In computer science , the ostrich algorithm is a strategy of ignoring potential problems on the basis that they may be exceedingly rare to stick your head in the sand and pretend that there is no problem . This assumes that it is more cost effective to allow the problem to occur than to attempt its prevention. This approach may be used in dealing with deadlock s in concurrent programming if deadlocks are believed to be very rare, and if the cost of detection or prevention is high. Trade offs Convenience Correctness It is one of the methods of dealing with deadlocks. Other methods are avoidance banker s algorithm , prevention, detection and recovery. Some algorithms with poor worst case performance are commonly used because they only exhibit poor performance on artificial cases that do not occur in practice typical examples are the simplex algorithm and the type checking algorithm for Standard ML . Issues like integer overflow in programming languages with fixed width integers are also frequently ignored because they occur only in exceptional cases that don t arise for practical inputs. Hybrid approach Hybrid approach to using Ostrich algorithm is determining that the exceedingly rare case does not happen, and then switching from another costly algorithm to this one. The trade off here is that if circumstances change or are unaccounted for, the rare problem may re occur. An example can be found in the http nohardlockrwlocker.codeplex.com Non Hard Locking ReadWriteLocker site , where one has the option to determine where deadlocks might occur, and then turn off deadlock detection once one determines it doesn t need to be used. References http www.cs.rpi.edu academics courses fall04 os c10 index.html Ostrich algorithm http nohardlockrwlocker.codeplex.com Non Hard Locking Read Write Locker Category Concurrent algorithms algorithm stub cs P tros algoritmus de Vogel Strau Algorithmus el ja pt Algoritmo do avestruz uk ... more details
The DSW algorithm , or in full Day Stout Warren algorithm , is a method for efficiently balancing binary search tree s &mdash that is, decreasing their height to Big O notation O log n nodes, where n is the total number of nodes. Unlike a self balancing binary search tree , it does not do this incrementally during each operation, but periodically, so that its cost can be amortized analysis amortized over many operations. The algorithm was designed by Category People from Euclid, Ohio Quentin F. Stout and Bette Warren in their 1986 paper Tree Rebalancing in Optimal Time and Space , based on work done by Colin Day in 1976. The algorithm requires linear O n time and is in place algorithm in place . The original algorithm by Day generates as compact a tree as possible all levels of the tree are completely full except possibly the bottom most. The Stout Warren modification generates a complete binary tree, namely one in which the bottom most level is filled strictly from left to right. This is a useful transformation to perform if it is known that no more inserts will be done. A 2002 article by Timothy J. Rolfe has recently brought attention back to the DSW algorithm after a long hiatus the naming is from the section title 6.7.1 The DSW Algorithm in Adam Drozdek s Data Structures and Algorithms in C PWS Publishing Co., 1996 pp. 173 175. Rolfe cites two main advantages in circumstances in which one generates an entire binary search tree at the beginning of processing, followed by item look up access for the rest of processing and pedagogically within a course on data structures where one progresses from the binary search tree into self adjusting trees, since it gives a first exposure to doing rotations within a binary search tree. External links http penguin.ewu.edu trolfe DSWpaper An explanation and some experiments by Timothy J. Rolfe http www.eecs.umich.edu qstout pap CACM86.pdf The original paper by Stout and Warren http www.eecs.umich.edu qstout Prof. Quentin Stout s homepage ... more details
Unreferenced date December 2009 Huang s algorithm is an algorithm for detecting Termination analysis termination in a distributed system . The algorithm was proposed by Shing Tsaan Huang in 1989 in the Journal of Computers . Termination detection The basis of termination detection is in the concept of a distributed system process state. At any time, a process in a distributed system is either in an active state or in an idle state. An active process may become idle at any time but an idle process may only become active again upon receiving a computational message. Termination occurs when all processes in the distributed system become idle and there are no computational messages in transit. Algorithm Huang s algorithm can be described by the following Initially all processes are idle. A distributed task is started by a process sending a computational message to another process. This initial process to send the message is the controlling agent . The initial weight of the controlling agent is math w math usually 1 . The following rules are applied throughout the computation A process sending a message splits its current weight between itself and the message. A process receiving a message adds the weight of the message to itself. Upon becoming idle, a process sends a message containing its entire weight back to the controlling agent. Termination occurs when the controlling agent has a weight of math w math and is in the idle state. Some weaknesses to Huang s algorithm are that it is unable to detect termination if a message is lost in transit or if a process fails while in an active state. See also Dijkstra Scholten algorithm DEFAULTSORT Huang s Algorithm Category Termination algorithms ... more details
