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  • Finding minimum cut-sets between bounded subgraphs

    - by Tore
    If a game map is partitioned into subgraphs, how to minimize edges between subgraphs? I have a problem, Im trying to make A* searches through a grid based game like pacman or sokoban, but i need to find "enclosures". What do i mean by enclosures? subgraphs with as few cut edges as possible given a maximum size and minimum size for number of vertices for each subgraph that act as a soft constraints. Alternatively you could say i am looking to find bridges between subgraphs, but its generally the same problem. Given a game that looks like this, what i want to do is find enclosures so that i can properly find entrances to them and thus get a good heuristic for reaching vertices inside these enclosures. So what i want is to find these colored regions on any given map. My Motivation The reason for me bothering to do this and not just staying content with the performance of a simple manhattan distance heuristic is that an enclosure heuristic can give more optimal results and i would not have to actually do the A* to get some proper distance calculations and also for later adding competitive blocking of opponents within these enclosures when playing sokoban type games. Also the enclosure heuristic can be used for a minimax approach to finding goal vertices more properly. A possible solution to the problem is the Kernighan-Lin algorithm: function Kernighan-Lin(G(V,E)): determine a balanced initial partition of the nodes into sets A and B do A1 := A; B1 := B compute D values for all a in A1 and b in B1 for (i := 1 to |V|/2) find a[i] from A1 and b[i] from B1, such that g[i] = D[a[i]] + D[b[i]] - 2*c[a][b] is maximal move a[i] to B1 and b[i] to A1 remove a[i] and b[i] from further consideration in this pass update D values for the elements of A1 = A1 / a[i] and B1 = B1 / b[i] end for find k which maximizes g_max, the sum of g[1],...,g[k] if (g_max > 0) then Exchange a[1],a[2],...,a[k] with b[1],b[2],...,b[k] until (g_max <= 0) return G(V,E) My problem with this algorithm is its runtime at O(n^2 * lg(n)), i am thinking of limiting the nodes in A1 and B1 to the border of each subgraph to reduce the amount of work done. I also dont understand the c[a][b] cost in the algorithm, if a and b do not have an edge between them is the cost assumed to be 0 or infinity, or should i create an edge based on some heuristic. Do you know what c[a][b] is supposed to be when there is no edge between a and b? Do you think my problem is suitable to use a multi level problem? Why or why not? Do you have a good idea for how to reduce the work done with the kernighan-lin algorithm for my problem?

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  • How does an unsharp mask work?

    - by Bob Aman
    I've been playing around with image processing lately, and I'd like to know how the unsharp mask algorithm works. I'm looking at the source code for Gimp and it's implementation, but so far I'm still in the dark about how it actually works. I need to implement it for a project I'm working on, but I'd like to actually understand the algorithm I'm using.

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  • List all possible combinations of k integers between 1...n (n choose k)

    - by Asaf R
    Hi, Out of no particular reason I decided to look for an algorithm that produces all possible choices of k integers between 1...n, where the order amongst the k integer doesn't matter (the n choose k thingy). From the exact same reason, which is no reason at all, I also implemented it in C#. My question is: Do you see any mistake in my algorithm or code? And, more importantly, can you suggest a better algorithm? Please pay more attention to the algorithm than the code itself. It's not the prettiest code I've ever written, although do tell if you see an error. EDIT: Alogirthm explained - We hold k indices. This creates k nested for loops, where loop i's index is indices[i]. It simulates k for loops where indices[i+1] belongs to a loop nested within the loop of indices[i]. indices[i] runs from indices[i - 1] + 1 to n - k + i + 1. CODE: public class AllPossibleCombination { int n, k; int[] indices; List<int[]> combinations = null; public AllPossibleCombination(int n_, int k_) { if (n_ <= 0) { throw new ArgumentException("n_ must be in N+"); } if (k_ <= 0) { throw new ArgumentException("k_ must be in N+"); } if (k_ > n_) { throw new ArgumentException("k_ can be at most n_"); } n = n_; k = k_; indices = new int[k]; indices[0] = 1; } /// <summary> /// Returns all possible k combination of 0..n-1 /// </summary> /// <returns></returns> public List<int[]> GetCombinations() { if (combinations == null) { combinations = new List<int[]>(); Iterate(0); } return combinations; } private void Iterate(int ii) { // // Initialize // if (ii > 0) { indices[ii] = indices[ii - 1] + 1; } for (; indices[ii] <= (n - k + ii + 1); indices[ii]++) { if (ii < k - 1) { Iterate(ii + 1); } else { int[] combination = new int[k]; indices.CopyTo(combination, 0); combinations.Add(combination); } } } } I apologize for the long question, it might be fit for a blog post, but I do want the community's opinion here. Thanks, Asaf

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  • Speed boost to adjacency matrix

    - by samoz
    I currently have an algorithm that operates on an adjacency matrix of size n by m. In my algorithm, I need to zero out entire rows or columns at a time. My implementation is currently O(m) or O(n) depending on if it's a column or row. Is there any way to zero out a column or row in O(1) time?

