to make sure everything gets updated cleanly during backpropagation, but you can also simply decide to not use any locks / blocking etc. at all, there's already enough randomness in all the simulations anyway so if you lose information from a couple of simulations here and there due to naively-implemented parallelization it really doesn't hurt too much.
As for data structures, unlike algorithms like minimax, you actually do need to explicitly build a tree and store it in memory (it is built up gradually as the algorithm is running). So, you'll want a general tree data structure with Nodes that have a list of successor / child Nodes, and also a pointer back to the parent Node (required for backpropagation of simulation outcomes).
What type of limits would we expect to see on a single machine? (could we run concurrently across many cores... gpu maybe?)
Running across many cores can be done yes (see point about parallelization above). I don't see any part of the algorithm being particularly well-suited for GPU implementations (there are no large matrix multiplications or anything like that), so GPU is unlikely to be interesting.
If each branch results in a completely new game being played, (this could reach the millions) how do we keep the overall system stable? & how can we reuse branches already played?
In the most commonly-described implementation, the algorithm creates only one new node to store in memory per iteration/simulation in the expansion phase (the first node encountered after the Selection phase). All other game states generated in the play-out phase of the same simulation do not get any nodes to store in memory at all. This keeps memory usage in check, it means your tree only grows relatively slowly (at a rate of 1 node per simulation). It does mean you get slightly less re-usage of previously-simulated branches, because you don't store everything you see in memory. You can choose to implement a different strategy for the expansion phase (for example, create new nodes for all game states generated in the play-out phase). You'll have to carefully monitor memory usage if you do this though.

What data structure and algorithms to use to optimize concurrent jobs?

I have a series of file-watchers that trigger jobs. The file-watchers look, every fixed interval of time, in their list and, if they find a file, they trigger a job. If not, they wait, coming back after that mentioned interval.
Some jobs are dependent on others, so running them in a proper order and with proper parallelism would be a good optimization. But I do not want to think about this myself.
What data structure and algorithms should I use to ask a computer to tell me what job to assign to what file-watcher (and in what order to put them)?
As input, I have the dependencies between the jobs, the arrival time of files for each job and a number of watchers. (For starter, I will pretend each jobs takes same amount of time). How do I spread the jobs between the watchers, to avoid unnecessary waiting gaps and to obtain faster run time?
(I am looking forward tackling this optimization in an algorithmic way, but would like to start with some expert advice)
EDIT : so far I understood the fact the I need a DAG (Directed acyclic graph) to represent the dependencies and that I need to play with Topological sorting in order to optimize. But this responds with a one execution line, one thread. What if I have more, say 7?

How to handle multiple optimal edit paths implementing Needleman-Wunsche algorithm?

Trying to implement Needleman-Wunsche algorithm for biological sequences comparison. In some circumstances there exist multiple optimal edit paths.
What is the common practice in bio-seq-compare tools handling this? Any priority/preferences among substitute/insert/deletion?
If I want to keep multiple edit paths in memory, any data structure is recommended? Or generally, how to store paths with branches and merges?
Any comments appreciated.
If two paths are have identical scores, that means that the likelihood of them is the same no matter which kinds of operations they used. Priority for substitutions vs. insertions or deletions has already been handled in getting that score. So if two scores are the same, common practice is to break the tie arbitrarily.
You should be able to handle this by recording all potential cells that you could have arrived at the current one from in your traceback matrix. Then, during traceback, start a separate branch whenever you come to a branching point. In order to allow for merges too, store some additional data about each cell (how will depend on what language you're using) indicating how many different paths left from it. Then, during traceback, wait at a given cell until that number of paths have arrived back at it, and then merge them into one. You can either be following the different branches with true parallel processing, or by just alternating which one you are advancing.
Unless you have an a reason to prefer one input sequence over the other in advance it should not matter.
Otherwise you might consider seq_a as the vertical axis and seq_b as the horizontal axis then always choose to step in your preferred direction if there is a tie to break ... but I'm not convincing myself there is any difference to the to alignment assuming one favors one of the starting sequences over the other
As a lot of similar algorithms, Needleman-Wunsche one is just a task of finding the shortest way into a graph (square grid in this case). So I would use A* for defining a sequence & store the possible paths as a dictionary with nodes passes.

