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  • finding shortest valid path in a colored-edge graphs

    - by user1067083
    Given a directed graph G, with edges colored either green or purple, and a vertex S in G, I must find an algorithm that finds the shortest path from s to each vertex in G so the path includes at most two purple edges (and green as much as needed). I thought of BFS on G after removing all the purple edges, and for every vertex that the shortest path is still infinity, do something to try to find it, but I'm kinda stuck, and it takes alot of the running time as well... Any other suggestions? Thanks in advance

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  • How to analyze the efficiency of this algorithm Part 2

    - by Leonardo Lopez
    I found an error in the way I explained this question before, so here it goes again: FUNCTION SEEK(A,X) 1. FOUND = FALSE 2. K = 1 3. WHILE (NOT FOUND) AND (K < N) a. IF (A[K] = X THEN 1. FOUND = TRUE b. ELSE 1. K = K + 1 4. RETURN Analyzing this algorithm (pseudocode), I can count the number of steps it takes to finish, and analyze its efficiency in theta notation, T(n), a linear algorithm. OK. This following code depends on the inner formulas inside the loop in order to finish, the deal is that there is no variable N in the code, therefore the efficiency of this algorithm will always be the same since we're assigning the value of 1 to both A & B variables: 1. A = 1 2. B = 1 3. UNTIL (B > 100) a. B = 2A - 2 b. A = A + 3 Now I believe this algorithm performs in constant time, always. But how can I use Algebra in order to find out how many steps it takes to finish?

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  • Find optimal/good-enough strategy and AI for the game 'Proximity'?

    - by smci
    'Proximity' is a strategy game of territorial domination similar to Othello, Go and Risk. Two players, uses a 10x12 hex grid. Game invented by Brian Cable in 2007. Seems to be a worthy game for discussing a) optimal algorithm then b) how to build an AI. Strategies are going to be probabilistic or heuristic-based, due to the randomness factor, and the insane branching factor (20^120). So it will be kind of hard to compare objectively. A compute time limit of 5s per turn seems reasonable. Game: Flash version here and many copies elsewhere on the web Rules: here Object: to have control of the most armies after all tiles have been placed. Each turn you received a randomly numbered tile (value between 1 and 20 armies) to place on any vacant board space. If this tile is adjacent to any ally tiles, it will strengthen each tile's defenses +1 (up to a max value of 20). If it is adjacent to any enemy tiles, it will take control over them if its number is higher than the number on the enemy tile. Thoughts on strategy: Here are some initial thoughts; setting the computer AI to Expert will probably teach a lot: minimizing your perimeter seems to be a good strategy, to prevent flips and minimize worst-case damage like in Go, leaving holes inside your formation is lethal, only more so with the hex grid because you can lose armies on up to 6 squares in one move low-numbered tiles are a liability, so place them away from your main territory, near the board edges and scattered. You can also use low-numbered tiles to plug holes in your formation, or make small gains along the perimeter which the opponent will not tend to bother attacking. a triangle formation of three pieces is strong since they mutually reinforce, and also reduce the perimeter Each tile can be flipped at most 6 times, i.e. when its neighbor tiles are occupied. Control of a formation can flow back and forth. Sometimes you lose part of a formation and plug any holes to render that part of the board 'dead' and lock in your territory/ prevent further losses. Low-numbered tiles are obvious-but-low-valued liabilities, but high-numbered tiles can be bigger liabilities if they get flipped (which is harder). One lucky play with a 20-army tile can cause a swing of 200 (from +100 to -100 armies). So tile placement will have both offensive and defensive considerations. Comment 1,2,4 seem to resemble a minimax strategy where we minimize the maximum expected possible loss (modified by some probabilistic consideration of the value ß the opponent can get from 1..20 i.e. a structure which can only be flipped by a ß=20 tile is 'nearly impregnable'.) I'm not clear what the implications of comments 3,5,6 are for optimal strategy. Interested in comments from Go, Chess or Othello players. (The sequel ProximityHD for XBox Live, allows 4-player -cooperative or -competitive local multiplayer increases the branching factor since you now have 5 tiles in your hand at any given time, of which you can only play one. Reinforcement of ally tiles is increased to +2 per ally.)

