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  • Pseudo-quicksort time complexity

    - by Ord
    I know that quicksort has O(n log n) average time complexity. A pseudo-quicksort (which is only a quicksort when you look at it from far enough away, with a suitably high level of abstraction) that is often used to demonstrate the conciseness of functional languages is as follows (given in Haskell): quicksort :: Ord a => [a] -> [a] quicksort [] = [] quicksort (p:xs) = quicksort [y | y<-xs, y<p] ++ [p] ++ quicksort [y | y<-xs, y>=p] Okay, so I know this thing has problems. The biggest problem with this is that it does not sort in place, which is normally a big advantage of quicksort. Even if that didn't matter, it would still take longer than a typical quicksort because it has to do two passes of the list when it partitions it, and it does costly append operations to splice it back together afterwards. Further, the choice of the first element as the pivot is not the best choice. But even considering all of that, isn't the average time complexity of this quicksort the same as the standard quicksort? Namely, O(n log n)? Because the appends and the partition still have linear time complexity, even if they are inefficient.

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  • Windows Web Server 2008 R2 Server Core local password complexity

    - by Dennis Allen
    How can I disable the local user account password complexity settings on Windows 2008 R2 "Server Core"? I am trying to migrate our windows 2003 web server to windows 2008 R2. I am trying to see if I can use the "Server Core" install, and it has been a very internet search intensive experience. What I can't find out how to do is to find out how to disable password complexity for local user accounts. While our user account generator currently creates nice strong passwords, there was a time when this was not the case and unfortunately forcing the users to change their password is not an option at this time. Any help greatly appreciated. Dennis

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  • Time complexity O() of isPalindrome()

    - by Aran
    I have this method, isPalindrome(), and I am trying to find the time complexity of it, and also rewrite the code more efficiently. boolean isPalindrome(String s) { boolean bP = true; for(int i=0; i<s.length(); i++) { if(s.charAt(i) != s.charAt(s.length()-i-1)) { bP = false; } } return bP; } Now I know this code checks the string's characters to see whether it is the same as the one before it and if it is then it doesn't change bP. And I think I know that the operations are s.length(), s.charAt(i) and s.charAt(s.length()-i-!)). Making the time-complexity O(N + 3), I think? This correct, if not what is it and how is that figured out. Also to make this more efficient, would it be good to store the character in temporary strings?

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  • What is the complexity of this c function

    - by Bunny Rabbit
    what is the complexity of the following c Function ? double foo (int n) { int i; double sum; if (n==0) return 1.0; else { sum = 0.0; for (i =0; i<n; i++) sum +=foo(i); return sum; } } Please don't just post the complexity can you help me in understanding how to go about it . EDIT: It was an objective question asked in an exam and the Options provided were 1.O(1) 2.O(n) 3.O(n!) 4.O(n^n)

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  • Help with algorithmic complexity in custom merge sort implementation

    - by bitcycle
    I've got an implementation of the merge sort in C++ using a custom doubly linked list. I'm coming up with a big O complexity of n^2, based on the merge_sort() slice operation. But, from what I've read, this algorithm should be n*log(n), where the log has a base of two. Can someone help me determine if I'm just determining the complexity incorrectly, or if the implementation can/should be improved to achieve n*log(n) complexity? If you would like some background on my goals for this project, see my blog. I've added comments in the code outlining what I understand the complexity of each method to be. Clarification - I'm focusing on the C++ implementation with this question. I've got another implementation written in Python, but that was something that was added in addition to my original goal(s).

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  • Search Complexity of a Hashtable within a Hashtable?

    - by spacker_lechuck
    Say we have a hashtable of size m, and at each bucket we store a hashtable of size p. What would the worst case/average case search complexity be? I am inclined to say that since computing a hash function is still atomic, the only worst case scenario is if the value is at the end of the linked list in the hashtable of size p, so O(n)? I have no idea how to calculate the average case for this scenario and would appreciate any pointers!

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  • Complexity in using Binary search and Trie

    - by user121196
    given a large list of alphabetically sorted words in a file,I need to write a program that, given a word x, determines if x is in the list. Preprocessing is ok since I will be calling this function many times over different inputs. priorties: 1. speed. 2. memory I already know I can use (n is number of words, m is average length of the words) 1. a trie, time is O(log(n)), space(best case) is O(log(n*m)), space(worst case) is O(n*m). 2. load the complete list into memory, then binary search, time is O(log(n)), space is O(n*m) I'm not sure about the complexity on tri, please correct me if they are wrong. Also are there other good approaches?

