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• Graph drawing for the Web 2.0

  - by tokel

  Hi. There are a lot of chart drawing libraries out there, but what I am looking for is an interactive(!) graph (nodes and edges) drawing library. At best some kind of AJAX, but I am also open for other technologies (Java, Flash). However I would really prefer an AJAX implementation. Also only Open Source framework suggestions please (I already know about yFiles). The thing I have in mind is a bit like GWTUML. That is quite nice already, but misses an API for their graph drawing. It seems that it is an custom implementation for their product. Also some layout algorithms would be nice. Is there really no library around for that task? I wonder a bit as there are so many chart libraries available. Let me emphasize again (seems to be necessary cause of the first two comments): I am NOT looking for another chart library! Regards, Kai P.S. Things I know about already: JUNG (Java), Prefuse (Java), GINY (Java), yFiles (AJAX, but not Open Source). Just another graph library I found (Javascript, not sure if it is still maintained): Graph Gear

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• Why is my multithreaded Java program not maxing out all my cores on my machine?

  - by James B

  Hi, I have a program that starts up and creates an in-memory data model and then creates a (command-line-specified) number of threads to run several string checking algorithms against an input set and that data model. The work is divided amongst the threads along the input set of strings, and then each thread iterates the same in-memory data model instance (which is never updated again, so there are no synchronization issues). I'm running this on a Windows 2003 64-bit server with 2 quadcore processors, and from looking at Windows task Manager they aren't being maxed-out, (nor are they looking like they are being particularly taxed) when I run with 10 threads. Is this normal behaviour? It appears that 7 threads all complete a similar amount of work in a similar amount of time, so would you recommend running with 7 threads instead? Should I run it with more threads?...Although I assume this could be detrimental as the JVM will do more context switching between the threads. Alternatively, should I run it with fewer threads? Alternatively, what would be the best tool I could use to measure this?...Would a profiling tool help me out here - indeed, is one of the several profilers better at detecting bottlenecks (assuming I have one here) than the rest? Note, the server is also running SQL Server 2005 (this may or may not be relevant), but nothing much is happening on that database when I am running my program. Note also, the threads are only doing string matching, they aren't doing any I/O or database work or anything else they may need to wait on. Thanks in advance, -James

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• A function where small changes in input always result in large changes in output

  - by snowlord

  I would like an algorithm for a function that takes n integers and returns one integer. For small changes in the input, the resulting integer should vary greatly. Even though I've taken a number of courses in math, I have not used that knowledge very much and now I need some help... An important property of this function should be that if it is used with coordinate pairs as input and the result is plotted (as a grayscale value for example) on an image, any repeating patterns should only be visible if the image is very big. I have experimented with various algorithms for pseudo-random numbers with little success and finally it struck me that md5 almost meets my criteria, except that it is not for numbers (at least not from what I know). That resulted in something like this Python prototype (for n = 2, it could easily be changed to take a list of integers of course): import hashlib def uniqnum(x, y): return int(hashlib.md5(str(x) + ',' + str(y)).hexdigest()[-6:], 16) But obviously it feels wrong to go over strings when both input and output are integers. What would be a good replacement for this implementation (in pseudo-code, python, or whatever language)?

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• Bored with CS. What can I study that will make an impact?

  - by Eric Martinez

  So I'm going to an average university, majoring in CS. I haven't learned a damn thing and am in my third year. I've come to be really bored with studying CS. Initially, I was kind of misinformed and thought majoring in CS would make me a good "product creator". I make my money combining programming and business/marketing. But I have always done programming for the love of the art. I find things like algorithms interesting and want to be able to use CS to solve real world problems. I like the idea of bioinformatics and other hybrid studies. I'm not good enough, yet I hope, to really make a significant effort in those areas but I aspire to be. What are some other fields, open problems, and otherwise cool stuff to apply CS knowledge to in the real world? I'm really looking for something that will motivate me and re-excite me to continue studying CS. Edit: Like someone mentioned below. I am very interesting in the idea of being able to use computer science to help answer fundamental questions of life and the universe. But I'm not sure what is possible or how to begin.

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• Open source gravatar-like implementations?