The Warnock algorithm is a Hidden surface determination hidden surface algorithm invented by John Warnock that is typically used in the field of computer graphics . ref cite web title A hidden surface algorithm for computer generated halftone pictures last Warnock first John authorlink John Warnock url http portal.acm.org citation.cfm?id 905316&dl ACM publisher University of Utah format HTML gateway to PDF year 1969 quote The algorithm was Warnock s doctoral thesis. , 32 pages br Also http www.dtic.mil cgi bin GetTRDoc?AD AD753671&Location U2&doc GetTRDoc.pdf ref It solves the problem of rendering a complicated image by recursive subdivision of a scene until areas are obtained that are trivial to compute. In other words, if the scene is simple enough to compute efficiently then it is rendered otherwise it is divided into smaller parts which are likewise tested for simplicity. ref cite book last Daintith first John coauthors Wright, Edmund year 2009 title Oxford Dictionary of Computing publisher Oxford University Press isbn 978 0199234004 , 608 pages ref This is a divide and conquer algorithm with analysis of algorithms run time of math O np math , where n is the number of polygons and p is the number of pixels in the viewport. The inputs are a list of polygons and a viewport. The best case is that if the list of polygons is simple, then draw the polygons in the viewport. Simple is defined as one polygon or a viewport that is one pixel in size. The continuous step is to split the viewport into 4 equally sized quadrants and to recursively call the algorithm for each quadrant, with a polygon list modified such that it only contains polygons that are visible in that quadrant. References reflist External links http medialab.di.unipi.it web IUM Waterloo node68.html A summary of the Warnock Algorithm DEFAULTSORT Warnock Algorithm Category Computer graphics algorithms compu prog stub de Warnock Algorithmus pl Algorytm Warnocka ... more details
The Berkeley algorithm is a method of clock synchronisation in distributed computing which assumes no machine has an accurate time source. It was developed by Gusella and Zatti at the University of California, Berkeley in 1989 ref Citation title The accuracy of the clock synchronization achieved by TEMPO in Berkeley UNIX 4.3BSD journal Software Engineering, IEEE Transactions on volume 15 issue 7 year 1989 pages 847 853 url http ieeexplore.ieee.org xpl freeabs all.jsp?arnumber 29484 publisher IEEE author Gusella, R. Zatti, S. doi 10.1109 32.29484 ref and like Cristian s algorithm is intended for use within intranets . The algorithm Unlike Cristian s algorithm the server process in Berkeley algorithm, called the master periodically polls other slave process. Generally speaking the algorithm is as follows A master is chosen via an election process such as Chang and Roberts algorithm . The master polls the slaves who reply with their time in a similar way to Cristian s algorithm . The master observes the round trip time RTT of the messages and estimates the time of each slave and its own. The master then averages the clock times, ignoring any values it receives far outside the values of the others. Instead of sending the updated current time back to the other process, the master then sends out the amount positive or negative that each slave must adjust its clock. This avoids further uncertainty due to RTT at the slave processes. With this method the average cancels out individual clock s tendencies to drift. Gusella and Zatti released results involving 15 computers whose clocks were synchronised to within about 20 25 milliseconds using their protocol. Computer systems normally avoid rewinding their clock when they receive a negative clock alteration from the master. Doing so would break the property of monotonic time, which is a fundamental assumption in certain algorithms in the system itself or in programs such as Make software make . A simple solution to this problem ... more details
multiple image direction vertical width 350 footer Example of Ruppert s algorithm image1 RuppertsAlgorithm input.png alt1 Ruppert s Algorithm input caption1 Input planar straight line graph image2 RuppertsAlgorithm output.png alt2 Output conforming Delaunay triangulation caption2 Output conforming Delaunay triangulation In mesh generation , Ruppert s algorithm , also known as Delaunay refinement , is an algorithm for creating quality Delaunay triangulation s. The algorithm takes a planar straight ... Ruppert title A Delaunay refinement algorithm for quality 2 dimensional mesh generation journal Journal of Algorithms year 1995 issue 3 pages 548 585 volume 18 ref Ruppert s algorithm for two dimensional quality mesh generation is perhaps the first theoretically guaranteed meshing algorithm to be truly ... Algorithm url http www.cs.cmu.edu quake tripaper triangle3.html accessdate April 2010 ref Motivation ... by using an unstructured grid . The computer uses Ruppert s algorithm or some similar meshing algorithm ... thumb 350px Intermediate triangulations of