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  • Algorithm complexity question

    - by Itsik
    During a recent job interview, I was asked to give a solution to the following problem: Given a string s (without spaces) and a dictionary, return the words in the dictionary that compose the string. For example, s= peachpie, dic= {peach, pie}, result={peach, pie}. I will ask the the decision variation of this problem: if s can be composed of words in the dictionary return yes, otherwise return no. My solution to this was in backtracking (written in Java) public static boolean words(String s, Set<String> dictionary) { if ("".equals(s)) return true; for (int i=0; i <= s.length(); i++) { String pre = prefix(s,i); // returns s[0..i-1] String suf = suffix(s,i); // returns s[i..s.len] if (dictionary.contains(pre) && words(suf, dictionary)) return true; } return false; } public static void main(String[] args) { Set<String> dic = new HashSet<String>(); dic.add("peach"); dic.add("pie"); dic.add("1"); System.out.println(words("peachpie1", dic)); // true System.out.println(words("peachpie2", dic)); // false } What is the time complexity of this solution? I'm calling recursively in the for loop, but only for the prefix's that are in the dictionary. Any idea's?

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  • Time complexity of a powerset generating function

    - by Lirik
    I'm trying to figure out the time complexity of a function that I wrote (it generates a power set for a given string): public static HashSet<string> GeneratePowerSet(string input) { HashSet<string> powerSet = new HashSet<string>(); if (string.IsNullOrEmpty(input)) return powerSet; int powSetSize = (int)Math.Pow(2.0, (double)input.Length); // Start at 1 to skip the empty string case for (int i = 1; i < powSetSize; i++) { string str = Convert.ToString(i, 2); string pset = str; for (int k = str.Length; k < input.Length; k++) { pset = "0" + pset; } string set = string.Empty; for (int j = 0; j < pset.Length; j++) { if (pset[j] == '1') { set = string.Concat(set, input[j].ToString()); } } powerSet.Add(set); } return powerSet; } So my attempt is this: let the size of the input string be n in the outer for loop, must iterate 2^n times (because the set size is 2^n). in the inner for loop, we must iterate 2*n times (at worst). 1. So Big-O would be O((2^n)*n) (since we drop the constant 2)... is that correct? And n*(2^n) is worse than n^2. if n = 4 then (4*(2^4)) = 64 (4^2) = 16 if n = 100 then (10*(2^10)) = 10240 (10^2) = 100 2. Is there a faster way to generate a power set, or is this about optimal?

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  • Suggest a good method with least lookup time complexity

    - by Amrish
    I have a structure which has 3 identifier fields and one value field. I have a list of these objects. To give an analogy, the identifier fields are like the primary keys to the object. These 3 fields uniquely identify an object. Class { int a1; int a2; int a3; int value; }; I would be having a list of say 1000 object of this datatype. I need to check for specific values of these identity key values by passing values of a1, a2 and a3 to a lookup function which would check if any object with those specific values of a1, a2 and a3 is present and returns that value. What is the most effective way to implement this to achieve a best lookup time? One solution I could think of is to have a 3 dimensional matrix of length say 1000 and populate the value in it. This has a lookup time of O(1). But the disadvantages are. 1. I need to know the length of array. 2. For higher identity fields (say 20), then I will need a 20 dimension matrix which would be an overkill on the memory. For my actual implementation, I have 23 identity fields. Can you suggest a good way to store this data which would give me the best look up time?

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  • How should I change my Graph structure (very slow insertion)?