  - by Tauren

  I'm already using gravatar icons for the users of my web service. However, I'm finding several problems with this approach: Only a small percentage of the users take the time to set up a gravatar profile. My users are not tech-savvy, but would be likely to add a dedicated photo to my site. Users of my service are encouraged to use images that depict them in proper uniform for the industry my service relates to. They wouldn't want that same picture to be used for personal purposes throughout the internet. They would not take the time or effort to manage a separate email address and gravatar account just to have an "in-uniform" profile photo for my service. Before I implement my own profile image feature, I was wondering if there are any open-source solutions that I could leverage with similar features to gravatar. Specifically: The ability to display any size thumbnail (up to 512px would be fine) Takes care of caching different sized thumbnails Has support for something like identicons, preferably pluggable with different style algorithms (monsters, etc.), even better if I can customize these Ability to fall-back to gravatar if no photo found Does anything like this exist? I haven't found it yet if it does.

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• Solving problems involving more complex data structures with CUDA

  - by Nils

  So I read a bit about CUDA and GPU programming. I noticed a few things such that access to global memory is slow (therefore shared memory should be used) and that the execution path of threads in a warp should not diverge. I also looked at the (dense) matrix multiplication example, described in the programmers manual and the nbody problem. And the trick with the implementation seems to be the same: Arrange the calculation in a grid (which it already is in case of the matrix mul); then subdivide the grid into smaller tiles; fetch the tiles into shared memory and let the threads calculate as long as possible, until it needs to reload data from the global memory into shared memory. In case of the nbody problem the calculation for each body-body interaction is exactly the same (page 682): bodyBodyInteraction(float4 bi, float4 bj, float3 ai) It takes two bodies and an acceleration vectors. The body vector has four components it's position and the weight. When reading the paper, the calculation is understood easily. But what is if we have a more complex object, with a dynamic data structure? For now just assume that we have an object (similar to the body object presented in the paper) which has a list of other objects attached and the number of objects attached is different in each thread. How could I implement that without having the execution paths of the threads to diverge? I'm also looking for literature which explains how different algorithms involving more complex data structures can be effectively implemented in CUDA.

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• Any book on designing and implementing a CRPG engine?

  - by Fabzter

  Hi! First, let me tell you, I am not really interested in making my own rpg engine (at least not in the near future, hehe), but I do feel like I want to understand the internals of how a rpg engine works. Why? Well, because I like to read about programming and design, It keeps me motivated and excited, and because I know I will learn a lot, for, even when I have been programming for some years now, I never stop considering myself an ignorant... there are simply SO many things involving a game engine (specially rpg ones, like branching storylines, and items and economics!) I'm eager to know. I've been searching (and thus, finding) lots of info online, but it is never focused in what I'm interested (most of it talks about the mathematics and AI algorithms implementation, which I know quite well), which is the design of overall structure, patterns, scripting engine, decision engine... damn, so many things I can't even imagine, since I've never done any game programming. I hope you know have an idea of how I feel, and how I want to learn for the sake of learning, and why would I want you to tell me if you know if there exist books touching the topics that interest me the most.

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• simple Java "service provider frameworks"?

  - by Jason S

  I refer to "service provider framework" as discussed in Chapter 2 of Effective Java, which seems like exactly the right way to handle a problem I am having, where I need to instantiate one of several classes at runtime, based on a String to select which service, and an Configuration object (essentially an XML snippet): But how do I get the individual service providers (e.g. a bunch of default providers + some custom providers) to register themselves? interface FooAlgorithm { /* methods particular to this class of algorithms */ } interface FooAlgorithmProvider { public FooAlgorithm getAlgorithm(Configuration c); } class FooAlgorithmRegistry { private FooAlgorithmRegistry() {} static private final Map<String, FooAlgorithmProvider> directory = new HashMap<String, FooAlgorithmProvider>(); static public FooAlgorithmProvider getProvider(String name) { return directory.get(serviceName); } static public boolean registerProvider(String name, FooAlgorithmProvider provider) { if (directory.containsKey(name)) return false; directory.put(name, provider); return true; } } e.g. if I write custom classes MyFooAlgorithm and MyFooAlgorithmProvider to implement FooAlgorithm, and I distribute them in a jar, is there any way to get registerProvider to be called automatically, or will my client programs that use the algorithm have to explicitly call FooAlgorithmRegistry.registerProvider() for each class they want to use?

