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• How to speed up calculation of length of longest common substring?

  - by eSKay

  I have two very large strings and I am trying to find out their Longest Common Substring. One way is using suffix trees (supposed to have a very good complexity, though a complex implementation), and the another is the dynamic programming method (both are mentioned on the Wikipedia page linked above). Using dynamic programming The problem is that the dynamic programming method has a huge running time (complexity is O(n*m), where n and m are lengths of the two strings). What I want to know (before jumping to implement suffix trees): Is it possible to speed up the algorithm if I only want to know the length of the common substring (and not the common substring itself)?

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• linear interpolation on 8bit microcontroller

  - by JB

  I need to do a linear interpolation over time between two values on an 8 bit PIC microcontroller (Specifically 16F627A but that shouldn't matter) using PIC assembly language. Although I'm looking for an algorithm here as much as actual code. I need to take an 8 bit starting value, an 8 bit ending value and a position between the two (Currently represented as an 8 bit number 0-255 where 0 means the output should be the starting value and 255 means it should be the final value but that can change if there is a better way to represent this) and calculate the interpolated value. Now PIC doesn't have a divide instruction so I could code up a general purpose divide routine and effectivly calculate (B-A)/(x/255)+A at each step but I feel there is probably a much better way to do this on a microcontroller than the way I'd do it on a PC in c++ Has anyone got any suggestions for implementing this efficiently on this hardware?

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• Ranking based string matching algorithm..for Midi Music

  - by Taha

  i am working on midi music project. What i am trying to do is:- matching the Instrument midi track with the similar instrument midi track... for example Flute track in a some midi music is matched against the Flute track in some other music midi file... After matching ,the results should come ranking wise according to their similarity.. Like 1) track1 2) track2 3) track3 I have this sort of string coming from my midi music .. F4/0.01282051282051282E4/0.01282051282051282Eb4/0.01282051282051282 D4/0.01282051282051282C#4/0.01282051282051282C4/0.01282051282051282 Which ranking algorithm with good metrics should i use for such data ? Thanking you in anticipation!

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• reservoir sampling problem

  - by eSKay

  This MSDN article proves the correctness of Reservoir Sampling algorithm as follows: Base case is trivial. For the k+1st case, the probability a given element i with position <= k is in R is s/k. The probability i is replaced is the probability k+1st element is chosen multiplied by i being chosen to be replaced, which is: s/(k+1) * 1/s = 1/(k+1), and prob that i is not replaced is k/k+1. So any given element's probability of lasting after k+1 rounds is: (chosen in k steps, and not removed in k steps) = s/k * k/(k+1), which is s/(k+1). So, when k+1 = n, any element is present with probability s/n. about step 3: What are the k+1 rounds mentioned? What is chosen in k steps, and not removed in k steps? Why are we only calculating this probability for elements that were already in R after the first s steps?

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• Print "1 followed by googolplex number of zeros" [closed]

  - by Rajan

  Assuming we are not concerned about running time of the program (which is practically infinite for human mortals), we want to print out in base 10, the exact value of 10^(googolplex), one digit at a time (mostly zeros). Describe an algorithm (which can be coded on current day computers), or write a program to do this. Since we cannot practically check the output, so we will rely on collective opinion on the correctness of the program. NOTE : I do not know the solution, or whether a solution exists or not. The problem is my own invention. To those readers who think this is not a CS question... kindly reconsider. This is difficult and bit theoretical but definitely CS.

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• Cross-platform (microcontroller-PC) algorithm development

  - by Kyr

  Hello people! I was asked to develop a algorithm for network application on C. This project will be developed on Linux for PC and then it will be transferred to a more portable platform, something that will include a microcontroller. There are many microcontroller/companies out there that provide very nice and large libraries for TCP/IP. This software will hold statistics on the network performance. The whole idea of a cross platform (uC - PC) seems rubbish to me cause eventually the code should be written in a more platform specific way for the microcontroller, but I am not expert to judge anyway. Is there any clever way of doing this or is there a anyone that did this before? My brainstorming has "Wrapper library" and "Matlab"... Any ideas? Thx!

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• How to spread changes in oriented graph?

  - by joseph

  Hello. I have oriented graph. Graph can be strongly connected. Every vertix can have a set of anything, for example letters. The set is user editable. Every vertix makes intersection of sets in previous vertices (only one step back). But now, there is problem: When I update set of one vertex, the change should expand to all vertices and uptate their intersection of sets of previous vertices. How to do every vertex have correct intersection after update of any vertex? Restriction: algorithm must avoid to stick in infinity. Any idea how to solve it?