    - by Nazgulled
    Hi, This program I'm doing is about a social network, which means there are users and their profiles. The profiles structure is UserProfile. Now, there are various possible Graph implementations and I don't think I'm using the best one. I have a Graph structure and inside, there's a pointer to a linked list of type Vertex. Each Vertex element has a value, a pointer to the next Vertex and a pointer to a linked list of type Edge. Each Edge element has a value (so I can define weights and whatever it's needed), a pointer to the next Edge and a pointer to the Vertex owner. I have a 2 sample files with data to process (in CSV style) and insert into the Graph. The first one is the user data (one user per line); the second one is the user relations (for the graph). The first file is quickly inserted into the graph cause I always insert at the head and there's like ~18000 users. The second file takes ages but I still insert the edges at the head. The file has about ~520000 lines of user relations and takes between 13-15mins to insert into the Graph. I made a quick test and reading the data is pretty quickly, instantaneously really. The problem is in the insertion. This problem exists because I have a Graph implemented with linked lists for the vertices. Every time I need to insert a relation, I need to lookup for 2 vertices, so I can link them together. This is the problem... Doing this for ~520000 relations, takes a while. How should I solve this? Solution 1) Some people recommended me to implement the Graph (the vertices part) as an array instead of a linked list. This way I have direct access to every vertex and the insertion is probably going to drop considerably. But, I don't like the idea of allocating an array with [18000] elements. How practically is this? My sample data has ~18000, but what if I need much less or much more? The linked list approach has that flexibility, I can have whatever size I want as long as there's memory for it. But the array doesn't, how am I going to handle such situation? What are your suggestions? Using linked lists is good for space complexity but bad for time complexity. And using an array is good for time complexity but bad for space complexity. Any thoughts about this solution? Solution 2) This project also demands that I have some sort of data structures that allows quick lookup based on a name index and an ID index. For this I decided to use Hash Tables. My tables are implemented with separate chaining as collision resolution and when a load factor of 0.70 is reach, I normally recreate the table. I base the next table size on this http://planetmath.org/encyclopedia/GoodHashTablePrimes.html. Currently, both Hash Tables hold a pointer to the UserProfile instead of duplication the user profile itself. That would be stupid, changing data would require 3 changes and it's really dumb to do it that way. So I just save the pointer to the UserProfile. The same user profile pointer is also saved as value in each Graph Vertex. So, I have 3 data structures, one Graph and two Hash Tables and every single one of them point to the same exact UserProfile. The Graph structure will serve the purpose of finding the shortest path and stuff like that while the Hash Tables serve as quick index by name and ID. What I'm thinking to solve my Graph problem is to, instead of having the Hash Tables value point to the UserProfile, I point it to the corresponding Vertex. It's still a pointer, no more and no less space is used, I just change what I point to. Like this, I can easily and quickly lookup for each Vertex I need and link them together. This will insert the ~520000 relations pretty quickly. I thought of this solution because I already have the Hash Tables and I need to have them, then, why not take advantage of them for indexing the Graph vertices instead of the user profile? It's basically the same thing, I can still access the UserProfile pretty quickly, just go to the Vertex and then to the UserProfile. But, do you see any cons on this second solution against the first one? Or only pros that overpower the pros and cons on the first solution? Other Solution) If you have any other solution, I'm all ears. But please explain the pros and cons of that solution over the previous 2. I really don't have much time to be wasting with this right now, I need to move on with this project, so, if I'm doing to do such a change, I need to understand exactly what to change and if that's really the way to go. Hopefully no one fell asleep reading this and closed the browser, sorry for the big testament. But I really need to decide what to do about this and I really need to make a change. P.S: When answering my proposed solutions, please enumerate them as I did so I know exactly what are you talking about and don't confuse my self more than I already am.

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  • Time complexity to fill hash table (homework)?

    - by Heathcliff
    This is a homework question, but I think there's something missing from it. It asks: Provide a sequence of m keys to fill a hash table implemented with linear probing, such that the time to fill it is minimum. And then Provide another sequence of m keys, but such that the time fill it is maximum. Repeat these two questions if the hash table implements quadratic probing I can only assume that the hash table has size m, both because it's the only number given and because we have been using that letter to address a hash table size before when describing the load factor. But I can't think of any sequence to do the first without knowing the hash function that hashes the sequence into the table. If it is a bad hash function, such that, for instance, it hashes every entry to the same index, then both the minimum and maximum time to fill it will take O(n) time, regardless of what the sequence looks like. And in the average case, where I assume the hash function is OK, how am I suppossed to know how long it will take for that hash function to fill the table? Aren't these questions linked to the hash function stronger than they are to the sequence that is hashed? As for the second question, I can assume that, regardless of the hash function, a sequence of size m with the same key repeated m-times will provide the maximum time, because it will cause linear probing from the second entry on. I think that will take O(n) time. Is that correct? Thanks

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  • O(N log N) Complexity - Similar to linear?