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• Mathematics for Computer Science Students

  - by Ender

  To cut a long story short, I am a CS student that has received no formal Post-16 Maths education for years. Right now even my Algebra is extremely rusty and I have a couple of months to shape up my skills. I've got a couple of video lectures in my bookmarks, consisting of: Pre-Calculus Algebra Calculus Probability Introduction to Statistics Differential Equations Linear Algebra My aim as of today is to be able to read the CLRS book Introduction to Algorithms and be able to follow the Mathematical notation in that, as well as being able to confidently read and back-up any arguments written in Mathematical notation. Aside from these video lectures, can anyone recommend any good books to help teach someone wishing to go from a low-foundation level to a more advanced level of Mathematics? Just as a note, I've taken a first-year module in Analytical Modelling, so I understand some of the basic concepts of Discrete Mathematics. EDIT: Just a note to those that are looking to learn Linear Algebra using the Video Lectures I have posted up. Peteris Krumins' Blog contains a run-through of these lecture notes as well as his own commentary and lecture notes, an invaluable resource for those looking to follow the lectures too.

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• Is there an algorithm to securely split a message into x parts requiring at least y parts to reassem

  - by Aaron

  Is there an algorithm to securely split a message into x parts requiring at least y parts to reassemble? Obviously, y <= x. An example: Say that I have a secret message that I only want to be read in the event of my death. As a way to ensure this, I give a fraction of the message to ten friends. Now, I can't guaranty that all my friends will be able to put their messages together to recover the original. So, I construct each message fraction in such a way so as to only require any 5 friends to put their parts together to reconstruct the whole. However, owning less than 5 parts will not give anything away about the message, except possibly the length. My question is, is this possible? What algorithms might I look at to accomplish this? Clarification edit: The important part of this is the cryptographic strength. An attacker should not be able to recover the message, either in whole or in part with less than y parts.

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• Custom listbox sorting

  - by Arcadian

  I need to sort the data contained within a number of listboxes. The user will be able to select between two different types of sorting using radio boxes, one of which is checked by default on form load. I have created the IF statements needed in order to test whether the checked condition is true for that radio button. but i need some help to create the custom sort algorithms. Each list with contain similar looking data, the only difference in the prefix with which each line starts. For example each line in the first listbox starts with the prefix "G30" and the second listbox will be "G31" and so on. There are 10 listboxes in total (G30-G39 in terms of prefixes). The first search algorithm has to sort the lines by the number order of the first 13 chars. Example: This is how the data looks before sorting G35:45:58:11 JG07 G35:45:20:41 JG01 G35:58:20:21 JG03 G35:66:22:20 JG05 G35:45:85:21 JG02 G35:64:56:11 JG03 G35:76:35:11 JG02 G35:77:97:12 JG03 G35:54:29:11 JG01 G35:55:51:20 JG01 G35:76:24:20 JG06 G35:76:55:11 JG01 and this is how it should look after sorting G35:45:20:41 JG01 G35:45:58:11 JG07 G35:45:85:21 JG02 G35:54:29:11 JG01 G35:55:51:20 JG01 G35:58:20:21 JG03 G35:64:56:11 JG03 G35:66:22:20 JG05 G35:76:24:20 JG06 G35:76:35:11 JG02 G35:76:55:11 JG01 G35:77:97:12 JG03 as you can see, the prefixes are the same. so it is sorted, lowest first, by the next pair integers, then the next pair and the next but not by the value after "JG". the second sort algorithm will ignore the first 13 chars and sort by order of the value after "JG", highest first. any help? theres some rep in it for you :) thanks in advance

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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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• Calculate total batch upload transfer percent with limited information