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  • Calculate shortest path through a grocery store

    - by Bart
    Hi, I'm trying to find a way to find the shortest path through a grocery store, visiting a list of locations (shopping list). The path should start at a specified startposition and can end at multiple endpositions (there are multiple checkout counters). Also, I have some predefined constraints on the path, such as "item x on the shopping list needs to be the last, second last, or third last item on the path". There is a function that will return true or false for a given path. Finally, this needs to be calculated with limited cpu power (on a smartphone) and within a second or so. If this isn't possible, then an approximation to the optimal path is also ok. Is this possible? So far I think I need to start by calculating the distance between every item on the list using something like A* or Dijkstra's. After that, should I treat it like the travelling salesman problem? Because in my problem there is a specified startnode, specified endnodes, and some constraints, which are not in the travelling salesman problem. Any help would be appreciated :)

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  • Finding the Reachability Count for all vertices of a DAG

    - by ChrisH
    I am trying to find a fast algorithm with modest space requirements to solve the following problem. For each vertex of a DAG find the sum of its in-degree and out-degree in the DAG's transitive closure. Given this DAG: I expect the following result: Vertex # Reacability Count Reachable Vertices in closure 7 5 (11, 8, 2, 9, 10) 5 4 (11, 2, 9, 10) 3 3 (8, 9, 10) 11 5 (7, 5, 2, 9, 10) 8 3 (7, 3, 9) 2 3 (7, 5, 11) 9 5 (7, 5, 11, 8, 3) 10 4 (7, 5, 11, 3) It seems to me that this should be possible without actually constructing the transitive closure. I haven't been able to find anything on the net that exactly describes this problem. I've got some ideas about how to do this, but I wanted to see what the SO crowd could come up with.

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  • Can you find a pattern to sync files knowing only dates and filenames?

    - by Robert MacLean
    Imagine if you will a operating system that had the following methods for files Create File: Creates (writes) a new file to disk. Calling this if a file exists causes a fault. Update File: Updates an existing file. Call this if a file doesn't exist causes a fault. Read File: Reads data from a file. Enumerate files: Gets all files in a folder. Files themselves in this operating system only have the following meta data: Created Time: The original date and time the file was created, by the Create File method. Modified Time: The date and time the file was last modified by the Update File method. If the file has never been modified, this will equal the Create Time. You have been given the task of writing an application which will sync the files between two directories (lets call them bill and ted) on a machine. However it is not that simple, the client has required that The application never faults (see methods above). That while the application is running the users can add and update files and those will be sync'd next time the application runs. Files can be added to either the ted or bill directories. File names cannot be altered. The application will perform one sync per time it is run. The application must be almost entirely in memory, in other words you cannot create a log of filenames and write that to disk and then check that the next time. The exception to point 6 is that you can store date and times between runs. Each date/time is associated with a key labeled A through J (so you have 10 to use) so you can compare keys between runs. There is no way to catch exceptions in the application. Answer will be accepted based on the following conditions: First answer to meet all requirements will be accepted. If there is no way to meet all requirements, the answer which ensures the smallest amount of missed changes per sync will be accepted. A bounty will be created (100 points) as soon as possible for the prize. The winner will be selected one day before the bounty ends. Please ask questions in the comments and I will gladly update and refine the question on those.

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  • 3d symmetry search algorithm

    - by aaa
    this may be more appropriate for math overflow, but nevertheless: Given 3d structure (for example molecule), what is a good approach/algorithm to find symmetry (rotational/reflection/inversion/etc.)? I came up with brute force naive algorithm, but it seems there should be better approach. I am not so much interested in genetic algorithms as I would like best symmetry rather then almost the best symmetry link to website/paper would be great. thanks

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  • client-server syncing methodology [theoretical]