Ruppert s algorithmAlgorithm Description The algorithm begins with a Delaunay triangulation of the input vertices and then consists of two .... Practical Usage Without modification Ruppert s algorithm is guaranteed to terminate and generate ... near small input angles, the algorithm can be extended to handle any straight line input. ref ... International Meshing Roundtable pages 165 181 year 2005 ref Ruppert s algorithm can be naturally ... tetrahedron. An extension of Ruppert s algorithm in two dimensions is implemented in the freely available Triangle package. Two variants of Ruppert s algorithm in this package are guaranteed to terminate ... the algorithm to fail with a threshold greater than 29.06 degrees. ref cite arxiv last Rand first Alexander title Improved Examples of Non Termination for Ruppert s Algorithm year 2011 eprint 1103.3903 class cs.CG . ref See also Chew s second algorithm Delaunay triangulation Local feature size ... more details
Distinguish Schlemiel the Painter s algorithm The painter s algorithm , also known as a priority fill , is one of the simplest solutions to the visibility problem in 3D computer graphics . When projecting a 3D scene onto a 2D plane, it is necessary at some point to decide which polygon s are visible, and which are Hidden surface determination hidden . The name painter s algorithm refers to the technique employed by many painters of painting distant parts of a scene before parts which are nearer thereby covering some areas of distant parts. The painter s algorithm sorts all the polygons in a scene by their depth and then paints them in this order, farthest to closest. It will paint over the parts that are normally not visible thus solving the visibility problem at the cost of having painted ..., are painted. File Painters problem.svg thumb right frame Overlapping polygons can cause the algorithm to fail The algorithm can fail in some cases, including cyclic overlap or piercing polygons. In the case ..., the offending polygons must be cut to allow sorting. Newell s algorithm , proposed in 1972, provides ..., the painter s algorithm can be inefficient. It forces the system to rendering computer graphics ... scene. This means that, for detailed scenes, the painter s algorithm can overly tax the computer hardware. A reverse painter s algorithm is sometimes used, in which objects nearest to the viewer ... by nearby objects. However, the reverse algorithm suffers from many of the same problems as the standard version. These and other flaws with the algorithm led to the development of Z buffering Z buffer techniques, which can be viewed as a development of the painter s algorithm, by resolving .... Even in such systems, a variant of the painter s algorithm is sometimes employed. As Z buffer implementations ... 2008 , drawing the affected edges of both polygons in the order given by painter s algorithm. This means that some pixels are actually drawn twice as in the full painters algorithm but this happens ... more details
Context date October 2009 Multilevel Coordinate Search MSC is an algorithm for bound constrained global optimization using function mathematics function values only. To do so, the n dimensional search space is represented by a set of non intersecting hypercubes boxes . The boxes are then iteratively split along an axis plane according to the value of the function at a representative point of the box and the box s size. These two splitting criteria combine to form a global search by splitting large boxes and a local search by splitting areas for which the function value is good. Additionally a local search combining a quadratic interpolant of the function and line search es can be used to augment performance of the algorithm. External links http www.mat.univie.ac.at neum software mcs Homepage of the algorithm http www.mat.univie.ac.at neum glopt janka dix sze eng.html Performance of the algorithm relative to others Category Optimization algorithms and methods mathapplied stub ... more details
orphan date April 2010 GrowCut is an interactive segmentation algorithm . It uses Cellular automaton Cellular Automaton as an image model. Automata evolution models segmentation process. Each cell of the automata has some label in case of binary segmentation object , background and empty . During Automata theory automata evolution some cells capture their neighbours, replacing their labels. In GrowCut, a user vaguely draws some strokes inside the object of interest with an object brush, and outside the object with a background brush. In simple cases only a few strokes suffice for segmentation . Image GrowCut Algorithm Demo.gif thumb GrowCut demo References cite conference author V. Vezhnevets, V. Konouchine title Grow Cut Interactive Multi Label N D Image Segmentation booktitle Proc. Graphicon year 2005 pages 150&ndash 156 url http graphics.cs.msu.ru en publications text gc2005vk.pdf External links http www.growcut.com a Photoshop plugin, which implements GrowCut algorithm DEFAULTSORT Growcut Algorithm Category Image processing ... more details