  - by GONeale

  Hi there, I have a system which uploads to a server file by file and displays a progress bar on file upload progress, then underneath a second progress bar which I want to indicate percentage of batch complete across all files queued to upload. Information and algorithms I can work out are: Bytes Sent / Total Bytes To Send = First progress bar (eg. 512KB of 1024KB (50%)) That works fine. However supposing I have two other files left to upload, but both file sizes are unknown (as this is only known once the file is about to commence upload, at which point it is compressed and file size is determined) how would I go about making my third progress bar? I didn't think this would be possible as I would need "Total Bytes Sent" / "Total Bytes To Send", to replicate the logic of my first progress bar on a larger scale, however I did get a version working: "Current file number we are on" / "total number of files to send" returning the percentage through the batch, however obviously will not incrementally update and it's pretty crude. So on further thinking I thought if I could incorporate the current file % with this algorithm I could perhaps get the correct progress percentage of my batch's current point. I tried this algorithm, but alas to no such avail (sorry to any math heads, it's probably quite apparent why it won't work) ("Current file number we are on" / "total number of files to send") * ("Bytes Sent" / "Total Bytes To Send") For example I thought I was on the right track when testing with this example: 2/3 (2nd of 3rd file) = 66% (this is right so far) but then when I added * 0.20 (for indicating only 20% of 2nd file has uploaded) we went back to 13%. What I need is only a little over 33%! I did try the inverse at 0.80 and a (2/3 * (2/3 * 0.2)) Can this be done without knowing entire bytes in batch to upload? Please help! Thank you!

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• How to perform spatial partitioning in n-dimensions?

  - by kevin42

  I'm trying to design an implementation of Vector Quantization as a c++ template class that can handle different types and dimensions of vectors (e.g. 16 dimension vectors of bytes, or 4d vectors of doubles, etc). I've been reading up on the algorithms, and I understand most of it: here and here I want to implement the Linde-Buzo-Gray (LBG) Algorithm, but I'm having difficulty figuring out the general algorithm for partitioning the clusters. I think I need to define a plane (hyperplane?) that splits the vectors in a cluster so there is an equal number on each side of the plane. [edit to add more info] This is an iterative process, but I think I start by finding the centroid of all the vectors, then use that centroid to define the splitting plane, get the centroid of each of the sides of the plane, continuing until I have the number of clusters needed for the VQ algorithm (iterating to optimize for less distortion along the way). The animation in the first link above shows it nicely. My questions are: What is an algorithm to find the plane once I have the centroid? How can I test a vector to see if it is on either side of that plane?

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• Returning recursive ternary freaks out

  - by David Titarenco

  Hi, assume this following function: int binaryTree::findHeight(node *n) { if (n == NULL) { return 0; } else { return 1 + max(findHeight(n->left), findHeight(n->right)); } } Pretty standard recursive treeHeight function for a given binary search tree binaryTree. Now, I was helping a friend (he's taking an algorithms course), and I ran into some weird issue with this function that I couldn't 100% explain to him. With max being defined as max(a,b) ((a)>(b)?(a):(b)) (which happens to be the max definition in windef.h), the recursive function freaks out (it runs something like n^n times where n is the tree height). This obviously makes checking the height of a tree with 3000 elements take very, very long. However, if max is defined via templating, like std does it, everything is okay. So using std::max fixed his problem. I just want to know why. Also, why does the countLeaves function work fine, using the same programmatic recursion? int binaryTree::countLeaves(node *n) { if (n == NULL) { return 0; } else if (n->left == NULL && n->right == NULL) { return 1; } else { return countLeaves(n->left) + countLeaves(n->right); } } Is it because in returning the ternary function, the values a => countLeaves(n->left) and b => countLeaves(n->right) were recursively double called simply because they were the resultants? Thank you!

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• Proving that the distance values extracted in Dijkstra's algorithm is non-decreasing?

  - by Gail

  I'm reviewing my old algorithms notes and have come across this proof. It was from an assignment I had and I got it correct, but I feel that the proof certainly lacks. The question is to prove that the distance values taken from the priority queue in Dijkstra's algorithm is a non-decreasing sequence. My proof goes as follows: Proof by contradiction. Fist, assume that we pull a vertex from Q with d-value 'i'. Next time, we pull a vertex with d-value 'j'. When we pulled i, we have finalised our d-value and computed the shortest-path from the start vertex, s, to i. Since we have positive edge weights, it is impossible for our d-values to shrink as we add vertices to our path. If after pulling i from Q, we pull j with a smaller d-value, we may not have a shortest path to i, since we may be able to reach i through j. However, we have already computed the shortest path to i. We did not check a possible path. We no longer have a guaranteed path. Contradiction.