    - by gav
    Hey All, So I think I'm going to get buried for asking such a trivial but I'm a little confused about something. I have implemented quicksort in Java and C and I was doing some basic comparissons. The graph came out as two straight lines, with the C being 4ms faster than the Java counterpart over 100,000 random integers. The code for my tests can be found here; android-benchmarks I wasn't sure what an (n log n) line would look like but I didn't think it would be straight. I just wanted to check that this is the expected result and that I shouldn't try to find an error in my code. I stuck the formula into excel and for base 10 it seems to be a straight line with a kink at the start. Is this because the difference between log(n) and log(n+1) increases linearly? Thanks, Gav

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  • Complexity of subset product

    - by threenplusone
    I have a set of numbers produced using the following formula with integers 0 < x < a. f(x) = f(x-1)^2 % a For example starting at 2 with a = 649. {2, 4, 16, 256, 636, 169, 5, 25, 649, 576, 137, ...} I am after a subset of these numbers that when multiplied together equals 1 mod N. I believe this problem by itself to be NP-complete (based on similaries to Subset-Sum problem). However starting with any integer (x) gives the same solution pattern. Eg. a = 649 {2, 4, 16, 256, 636, 169, 5, 25, 649, 576, 137, ...} = 16 * 5 * 576 = 1 % 649 {3, 9, 81, 71, 498, 86, 257, 500, 135, 53, 213, ...} = 81 * 257 * 53 = 1 % 649 {4, 16, 256, 636, 169, 5, 25, 649, 576, 137, 597, ...} = 256 * 25 * 137 = 1 % 649 I am wondering if this additional fact makes this problem solvable faster? Or if anyone has run into this problem previously or has any advice?

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  • A Guided Tour of Complexity

