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• computing "node closure" of graph with removal

  - by Fakrudeen

  Given a directed graph, the goal is to combine the node with the nodes it is pointing to and come up with minimum number of these [lets give the name] super nodes. The catch is once you combine the nodes you can't use those nodes again. [first node as well as all the combined nodes - that is all the members of one super node] The greedy approach would be to pick the node with maximum out degree and combine that node with nodes it is pointing to and remove all of them. Do this every time with the nodes which are not removed yet from graph. The greedy is O(V), but this won't necessarily output minimum number super nodes. So what is the best algorithm to do this?

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• Find optimal 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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• Write a compiler for a language that looks ahead and multiple files?

  - by acidzombie24

  In my language I can use a class variable in my method when the definition appears below the method. It can also call methods below my method and etc. There are no 'headers'. Take this C# example. class A { public void callMethods() { print(); B b; b.notYetSeen(); public void print() { Console.Write("v = {0}", v); } int v=9; } class B { public void notYetSeen() { Console.Write("notYetSeen()\n"); } } How should I compile that? what i was thinking is: pass1: convert everything to an AST pass2: go through all classes and build a list of define classes/variable/etc pass3: go through code and check if there's any errors such as undefined variable, wrong use etc and create my output But it seems like for this to work I have to do pass 1 and 2 for ALL files before doing pass3. Also it feels like a lot of work to do until I find a syntax error (other than the obvious that can be done at parse time such as forgetting to close a brace or writing 0xLETTERS instead of a hex value). My gut says there is some other way. Note: I am using bison/flex to generate my compiler.

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• I need an algorithm to get the chromatic number of a graph.

  - by Carlos Sanchez

  Given the adjacency matrix of a graph, I need to obtain the chromatic number (minimum number of colours needed to paint every node of a graph so that adjacent nodes get different colours). Preferably it should be a java algorithm, and I don't care about performance. Thanks.

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• Windows Service with a Logon user set

  - by David.Chu.ca

  I have a service running in a box with Windows XP and a box of Server (2008). The service is configured as autmactic mode with a logon user/pwd set. The log on user is a local user. The service requires this user setting in order to run. The issue I have right now is that the box intermittently reboot itself. I am going to investigate what is causing the reboot (hardware or application). Regardless the reason, what I need is that the service should be able to recover itself into running state after the reboot. I think the configuration should be able achieve this goal since the user/pwd having been set and its mode being automatic. Do I need to log in as that user to bring the service back? (sometimes the reboot happens in the midnight) I am not sure if there is any difference between Windows XP and Windows Server (2008). The only thing I realize is that when there is a unexpected reboot, the Windows Server will prompt a dialog to explain the previous reboot. Will this prevent any automatic service running or the service will run only the reason has been set?

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• How does a compiler initially compile itself?

  - by jdk

  I recently read the Mono C# compiler is able to compile itself. Cool. In the past I've heard of other languages doing the same. It twists my mind - seems like a chicken and egg problem. What comes first, second and third, etc?...

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• What is the exact problem with multiple inheritance?

  - by Totophil

  I can see people asking all the time whether multiple inheritance should be included into the next version of C# or Java and C++ folks, who are fortunate enough to have this ability, say that this is like giving someone a rope to eventually hang themselves. What’s the matter with the multiple inheritance? Are there any concrete samples?

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• I've got a ComboBox that's giving me grief in WPF using the MVVM pattern

  - by Mike

  Here's my code: <ComboBox Grid.Column="1" Grid.Row="9" ItemsSource="{Binding Path=PriorityEntries}" SelectedItem="{Binding Path=Priority,Mode=TwoWay}"/> The comboBox is bound properly with PriorityEntries, and when i change the value of the comboBox the "set" of the bound property(Priority) is called setting it to what it needs to be. However, when i close the UserControl that this combobox resides, it calls the set property again with a value of null and then sets what the selectedItem was to null. Why is the comboBox being bound again when I close the usercontrol. I tried setting the mode to OneTime, but that won't reflect any changes...

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• integer division properties

  - by aaa

  hi. does the following integer arithmetic property hold? (m/n)/l == m/(n*l) At first I thought I knew answer (does not hold), but now am not sure. Does it hold for all numbers or only for certain conditions, i.e. n > l?

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• Amazing families of algorithms over implicit graphs

  - by Diego de Estrada

  Dynamic programming is, almost by definition, to find a shortest/longest path on an implicit dag. Every DP algorithm just does this. An Holographic algorithm can be loosely described as something that counts perfect matchings in implicit planar graphs. So, my question is: are there any other families of algorithms that use well-known algorithms over implicit graphs to achieve a considerable speedup?

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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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• 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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• Big O complexity of simple for not always linear?

  - by i30817

  I'm sure most of you know that a nested loop has O(n^2) complexity if the function input size is n for(int i = 0; i < n; i++){ for(int j = 0; j < n; j++){ ... } } I think that this is similar, by a analogous argument, but i'm not sure can anyone confirm? for(int i = 0, max = n*n; i < max; i++{ ... } If so i guess that there is some kinds of code whose big O mapping is not immediately obvious besides recursion and subroutines.

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• Finding all cycles in graph

  - by nexeww

  How can I find (iterate over) ALL the cycles in a directed graph from/to a given node? For example, I want something like this: A->B->A A->B->C->A but not: B-C-B

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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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• How to set up that specific domains are tunneled to another server

  - by Peter Smit

  I am working at an university as research assistant. Often I would like to connect from home to university resources over http or ssh, but they are blocked from outside access. Therefore, they have a front-end ssh server where we can ssh into and from there to other hosts. For http access they advise to set up an ssh tunnel like this ssh -L 1234:proxyserver.university.fi:8080 publicsshserver.university.fi and put the proxy settings of your browser to point to port 1234 All nice and working, but I would not like to let all my other internet traffic go over this proxy server, and everytime I want to connect to the university I have to do this steps again. What would I like: - Set up a ssh tunnel everytime I log in my computer. I have a certificate, so no passwords are needed - Have a way to redirect some wildcard-domains always through the ssh-server first. So that when I type intra.university.fi in my browser, transparently the request is going through the tunnel. Same when I want to ssh into another resource within the university Is this possible? For the http part I think I maybe should set up my own local transparent proxy to have this easily done. How about the ssh part?

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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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• What hash function yields the shortest output?

  - by luvieere

  What is the shortest hash that can be obtained and why? What happens if you try to achieve a shorter one, is there a fixed limit or does it depend on the length of the hashed data and why?

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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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• 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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• 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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• Why are lists useful?

  - by David

  What would you use a list for that you couldn't use an array of objects for?

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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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