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• Media recommendation engine - Single user system - How to start

  - by Microkernel

  Hi guys, I want to implement a media recommendation engine. I saw a similar posts on this, but I think my requirements are bit different from those, so posting here. Here is the deal. I want to implement a recommendation engine for media players like VLC, which would be an engine that has to care for only single user. Like, it would be embedded in a media player on a PC which is typically used by single user. And it will start learning the likes and dislikes of the user and gradually learns what a user likes. Here it will not be able to find similar users for using their data for recommendation as its a single user system. So how to go about this? Or you can consider it as a recommendation engine that has to be put in say iPods, which has to learn about a single user and recommend music/Movies from the collections it has. I thought of start collecting the genre of music/movies (maybe even artist name) that user watches and recommend movies from the most watched Genre, but it look very crude, isn't it? So is there any algorithms I can use or any resources I can refer up to? Regards, MicroKernel :)

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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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• Is functional GUI programming possible?

  - by eman

  I've recently caught the FP bug (trying to learn Haskell), and I've been really impressed with what I've seen so far (first-class functions, lazy evaluation, and all the other goodies). I'm no expert yet, but I've already begun to find it easier to reason "functionally" than imperatively for basic algorithms (and I'm having trouble going back where I have to). The one area where current FP seems to fall flat, however, is GUI programming. The Haskell approach seems to be to just wrap imperative GUI toolkits (such as GTK+ or wxWidgets) and to use "do" blocks to simulate an imperative style. I haven't used F#, but my understanding is that it does something similar using OOP with .NET classes. Obviously, there's a good reason for this--current GUI programming is all about IO and side effects, so purely functional programming isn't possible with most current frameworks. My question is, is it possible to have a functional approach to GUI programming? I'm having trouble imagining what this would look like in practice. Does anyone know of any frameworks, experimental or otherwise, that try this sort of thing (or even any frameworks that are designed from the ground up for a functional language)? Or is the solution to just use a hybrid approach, with OOP for the GUI parts and FP for the logic? (I'm just asking out of curiosity--I'd love to think that FP is "the future," but GUI programming seems like a pretty large hole to fill.)

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• Need some ignition for learning Embedded Systems

  - by Rahul

  I'm very much interested in building applications for Embedded Devices. I'm in my 3rd year Electrical Engineering and I'm passionate about coding, algorithms, Linux OS, etc. And also by Googling I found out that Linux OS is one of the best OSes for Embedded devices(may be/may not be). I want to work for companies which work on mobile applications. I'm a newbie/naive to this domain & my skills include C/C++ & MySQL. I need help to get started in the domain of Embedded Systems; like how/where to start off, Hardware prerequisites, necessary programming skills, also what kind of Embedded Applications etc. I've heard of ARM, firmware, PIC Micorcontrollers; but I don't know anything & just need proper introduction about them. Thanx. P.S: I'm currently reading Bjarne Struotsup's lecture in C++ at Texas A&M University, and one chapter in it describes about Embedded Systems Programming.

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• Algorithm possible amounts (over)paid for a specific price, based on denominations

  - by Wrikken

  In a current project, people can order goods delivered to their door and choose 'pay on delivery' as a payment option. To make sure the delivery guy has enough change customers are asked to input the amount they will pay (e.g. delivery is 48,13, they will pay with 60,- (3*20,-)). Now, if it were up to me I'd make it a free field, but apparantly higher-ups have decided is should be a selection based on available denominations, without giving amounts that would result in a set of denominations which could be smaller. Example: denominations = [1,2,5,10,20,50] price = 78.12 possibilities: 79 (multitude of options), 80 (e.g. 4*20) 90 (e.g. 50+2*20) 100 (2*50) It's international, so the denominations could change, and the algorithm should be based on that list. The closest I have come which seems to work is this: for all denominations in reversed order (large=>small) add ceil(price/denomination) * denomination to possibles baseprice = floor(price/denomination) * denomination; for all smaller denominations as subdenomination in reversed order add baseprice + (ceil((price - baseprice) / subdenomination) * subdenomination) to possibles end for end for remove doubles sort Is seems to work, but this has emerged after wildly trying all kinds of compact algorithms, and I cannot defend why it works, which could lead to some edge-case / new countries getting wrong options, and it does generate some serious amounts of doubles. As this is probably not a new problem, and Google et al. could not provide me with an answer save for loads of pages calculating how to make exact change, I thought I'd ask SO: have you solved this problem before? Which algorithm? Any proof it will always work?