How to traverse a graph in parallel with 2 or n processes

I am searching on the internet in order to find some algorithm that can traverse a graph in parallel using 2 or n processes without one process stepping into a previously visited node of the other so I can speed up the total scanning task of the whole graph, but I can't find anything. Is there any algorithm that can help me do such task in parallel? is it worth it?
Note :
n processes share the same memory of visited and tovisit nodes
thank you
You can try the consumer-producer model for traversing the graph - but with some modifications from the pure model:
Read and write to the queue in blocks, rather then element at a time, also update the visited set in blocks. It will save you the synchronization time - which will be needed to be done less frequently.
When you do modify the queue (and visited set) - you should do some extra work to make sure you don't add data that was already visited since the set was last checked.
Note that with this approach - you are more then likely to search some vertices a few times - but you can bound it with the frequency the queue and visited set are updated.
Will it worth it? It is hard to say in these things - it is dependent on a lot of things (graph structure, size, queue implementation, ...).
You should run a few tests and try to fine tune the parameter for "how often to update", and check which is better empirically. You should use statistical tools (wilcoxon test is the de-facto standard for this usually) and determine if one is better then the other.
Unless the bulk of the time is spent on actual traversal, you could traverse the graph on a single thread, and queue up the work at each node to be processed in parallel from multiple processes. Once you have work in a queue, you can use a simple producer-consumer model.

Database for brute force solving board games

A few years back, researchers announced that they had completed a brute-force comprehensive solution to checkers.
I have been interested in another similar game that should have fewer states, but is still quite impractical to run a complete solver on in any reasonable time frame. I would still like to make an attempt, as even a partial solution could give valuable information.
Conceptually I would like to have a database of game states that has every known position, as well as its succeeding positions. One or more clients can grab unexplored states from the database, calculate possible moves, and insert the new states into the database. Once an endgame state is found, all states leading up to it can be updated with the minimax information to build a decision trees. If intelligent decisions are made to pick probable branches to explore, I can build information for the most important branches, and then gradually build up to completion over time.
Ignoring the merits of this idea, or the feasability of it, what is the best way to implement such a database? I made a quick prototype in sql server that stored a string representation of each state. It worked, but my solver client ran very very slow, as it puled out one state at a time and calculated all moves. I feel like I need to do larger chunks in memory, but the search space is definitely too large to store it all in memory at once.
Is there a database system better suited to this kind of job? I will be doing many many inserts, a lot of reads (to check if states (or equivalent states) already exist), and very few updates.
Also, how can I parallelize it so that many clients can work on solving different branches without duplicating too much work. I'm thinking something along the lines of a program that checks out an assignment, generates a few million states, and submits it back to be integrated into the main database. I'm just not sure if something like that will work well, or if there is prior work on methods to do that kind of thing as well.
In order to solve a game, what you really need to know per a state in your database is what is its game-theoretic value, i.e. if it's win for the player whose turn it is to move, or loss, or forced draw. You need two bits to encode this information per a state.
You then find as compact encoding as possible for that set of game states for which you want to build your end-game database; let's say your encoding takes 20 bits. It's then enough to have an array of 221 bits on your hard disk, i.e. 213 bytes. When you analyze an end-game position, you first check if the corresponding value is already set in the database; if not, calculate all its successors, calculate their game-theoretic values recursively, and then calculate using min/max the game-theoretic value of the original node and store in database. (Note: if you store win/loss/draw data in two bits, you have one bit pattern left to denote 'not known'; e.g. 00=not known, 11 = draw, 10 = player to move wins, 01 = player to move loses).
For example, consider tic-tac-toe. There are nine squares; every one can be empty, "X" or "O". This naive analysis gives you 39 = 214.26 = 15 bits per state, so you would have an array of 216 bits.
You undoubtedly want a task queue service of some sort, such as RabbitMQ - probably in conjunction with a database which can store the data once you've calculated it. Alternately, you could use a hosted service like Amazon's SQS. The client would consume an item from the queue, generate the successors, and enqueue those, as well as adding the outcome of the item it just consumed to the queue. If the state is an end-state, it can propagate scoring information up to parent elements by consulting the database.
Two caveats to bear in mind:
The number of items in the queue will likely grow exponentially as you explore the tree, with each work item causing several more to be enqueued. Be prepared for a very long queue.
Depending on your game, it may be possible for there to be multiple paths to the same game state. You'll need to check for and eliminate duplicates, and your database will need to be structured so that it's a graph (possibly with cycles!), not a tree.
The first thing that popped into my mind is the Linda-style of a shared 'whiteboard', where different processes can consume 'problems' off the whiteboard, add new problems to the whiteboard, and add 'solutions' to the whiteboard.
Perhaps the Cassandra project is the more modern version of Linda.
There have been many attempts to parallelize problems across distributed computer systems; Folding#Home provides a framework that executes binary blob 'cores' to solve protein folding problems. Distributed.net might have started the modern incarnation of distributed problem solving, and might have clients that you can start from.

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