    - by JoshReuben
    I just re-read Complexity – A Guided Tour by Melanie Mitchell , protégé of Douglas Hofstadter ( author of “Gödel, Escher, Bach”) http://www.amazon.com/Complexity-Guided-Tour-Melanie-Mitchell/dp/0199798109/ref=sr_1_1?ie=UTF8&qid=1339744329&sr=8-1 here are some notes and links:   Evolved from Cybernetics, General Systems Theory, Synergetics some interesting transdisciplinary fields to investigate: Chaos Theory - http://en.wikipedia.org/wiki/Chaos_theory – small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes for chaotic systems, rendering long-term prediction impossible. System Dynamics / Cybernetics - http://en.wikipedia.org/wiki/System_Dynamics – study of how feedback changes system behavior Network Theory - http://en.wikipedia.org/wiki/Network_theory – leverage Graph Theory to analyze symmetric  / asymmetric relations between discrete objects Algebraic Topology - http://en.wikipedia.org/wiki/Algebraic_topology – leverage abstract algebra to analyze topological spaces There are limits to deterministic systems & to computation. Chaos Theory definitely applies to training an ANN (artificial neural network) – different weights will emerge depending upon the random selection of the training set. In recursive Non-Linear systems http://en.wikipedia.org/wiki/Nonlinear_system – output is not directly inferable from input. E.g. a Logistic map: Xt+1 = R Xt(1-Xt) Different types of bifurcations, attractor states and oscillations may occur – e.g. a Lorenz Attractor http://en.wikipedia.org/wiki/Lorenz_system Feigenbaum Constants http://en.wikipedia.org/wiki/Feigenbaum_constants express ratios in a bifurcation diagram for a non-linear map – the convergent limit of R (the rate of period-doubling bifurcations) is 4.6692016 Maxwell’s Demon - http://en.wikipedia.org/wiki/Maxwell%27s_demon - the Second Law of Thermodynamics has only a statistical certainty – the universe (and thus information) tends towards entropy. While any computation can theoretically be done without expending energy, with finite memory, the act of erasing memory is permanent and increases entropy. Life & thought is a counter-example to the universe’s tendency towards entropy. Leo Szilard and later Claude Shannon came up with the Information Theory of Entropy - http://en.wikipedia.org/wiki/Entropy_(information_theory) whereby Shannon entropy quantifies the expected value of a message’s information in bits in order to determine channel capacity and leverage Coding Theory (compression analysis). Ludwig Boltzmann came up with Statistical Mechanics - http://en.wikipedia.org/wiki/Statistical_mechanics – whereby our Newtonian perception of continuous reality is a probabilistic and statistical aggregate of many discrete quantum microstates. This is relevant for Quantum Information Theory http://en.wikipedia.org/wiki/Quantum_information and the Physics of Information - http://en.wikipedia.org/wiki/Physical_information. Hilbert’s Problems http://en.wikipedia.org/wiki/Hilbert's_problems pondered whether mathematics is complete, consistent, and decidable (the Decision Problem – http://en.wikipedia.org/wiki/Entscheidungsproblem – is there always an algorithm that can determine whether a statement is true).  Godel’s Incompleteness Theorems http://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems  proved that mathematics cannot be both complete and consistent (e.g. “This statement is not provable”). Turing through the use of Turing Machines (http://en.wikipedia.org/wiki/Turing_machine symbol processors that can prove mathematical statements) and Universal Turing Machines (http://en.wikipedia.org/wiki/Universal_Turing_machine Turing Machines that can emulate other any Turing Machine via accepting programs as well as data as input symbols) that computation is limited by demonstrating the Halting Problem http://en.wikipedia.org/wiki/Halting_problem (is is not possible to know when a program will complete – you cannot build an infinite loop detector). You may be used to thinking of 1 / 2 / 3 dimensional systems, but Fractal http://en.wikipedia.org/wiki/Fractal systems are defined by self-similarity & have non-integer Hausdorff Dimensions !!!  http://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension – the fractal dimension quantifies the number of copies of a self similar object at each level of detail – eg Koch Snowflake - http://en.wikipedia.org/wiki/Koch_snowflake Definitions of complexity: size, Shannon entropy, Algorithmic Information Content (http://en.wikipedia.org/wiki/Algorithmic_information_theory - size of shortest program that can generate a description of an object) Logical depth (amount of info processed), thermodynamic depth (resources required). Complexity is statistical and fractal. John Von Neumann’s other machine was the Self-Reproducing Automaton http://en.wikipedia.org/wiki/Self-replicating_machine  . Cellular Automata http://en.wikipedia.org/wiki/Cellular_automaton are alternative form of Universal Turing machine to traditional Von Neumann machines where grid cells are locally synchronized with their neighbors according to a rule. Conway’s Game of Life http://en.wikipedia.org/wiki/Conway's_Game_of_Life demonstrates various emergent constructs such as “Glider Guns” and “Spaceships”. Cellular Automatons are not practical because logical ops require a large number of cells – wasteful & inefficient. There are no compilers or general program languages available for Cellular Automatons (as far as I am aware). Random Boolean Networks http://en.wikipedia.org/wiki/Boolean_network are extensions of cellular automata where nodes are connected at random (not to spatial neighbors) and each node has its own rule –> they demonstrate the emergence of complex  & self organized behavior. Stephen Wolfram’s (creator of Mathematica, so give him the benefit of the doubt) New Kind of Science http://en.wikipedia.org/wiki/A_New_Kind_of_Science proposes the universe may be a discrete Finite State Automata http://en.wikipedia.org/wiki/Finite-state_machine whereby reality emerges from simple rules. I am 2/3 through this book. It is feasible that the universe is quantum discrete at the plank scale and that it computes itself – Digital Physics: http://en.wikipedia.org/wiki/Digital_physics – a simulated reality? Anyway, all behavior is supposedly derived from simple algorithmic rules & falls into 4 patterns: uniform , nested / cyclical, random (Rule 30 http://en.wikipedia.org/wiki/Rule_30) & mixed (Rule 110 - http://en.wikipedia.org/wiki/Rule_110 localized structures – it is this that is interesting). interaction between colliding propagating signal inputs is then information processing. Wolfram proposes the Principle of Computational Equivalence - http://mathworld.wolfram.com/PrincipleofComputationalEquivalence.html - all processes that are not obviously simple can be viewed as computations of equivalent sophistication. Meaning in information may emerge from analogy & conceptual slippages – see the CopyCat program: http://cognitrn.psych.indiana.edu/rgoldsto/courses/concepts/copycat.pdf Scale Free Networks http://en.wikipedia.org/wiki/Scale-free_network have a distribution governed by a Power Law (http://en.wikipedia.org/wiki/Power_law - much more common than Normal Distribution). They are characterized by hubs (resilience to random deletion of nodes), heterogeneity of degree values, self similarity, & small world structure. They grow via preferential attachment http://en.wikipedia.org/wiki/Preferential_attachment – tipping points triggered by positive feedback loops. 2 theories of cascading system failures in complex systems are Self-Organized Criticality http://en.wikipedia.org/wiki/Self-organized_criticality and Highly Optimized Tolerance http://en.wikipedia.org/wiki/Highly_optimized_tolerance. Computational Mechanics http://en.wikipedia.org/wiki/Computational_mechanics – use of computational methods to study phenomena governed by the principles of mechanics. This book is a great intuition pump, but does not cover the more mathematical subject of Computational Complexity Theory – http://en.wikipedia.org/wiki/Computational_complexity_theory I am currently reading this book on this subject: http://www.amazon.com/Computational-Complexity-Christos-H-Papadimitriou/dp/0201530821/ref=pd_sim_b_1   stay tuned for that review!