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• CUDA: When to use shared memory and when to rely on L1 caching?

  - by Roger Dahl

  After Compute Capability 2.0 (Fermi) was released, I've wondered if there are any use cases left for shared memory. That is, when is it better to use shared memory than just let L1 perform its magic in the background? Is shared memory simply there to let algorithms designed for CC < 2.0 run efficiently without modifications? To collaborate via shared memory, threads in a block write to shared memory and synchronize with __syncthreads(). Why not simply write to global memory (through L1), and synchronize with __threadfence_block()? The latter option should be easier to implement since it doesn't have to relate to two different locations of values, and it should be faster because there is no explicit copying from global to shared memory. Since the data gets cached in L1, threads don't have to wait for data to actually make it all the way out to global memory. With shared memory, one is guaranteed that a value that was put there remains there throughout the duration of the block. This is as opposed to values in L1, which get evicted if they are not used often enough. Are there any cases where it's better too cache such rarely used data in shared memory than to let the L1 manage them based on the usage pattern that the algorithm actually has?

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• Matlab - Propagate points orthogonally on to the edge of shape boundaries

  - by Graham

  Hi I have a set of points which I want to propagate on to the edge of shape boundary defined by a binary image. The shape boundary is defined by a 1px wide white edge. I also have the coordinates of these points stored in a 2 row by n column matrix. The shape forms a concave boundary with no holes within itself made of around 2500 points. I want to cast a ray from each point from the set of points in an orthogonal direction and detect at which point it intersects the shape boundary at. What would be the best method to do this? Are there some sort of ray tracing algorithms that could be used? Or would it be a case of taking orthogonal unit vector and multiplying it by a scalar and testing after multiplication if the end point of the vector is outside the shape boundary. When the end point of the unit vector is outside the shape, just find the point of intersection? Thank you very much in advance for any help!

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• What does O(log n) mean exactly?

  - by Andreas Grech

  I am currently learning about Big O Notation running times and amortized times. I understand the notion of O(n) linear time, meaning that the size of the input affects the growth of the algorithm proportionally...and the same goes for, for example, quadratic time O(n2) etc..even algorithms, such as permutation generators, with O(n!) times, that grow by factorials. For example, the following function is O(n) because the algorithm grows in proportion to its input n: f(int n) { int i; for (i = 0; i < n; ++i) printf("%d", i); } Similarly, if there was a nested loop, the time would be O(n2). But what exactly is O(log n)? For example, what does it mean to say that the height of a complete binary tree is O(log n)? I do know (maybe not in great detail) what Logarithm is, in the sense that: log10 100 = 2, but I cannot understand how to identify a function with a logarithmic time.

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• Algorithm(s) for rearranging simple symbolic algebraic expressions

  - by Gabe Johnson

  Hi, I would like to know if there is a straightforward algorithm for rearranging simple symbolic algebraic expressions. Ideally I would like to be able to rewrite any such expression with one variable alone on the left hand side. For example, given the input: m = (x + y) / 2 ... I would like to be able to ask about x in terms of m and y, or y in terms of x and m, and get these: x = 2*m - y y = 2*m - x Of course we've all done this algorithm on paper for years. But I was wondering if there was a name for it. It seems simple enough but if somebody has already cataloged the various "gotchas" it would make life easier. For my purposes I won't need it to handle quadratics. (And yes, CAS systems do this, and yes I know I could just use them as a library. I would like to avoid such a dependency in my application. I really would just like to know if there are named algorithms for approaching this problem.)

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