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• algorithm for python itertools.permutations

  - by zaharpopov

  Can someone please explain algorithm for itertools.permutations routine in Python standard lib 2.6? I see its code in the documentation but don't undestand why it work? Thanks Code is: def permutations(iterable, r=None): # permutations('ABCD', 2) --> AB AC AD BA BC BD CA CB CD DA DB DC # permutations(range(3)) --> 012 021 102 120 201 210 pool = tuple(iterable) n = len(pool) r = n if r is None else r if r > n: return indices = range(n) cycles = range(n, n-r, -1) yield tuple(pool[i] for i in indices[:r]) while n: for i in reversed(range(r)): cycles[i] -= 1 if cycles[i] == 0: indices[i:] = indices[i+1:] + indices[i:i+1] cycles[i] = n - i else: j = cycles[i] indices[i], indices[-j] = indices[-j], indices[i] yield tuple(pool[i] for i in indices[:r]) break else: return

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• Distributing points over a surface within boundries

  - by vise

  I'm interested in a way (algorithm) of distributing a predefined number of points over a 4 sided surface like a square. The main issue is that each point has got to have a minimum and maximum proximity to each other (random between two predefined values). Basically the distance of any two points should not be closer than let's say 2, and a further than 3. My code will be implemented in ruby (the points are locations, the surface is a map), but any ideas or snippets are definitely welcomed as all my ideas include a fair amount of brute force.

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• Are there any worse sorting algorithms than Bogosort (a.k.a Monkey Sort)?

  - by womp

  My co-workers took me back in time to my University days with a discussion of sorting algorithms this morning. We reminisced about our favorites like StupidSort, and one of us was sure we had seen a sort algorithm that was O(n!). That got me started looking around for the "worst" sorting algorithms I could find. We postulated that a completely random sort would be pretty bad (i.e. randomize the elements - is it in order? no? randomize again), and I looked around and found out that it's apparently called BogoSort, or Monkey Sort, or sometimes just Random Sort. Monkey Sort appears to have a worst case performance of O(∞), a best case performance of O(n), and an average performance of O(n * n!). Are there any named algorithms that have worse average performance than O(n * n!)? Or are just sillier than Monkey Sort in general?

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• string matching algorithms used by lucene

  - by iamrohitbanga

  i want to know the string matching algorithms used by Apache Lucene. i have been going through the index file format used by lucene given here. it seems that lucene stores all words occurring in the text as is with their frequency of occurrence in each document. but as far as i know that for efficient string matching it would need to preprocess the words occurring in the Documents. example: search for "iamrohitbanga is a user of stackoverflow" (use fuzzy matching) in some documents. it is possible that there is a document containing the string "rohit banga" to find that the substrings rohit and banga are present in the search string, it would use some efficient substring matching. i want to know which algorithm it is. also if it does some preprocessing which function call in the java api triggers it.

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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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• BFS traversal of directed graph from a given node

  - by p1

  Hi, My understanding of basic BFS traversal for a graph is: BFS { Start from any node . Add it to que. Add it to visited array While(que is not empty) { remove head from queue. Print node; add all unvisited direct subchilds to que; mark them as visited } } However, if we have to traverse a DIRECTED graph from a given node and not all nodes are accessible from the given node [directly or indirectly] how do we use BFS for the same. Can you please explain in this graph as well: a= b = d = e = d a= c = d Here if the starting node is b , we never print a and c. Am I missing something in the algorithm. P.S: I used "HashMap adj = new HashMap();" to create the adjacencey list to store graph Any pointers are greatly appreciated. Thanks.

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• Software to Tune/Calibrate Properties for Heuristic Algorithms

  - by Karussell

  Today I read that there is a software called WinCalibra (scroll a bit down) which can take a text file with properties as input. This program can then optimize the input properties based on the output values of your algorithm. See this paper or the user documentation for more information (see link above; sadly doc is a zipped exe). Do you know other software which can do the same which runs under Linux? (preferable Open Source) EDIT: Since I need this for a java application I will now invest my research in java libraries like jgap. Other ideas and links would be appreciated!

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• synchronizing audio over a network

  - by sharkin

  I'm in startup of designing a client/server audio system which can stream audio arbitrarily over a network. One central server pumps out an audio stream and x number of clients receives the audio data and plays it. So far no magic needed and I have even got this scenario to work with VLC media player out of the box. However, the tricky part seems to be synchronizing the audio playback so that all clients are in audible synch (actual latency can be allowed as long as it is perceived to be in sync by a human listener). My question is if there's any known method or algorithm to use for these types of synchronization problems (video is probably solved the same way). My own initial thoughts centers around synchronizing clocks between physical machines and thereby creating a virtual "main timer" and somehow aligning audio data packets against it. Some products already solving the problem: http://www.sonos.com http://netchorus.com/ Any pointers are most welcome. Thanks. PS: This related question seem to have died long ago.

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• Question on multi-probe Local Sensitive Hashing

  - by Yijinsei

  Hey guys sorry to be asking this kind noob question, but because I really need some guidance on how to use Multi probe LSH pretty urgently, so I did not do much research myself. I realize there is a lib call LSHKIT available that implemented that algorithm, but I have trouble trying to figure out how to use it. Right now, I have a few thousand feature vector 296 dimension, each representing an image. The vector is used to query an user input image, to retrieve the most similar image. The method I used to derive the distance between vector is euclidean distance. I know this might be a rather noob question, but do you guys have knowledge on how should i implement multi probe LSH? I am really very grateful to any answer or response.