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  • Algorithm to compare people names to detect identicalness

    - by Pentium10
    I am working on address book synchronization algorithm. I would like to reuse some code if there exists, but couldn't find one yet. Does someone know about an algorithm that will tell me in numbers/float/procent how much two names are identical. Levenstein distance is not good in this approach, as names and our adddress books are matching the begining of each of the name sections. John Smith should match Smith Jon, Jonathan Smith, Johnny Smith

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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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  • shortest directed odd cycle

    - by gleb-pendler
    6.1.4 Describe an algorithm based on breadth-first search for finding a shortest odd cycle in a graph. 6.3.5 Describe an algorithm based on directed breadth-first search for finding a shortest directed odd cycle in a digraph. what is most importent is that it must be a directed graph not necessary bfs but must be the shortest directed odd cycle!!! Question was taken from "Graph Theory" by J.A. Bondy and U.S.R. Murty thanks in advance!!!

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  • Higher-order unification

    - by rwallace
    I'm working on a higher-order theorem prover, of which unification seems to be the most difficult subproblem. If Huet's algorithm is still considered state-of-the-art, does anyone have any links to explanations of it that are written to be understood by a programmer rather than a mathematician? Or even any examples of where it works and the usual first-order algorithm doesn't?

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  • Sliding window algorithm for activiting recognition MATLAB

    - by csc
    I want to write a sliding window algorithm for use in activity recognition. The training data is <1xN so I'm thinking I just need to take (say window_size=3) the window_size of data and train that. I also later want to use this algorithm on a matrix . I'm new to matlab so i need any advice/directions on how to implement this correctly.

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  • Is Collections.shuffle suitable for a poker algorithm?

    - by Kovu
    Hi, there is a poker-system in java, that uses Collections.shuffle() on all available cards before the cards are dealt. So a collection of 52 cards 2-9, J, Q, K, A in 4 types. After that we Collections.shuffle(). The problem is, that it seems (until now we didn't have big statistic, it's possible that we only see a lot of statistic inferences), that the algorithm is VERY unclearly. So, is Collections.shuffle() okay for a poker algorithm?

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  • Searching, Sorting and Graph Algorithms questions

    - by user177883
    Is there a resource that i can find different variations of searching, sorting and graph algorithm questions ? I have studied CLRS and Algorithm Design by Kleinberg. and solved some set of questions. I have also, checked SO for algorithms questions. Curious, if there is a resource you would highly recommend. EDIT: There is also this free ebook with many questions, that i was able to solve some of them.

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  • Algorithms for subgraph isomorphism detection

    - by Jack
    This a NP Complete problem. More info can be found here http://en.wikipedia.org/wiki/Subgraph_isomorphism_problem The most widely used algorithm is the one proposed by Ullman. Can someone please explain the algorithm to me. I read a paper by him and couldn't understand much. Also what other algorithms for this problem. I am working on an image processing project.

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  • String searching algorithm for Chinese characters.

    - by Jack Low
    There are Python code available for existing algorithms for normal string searching e.g. Boyer-Moore Algorithm. I am looking to use this on Chinese characters and it doesn't seem like the same implementation would work. What would I go about doing in order to make the algorithm work on Chinese characters? I am referring to this: http://en.literateprograms.org/Boyer-Moore_string_search_algorithm_(Python)#References

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  • What container is eaziest for combining Jpegs and MP3s as video?

    - by Ole Jak
    So I have N (for example 1000) Jpeg frames and 10*N ( for ex 100) seconds of MP3 sound I need some conteiner for Joining them into one Video file (10 frames/second) (beter popular like FLV or AVI or MOV). So what I need is algorithm or code example of combining my data into some popular format. (code example beter be in some language like C# Java or ActionScript or PHP, Algorithm should be theoreticly Implementable with ActionScript or PHP) Can any one, please help me with that?)

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  • Dijkstra's algorithm to find all the shortest paths possible

    - by Darksody
    Hello, I'm working on Dijkstra's algorithm,and i really need to find all the possible shortest paths,not just one.I'm using an adjacency matrix and i applied Dijkstra's algorithm,and i can find the shortest path.But i need to find all the paths with that minimum cost,i mean all the possible solutions,if they exist.If anyone have an ideea and can help me,i would really appreciate it.A link would be fine too. Thank you.

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  • A[i] * A[j] = k in O(nlog(n))

    - by gleb-pendler
    A is an Array of n positive int numbers k given int Algorithm should find if there is a pair of numbers which product gives the result a. A[i] * A[j] = k b. A[i] = A[j] + k if there is such a couple the algorithm should return thier index. thanks in advance.

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  • Efficiency of purely functional programming

    - by Sid
    Does anyone know what is the worst possible asymptotic slowdown that can happen when programming purely functionally as opposed to imperatively (i.e. allowing side-effects)? Clarification from comment by itowlson: is there any problem for which the best known non-destructive algorithm is asymptotically worse than the best known destructive algorithm, and if so by how much?

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  • Java - Collections.sort() performance

    - by msr
    Hello, Im using Collections.sort() to sort a LinkedList whose elements implements Comparable interface, so they are sorted in a natural order. In the javadoc documentation its said this method uses mergesort algorithm wich has n*log(n) performance. My question is if there is a more efficient algorithm to sort my LinkedList? The size of that list could be very high and sort will be also very frequent. Thanks!

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  • Antialiasing algorithm

    - by y_nk
    Hello, I'm looking for a good way to antialias a bitmap i'm generating with actionscript3. My goal would be to achieve this processing from scratch. I read a lot on the subject but the most common algorithm are looking too loud to work properly within my swf, because i'm using a scale2x algorithm to smooth the edges of my shape. It doesn't have to be colorfull, since my shape is black and white ! Any hint would be appreciated, thanks :)

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