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  • Linear time and quadratic time

    - by jasonline
    I'm just not sure... If you have a code that can be executed in either of the following complexities: (1) A sequence of O(n), like for example: two O(n) in sequence (2) O(n²) The preferred version would be the one that can be executed in linear time. Would there be a time such that the sequence of O(n) would be too much and that O(n²) would be preferred? In other words, is the statement C x O(n) < O(n²) always true for any constant C? If no, what are the factors that would affect the condition such that it would be better to choose the O(n²) complexity?

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  • Form, function and complexity in rule processing

    - by Charles Young
    Tim Bass posted on ‘Orwellian Event Processing’. I was involved in a heated exchange in the comments, and he has more recently published a post entitled ‘Disadvantages of Rule-Based Systems (Part 1)’. Whatever the rights and wrongs of our exchange, it clearly failed to generate any agreement or understanding of our different positions. I don't particularly want to promote further argument of that kind, but I do want to take the opportunity of offering a different perspective on rule-processing and an explanation of my comments. For me, the ‘red rag’ lay in Tim’s claim that “...rules alone are highly inefficient for most classes of (not simple) problems” and a later paragraph that appears to equate the simplicity of form (‘IF-THEN-ELSE’) with simplicity of function.   It is not the first time Tim has expressed these views and not the first time I have responded to his assertions.   Indeed, Tim has a long history of commenting on the subject of complex event processing (CEP) and, less often, rule processing in ‘robust’ terms, often asserting that very many other people’s opinions on this subject are mistaken.   In turn, I am of the opinion that, certainly in terms of rule processing, which is an area in which I have a specific interest and knowledge, he is often mistaken. There is no simple answer to the fundamental question ‘what is a rule?’ We use the word in a very fluid fashion in English. Likewise, the term ‘rule processing’, as used widely in IT, is equally difficult to define simplistically. The best way to envisage the term is as a ‘centre of gravity’ within a wider domain. That domain contains many other ‘centres of gravity’, including CEP, statistical analytics, neural networks, natural language processing and so much more. Whole communities tend to gravitate towards and build themselves around some of these centres. The term 'rule processing' is associated with many different technology types, various software products, different architectural patterns, the functional capability of many applications and services, etc. There is considerable variation amongst these different technologies, techniques and products. Very broadly, a common theme is their ability to manage certain types of processing and problem solving through declarative, or semi-declarative, statements of propositional logic bound to action-based consequences. It is generally important to be able to decouple these statements from other parts of an overall system or architecture so that they can be managed and deployed independently.  As a centre of gravity, ‘rule processing’ is no island. It exists in the context of a domain of discourse that is, itself, highly interconnected and continuous.   Rule processing does not, for example, exist in splendid isolation to natural language processing.   On the contrary, an on-going theme of rule processing is to find better ways to express rules in natural language and map these to executable forms.   Rule processing does not exist in splendid isolation to CEP.   On the contrary, an event processing agent can reasonably be considered as a rule engine (a theme in ‘Power of Events’ by David Luckham).   Rule processing does not live in splendid isolation to statistical approaches such as Bayesian analytics. On the contrary, rule processing and statistical analytics are highly synergistic.   Rule processing does not even live in splendid isolation to neural networks. For example, significant research has centred on finding ways to translate trained nets into explicit rule sets in order to support forms of validation and facilitate insight into the knowledge stored in those nets. What about simplicity of form?   Many rule processing technologies do indeed use a very simple form (‘If...Then’, ‘When...Do’, etc.)   However, it is a fundamental mistake to equate simplicity of form with simplicity of function.   It is absolutely mistaken to suggest that simplicity of form is a barrier to the efficient handling of complexity.   There are countless real-world examples which serve to disprove that notion.   Indeed, simplicity of form is often the key to handling complexity. Does rule processing offer a ‘one size fits all’. No, of course not.   No serious commentator suggests it does.   Does the design and management of large knowledge bases, expressed as rules, become difficult?   Yes, it can do, but that is true of any large knowledge base, regardless of the form in which knowledge is expressed.   The measure of complexity is not a function of rule set size or rule form.  It tends to be correlated more strongly with the size of the ‘problem space’ (‘search space’) which is something quite different.   Analysis of the problem space and the algorithms we use to search through that space are, of course, the very things we use to derive objective measures of the complexity of a given problem. This is basic computer science and common practice. Sailing a Dreadnaught through the sea of information technology and lobbing shells at some of the islands we encounter along the way does no one any good.   Building bridges and causeways between islands so that the inhabitants can collaborate in open discourse offers hope of real progress.