    - by Kenneth Ballenegger
    I'm in the progress of building an web-app that syncs with an iOS client. I'm currently tackling trying to figure out how to go about about syncing. I've come up with following two directions: I've got a fairly simple server web-app with a list of items. They are ordered by date modified and as such syncing the order does not matter. One direction I'm considering is to let the client deal with syncing. I've already got an API that lets the client get the data, as well as do certain actions on it, such as update, add or remove single items. I was considering: 1) on each sync asking the server for all items modified since the last successful sync and updating the local records based on what's returned by the server, and 2) building a persistent queue of create / remove / update requests on the client, and keeping them until confirmation by the server. The risk with this approach is that I'm basically asking each side to send changes to the other side, hoping it works smoothly, but risking a diversion at some point. This would probably be more bandwidth-efficient, though. The other direction I was considering was a more traditional model. I would have a "sync" process in which the client would send its whole list to the server (or a subset since last modified sync), the server would update the data on the server (by fixing conflicts by keeping the last modified item, and keeping deleted items with a deleted = 1 field), and the server would return an updated list of items (since last successful sync) which the client would then replace its data with. Thoughts?

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  • How is schoolbook long division an O(n^2) algorithm?

    - by eSKay
    Premise: This Wikipedia page suggests that the computational complexity of Schoolbook long division is O(n^2). Deduction: Instead of taking "Two n-digit numbers", if I take one n-digit number and one m-digit number, then the complexity would be O(n*m). Contradiction: Suppose you divide 100000000 (n digits) by 1000 (m digits), you get 100000, which takes six steps to arrive at. Now, if you divide 100000000 (n digits) by 10000 (m digits), you get 10000 . Now this takes only five steps. Conclusion: So, it seems that the order of computation should be something like O(n/m). Question: Who is wrong, me or Wikipedia, and where?

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  • How to draw a graph in LaTeX?

    - by Amir Rachum
    First of all, let me say I'm using LyX, though I have no problem using ERT. Secondly, what is the most simplest way to draw a simple graph like this in Latex? I've seen some documents with graphs and I've seen some examples, but I couldn't figure out how to just draw a simple graph - what packages do I need, etc?

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  • Complex behavior generated by simple computation

    - by Yuval A
    Stephen Wolfram gave a fascinating talk at TED about his work with Mathematica and Wolfram Alpha. Amongst other things, he pointed out how very simple computations can yield extremely complex behaviors. (He goes on to discuss his ambition for computing the entire physical universe. Say what you will, you gotta give the guy some credit for his wild ideas...) As an example he showed several cellular automata. What other examples of simple computations do you know of that yield fascinating results?

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  • Provable planarity of flowcharts

    - by Nikolaos Kavvadias
    Hi all I have a question: is there any reference (e.g. paper) with a proof of the planarity of flowchart layouts? Can anyone suggest an algorithm for generating flowchart (planar) layouts? I know that there are some code-to-flowchart tools out there, but i'm unaware of their internals. Thanks in advance -kavi

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  • How to minimize total cost of shortest path tree

    - by Michael
    I have a directed acyclic graph with positive edge-weights. It has a single source and a set of targets (vertices furthest from the source). I find the shortest paths from the source to each target. Some of these paths overlap. What I want is a shortest path tree which minimizes the total sum of weights over all edges. For example, consider two of the targets. Given all edge weights equal, if they share a single shortest path for most of their length, then that is preferable to two mostly non-overlapping shortest paths (fewer edges in the tree equals lower overall cost). Another example: two paths are non-overlapping for a small part of their length, with high cost for the non-overlapping paths, but low cost for the long shared path (low combined cost). On the other hand, two paths are non-overlapping for most of their length, with low costs for the non-overlapping paths, but high cost for the short shared path (also, low combined cost). There are many combinations. I want to find solutions with the lowest overall cost, given all the shortest paths from source to target. Does this ring any bells with anyone? Can anyone point me to relevant algorithms or analogous applications? Cheers!

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  • Can Haskell's Parsec library be used to implement a recursive descent parser with backup?