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• How to find a binary logarithm very fast? (O(1) at best)

  - by psihodelia

  Is there any very fast method to find a binary logarithm of an integer number? For example, given a number x=52656145834278593348959013841835216159447547700274555627155488768 such algorithm must find y=log(x,2) which is 215. x is always a power of 2. The problem seems to be really simple. All what is required is to find the position of the most significant 1 bit. There is a well-known method FloorLog, but it is not very fast especially for the very long multi-words integers. What is the fastest method?

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• Algorithm for parsing a flat tree into a non-flat tree

  - by Chad Johnson

  I have the following flat tree: id name parent_id is_directory =========================================================== 50 app 0 1 31 controllers 50 1 11 application_controller.rb 31 0 46 models 50 1 12 test_controller.rb 31 0 31 test.rb 46 0 and I am trying to figure out an algorithm for getting this into the following tree structuree: [{ id: 50, name: app, is_directory: true children: [{ id: 31, name: controllers, is_directory: true, children: [{ id: 11, name: application_controller.rb is_directory: false },{ id: 12, name: test_controller.rb, is_directory: false }], },{ id: 46, name: models, is_directory: true, children: [{ id: 31, name: test.rb, is_directory: false }] }] }] Can someone point me in the right direction? I'm looking for steps (eg. build an associative array; loop through the array looking for x; etc.).

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• image archive VS image strip

  - by DevA

  Hi, i've noticed that plenty of games / applications (very common on mobile builds) pack numerous images into an image strip. I figured that the advantages in this are making the program more tidy (file system - wise) and reducing (un)installation time. During the runtime of the application, the entire image strip is allocated and copied from FS to RAM. On the contrary, images can be stored in an image archive and unpacked during runtime to a number of image structures in RAM. The way I see it, the image strip approach is less efficient because of worse caching performance and because that even if the optimal rectangle packing algorithm is used, there will be empty spaces between the stored images in the strip, causing a waste of RAM. What are the advantages in using an image strip over using an image archive file?

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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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• How to judge the relative efficiency of algorithms given runtimes as functions of 'n'?

  - by Lopa

  Consider two algorithms A and B which solve the same problem, and have time complexities (in terms of the number of elementary operations they perform) given respectively by a(n) = 9n+6 b(n) = 2(n^2)+1 (i) Which algorithm is the best asymptotically? (ii) Which is the best for small input sizes n, and for what values of n is this the case? (You may assume where necessary that n0.) i think its 9n+6. guys could you please help me with whether its right or wrong?? and whats the answer for part b. what exactly do they want?

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• What's the best way to normalize scores for ranking things?

  - by beagleguy

  hi all, I'm curious how to do normalizing of numbers for a ranking algorithm let's say I want to rank a link based on importance and I have two columns to work with so a table would look like url | comments | views now I want to rank comments higher than views so I would first think to do comments*3 or something to weight it, however if there is a large view number like 40,000 and only 4 comments then the comments weight gets dropped out. So I'm thinking I have to normalize those scores down to a more equal playing field before I can weight them. Any ideas or pointers to how that's usually done? thanks

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• Popularity Algorithm - SQL / Django

  - by RadiantHex

  Hi folks, I've been looking into popularity algorithms used on sites such as Reddit, Digg and even Stackoverflow. Reddit algorithm: t = (time of entry post) - (Dec 8, 2005) x = upvotes - downvotes y = {1 if x > 0, 0 if x = 0, -1 if x < 0) z = {1 if x < 0, otherwise x} log(z) + (y * t)/45000 I have always performed simple ordering within SQL, I'm wondering how I should deal with such ordering. Should it be used to define a table, or could I build an SQL with the ordering within the formula (without hindering performance)? I am also wondering, if it is possible to use multiple ordering algorithms in different occasions, without incurring into performance problems. I'm using Django and PostgreSQL. Help would be much appreciated! ^^

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• How do people prove the correctness of Computer Vision methods?

  - by solvingPuzzles

  I'd like to pose a few abstract questions about computer vision research. I haven't quite been able to answer these questions by searching the web and reading papers. How does someone know whether a computer vision algorithm is correct? How do we define "correct" in the context of computer vision? Do formal proofs play a role in understanding the correctness of computer vision algorithms? A bit of background: I'm about to start my PhD in Computer Science. I enjoy designing fast parallel algorithms and proving the correctness of these algorithms. I've also used OpenCV from some class projects, though I don't have much formal training in computer vision. I've been approached by a potential thesis advisor who works on designing faster and more scalable algorithms for computer vision (e.g. fast image segmentation). I'm trying to understand the common practices in solving computer vision problems.

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• Explaining training method for AdaBoost algorithm

  - by konzti8

  Hi, I'm trying to understand the Haar feature method used for the training step in the AdaBoost algorithm. I don't understand the math that well so I'd appreciate more of a conceptual answer (as much as possible, anyway). Basically, what does it do? How do you choose positive and negative sets for what you want to select? Can it be generalized? What I mean by that is, can you choose it to find any kind of feature that you want no matter what the background is? So, for example, if I want to find some kind of circular blob - can I do that? I've also read that it is used on small patches for the images around the possible feature - does that mean you have to manually select that image patch or can it be automated to process the entire image? Is there matlab code for the training step? Thanks for any help...

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