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  • Splitting Graph into distinct polygons in O(E) complexity

    - by Arthur Wulf White
    If you have seen my last question: trapped inside a Graph : Find paths along edges that do not cross any edges How do you split an entire graph into distinct shapes 'trapped' inside the graph(like the ones described in my last question) with good complexity? What I am doing now is iterating over all edges and then starting to traverse while always taking the rightmost turn. This does split the graph into distinct shapes. Then I eliminate all the excess shapes (that are repeats of previous shapes) and return the result. The complexity of this algorithm is O(E^2). I am wondering if I could do it in O(E) by removing edges I already traversed previously. My current implementation of that returns unexpected results.

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  • Polygonal Triangulation - algorithm with O(n log n) complexity

    - by Arthur Wulf White
    I wish to triangulate a polygon I only have the outline of (p0, p1, p2 ... pn) like described in this question: polygon triangulation algorithm and this webpage: http://cgm.cs.mcgill.ca/~godfried/teaching/cg-projects/97/Ian/algorithm2.html I do not wish to learn the subject and have a deep understanding of it at the moment. I only want to see an effective algorithm that can be used out of the box. The one described in the site seems to be of somewhat high complexity O(n) for finding one ear. I heard this could be done in O(n log n) time. Is there any well known easy to use algorithm that I can translate port to use in my engine that runs with somewhat reasonable complexity? The reason I need to triangulate is that I wish to feel out a 2d-outline and render it 3d. Much like we fill out a 2d-outline in paint. I could use sprites. This would not serve cause I am planning to play with the resulting model on the z-axis, giving it different heights in the different areas. I would love to try the books that were mentioned, although I suspect that is not the answer most readers are hoping for when they read this Q & A format. Mostly I like to see a code snippet I can cut and paste with some modifications and start running.

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  • Prove 2^sqrt(log(n))= O(n^a)

    - by user1830621
    I posted a question similar to this earlier, although it seemed like it was much easier. I know the underlying principle of Big-O notation says that to prove that 2^sqrt(log(n)) is O(n^a), there must exist a positive value c for which c(n^a) = 2^sqrt(log(n)) for all values n = N. c*n^a >= 2^sqrt(log(n)) c >= 2^sqrt(log(n)) / n^a This number will always be positive so long as n 0. I suppose I could make N = 1 just to be safe. c = 2^sqrt(log(n)) / n^a N = 1 c*n^a = 2^sqrt(log(n) <= 2^log(n) for all values of n >= 1 Now, I know this is incorrect, because I could just as easily claim that the function 2^sqrt(log(n)) is O(n)...

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  • AAC.js : le décodeur audio JavaScript open source supporte le profile Low Complexity

    AAC.js : le dernier décodeur audio JavaScript de Official.fm Labs qui supporte le profile Low Complexity [IMG]http://media.tumblr.com/tumblr_m6wpozHbxB1qbis4g.png[/IMG] L'équipe de Official.fm Labs vient de sortir un codec audio qui pourrait d'ailleurs être le prochain codec le plus utilisé après le MP3, voire le surpasser. AAC.js est entièrement codé en JavaScript avec le framework Aurora.js qui facilite l'écriture de codecs. AAC, qui signifie Advanced Audio Codec, est l'un des codecs les plus courants et des noms comm...

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  • Handle complexity in large software projects

    - by Oliver Vogel
    I am a lead developer in a larger software projects. From time to time its getting hard to handle the complexity within this project. E. g. Have the whole big picture in mind all the time Keeping track of the teammates work results Doing Code Reviews Supply management with information etc. Are there best practices/ time management techniques to handle these tasks? Are there any tools to support you having an overview?

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