    - by Thor Thurn
    I've been considering using Haskell's Parsec parsing library to parse a subset of Java as a recursive descent parser as an alternative to more traditional parser-generator solutions like Happy. Parsec seems very easy to use, and parse speed is definitely not a factor for me. I'm wondering, though, if it's possible to implement "backup" with Parsec, a technique which finds the correct production to use by trying each one in turn. For a simple example, consider the very start of the JLS Java grammar: Literal: IntegerLiteral FloatingPointLiteral I'd like a way to not have to figure out how I should order these two rules to get the parse to succeed. As it stands, a naive implementation like this: literal = do { x <- try (do { v <- integer; return (IntLiteral v)}) <|> (do { v <- float; return (FPLiteral v)}); return(Literal x) } Will not work... inputs like "15.2" will cause the integer parser to succeed first, and then the whole thing will choke on the "." symbol. In this case, of course, it's obvious that you can solve the problem by re-ordering the two productions. In the general case, though, finding things like this is going to be a nightmare, and it's very likely that I'll miss some cases. Ideally, I'd like a way to have Parsec figure out stuff like this for me. Is this possible, or am I simply trying to do too much with the library? The Parsec documentation claims that it can "parse context-sensitive, infinite look-ahead grammars", so it seems like something like I should be able to do something here.

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  • Is information a subset of data?

    - by Jason Baker
    I apologize as I don't know whether this is more of a math question that belongs on mathoverflow or if it's a computer science question that belongs here. That said, I believe I understand the fundamental difference between data, information, and knowledge. My understanding is that information carries both data and meaning. One thing that I'm not clear on is whether information is data. Is information considered a special kind of data, or is it something completely different?

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  • Find all cycles in graph, redux

    - by Shadow
    Hi, I know there are a quite some answers existing on this question. However, I found none of them really bringing it to the point. Some argue that a cycle is (almost) the same as a strongly connected components (s. http://stackoverflow.com/questions/546655/finding-all-cycles-in-graph/549402#549402) , so one could use algorithms designed for that goal. Some argue that finding a cycle can be done via DFS and checking for back-edges (s. boost graph documentation on file dependencies). I now would like to have some suggestions on whether all cycles in a graph can be detected via DFS and checking for back-edges? My opinion is that it indeed could work that way as DFS-VISIT (s. pseudocode of DFS) freshly enters each node that was not yet visited. In that sense, each vertex exhibits a potential start of a cycle. Additionally, as DFS visits each edge once, each edge leading to the starting point of a cycle is also covered. Thus, by using DFS and back-edge checking it should indeed be possible to detect all cycles in a graph. Note that, if cycles with different numbers of participant nodes exist (e.g. triangles, rectangles etc.), additional work has to be done to discriminate the acutal "shape" of each cycle.

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  • What are logical and path queries

    - by NomeN
    I'm reading a paper which mentions that a language for refactoring has three specific requirements. functional features (like ML) logical queries (like Datalog) path queries (like Datalog) I know what they mean by functional features, but I'm not totally clear on the latter two and can't find a clear explanation either. Although I have a good idea after what I could find on the subjects, I need to be sure so here goes: Could the SO-community please clearly explain to me what logical queries and path queries are? Or at the very least what the people from the paper meant?

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  • Find all complete sub-graphs within a graph

    - by mvid
    Is there a known algorithm or method to find all complete sub-graphs within a graph? I have an undirected, unweighted graph and I need to find all subgraphs within it where each node in the subgraph is connected to each other node in the subgraph. Is there an existing algorithm for this?

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  • How do I compute the approximate entropy of a bit string?

    - by dreeves
    Is there a standard way to do this? Googling -- "approximate entropy" bits -- uncovers multiple academic papers but I'd like to just find a chunk of pseudocode defining the approximate entropy for a given bit string of arbitrary length. (In case this is easier said than done and it depends on the application, my application involves 16,320 bits of encrypted data (cyphertext). But encrypted as a puzzle and not meant to be impossible to crack. I thought I'd first check the entropy but couldn't easily find a good definition of such. So it seemed like a question that ought to be on StackOverflow! Ideas for where to begin with de-cyphering 16k random-seeming bits are also welcome...) See also this related question: http://stackoverflow.com/questions/510412/what-is-the-computer-science-definition-of-entropy

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