Dinic s algorithm is a strongly polynomial algorithm for computing the maximum flow in a flow network ... Yefim Dinitz title Algorithm for solution of a problem of maximum flow in a network with power estimation ... dinitz D70.pdf ref . The algorithm runs in math O V 2 E math time and is similar to the Edmonds Karp algorithm , which runs in math O VE 2 math time, in that it uses shortest augmenting paths. The introduction of the concepts of the level graph and blocking flow enable Dinic s algorithm to achieve ... contains no math s t math path. Algorithm Dinic s Algorithm Input A network math G V, E , c, s, t math ... math blocking flows in the algorithm, where math n math is the number of vertices in the network. The level ... s algorithm is math O V 2 E math . Using a data structure called dynamic trees , the running time ... time of Dinic s algorithm can be improved to math O VE log V math . Special cases In networks ... O V 2 3 math . Thus the algorithm runs in math O min V 2 3 , E 1 2 E math time. In networks arising ... math , therefore leading to the math O sqrt V E math time bound. The resulting algorithm is also known as Hopcroft Karp algorithm . More generally, this bound holds for any unit network a network in which ... 1983 p 102 Example The following is a simulation of the Dinic s algorithm. In the level graph math ... math G math math G f math math G L math 1. File Dinic algorithm G1.svg 300px File Dinic algorithm Gf1.svg 300px File Dinic algorithm GL1.svg 300px align left colspan 3 The blocking flow consists of math ... f math is 14. Note that each augmenting path in the blocking flow has 3 edges. 2. File Dinic algorithm G2.svg 300px File Dinic algorithm Gf2.svg 300px File Dinic algorithm GL2.svg 300px align left ... path has 4 edges. 3. File Dinic algorithm G3.svg 300px File Dinic algorithm Gf3.svg 300px File Dinic algorithm GL3.svg 300px align left colspan 3 Since math t math cannot be reached in math G f math . The algorithm ..., the number of edges in the augmenting path increases by at least 1. History Dinic s algorithm was published ... more details
The snapshot algorithm is an algorithm used in distributed systems for recording a consistent global state of an asynchronous communication asynchronous system. The algorithm discussed here is also known as Chandy Lamport Algorithm , after Leslie Lamport and K. Mani Chandy . History According to http research.microsoft.com users lamport pubs pubs.html chandy Leslie Lamport s website , The distributed snapshot algorithm described here came about when I visited Chandy, who was then at the University of Texas at Austin University of Texas in Austin . He posed the problem to me over dinner, but we had both had too much wine to think about it right then. The next morning, in the shower, I came up with the solution. When I arrived at Chandy s office, he was waiting for me with the same solution. It was defined in a paper titled http research.microsoft.com users lamport pubs chandy.pdf Distributed Snapshots Determining Global States of a Distributed System . Definition The assumptions of the algorithm are as follows There are no failures and all messages arrive intact and only once The communication channels are unidirectional and FIFO ordered There is a communication path between any two processes in the system Any process may initiate the snapshot algorithm The snapshot algorithm does not interfere with the normal execution of the processes Each process in the system records its local state and the state of its incoming channels The algorithm works using marker messages. Each process that wants to initiate a snapshot records its local state and sends a marker on each of its outgoing channels. All the other processes, upon receiving a marker, record their local state, the state ... it first recorded its local state. Some of the assumptions of the algorithm can be facilitated using a more reliable communication protocol such as Internet protocol suite TCP IP . The algorithm can ... algorithm works like this The observer process the process taking a snapshot Saves its own local state ... more details
In computer science , the Kosaraju Sharir algorithm is an algorithm to find the strongly connected component s of a directed graph . Alfred V. Aho Aho , John E. Hopcroft Hopcroft and Jeffrey D. Ullman Ullman credit it to an unpublished paper from 1978 by S. Rao Kosaraju and Micha Sharir . It makes use of the fact that the transpose graph the same graph with the direction of every edge reversed has exactly the same strongly connected components as the original graph. Kosaraju Sharir algorithm is simple and works as follows Let G be a directed graph and S be an empty stack data structure stack . While S does not contain all vertices Choose an arbitrary vertex v not in S. Perform a depth first search starting at v . Each time that depth first search finishes expanding a vertex u , push u onto S. Reverse the directions of all arcs to obtain the transpose graph. While S is nonempty Pop the top vertex v from S. Perform a depth first search starting at v . The set of visited vertices will give the strongly connected component containing v record this and remove all these vertices from the graph G and the stack S. Equivalently, breadth first search BFS can be used instead of depth first search. Complexity Provided the graph is described using an adjacency list , Kosaraju Sharir algorithm ... optimal because there is a matching lower bound any algorithm must examine all vertices and edges . It is the conceptually simplest efficient algorithm, but is not as efficient in practice as Tarjan s strongly connected components algorithm and Cheriyan Mehlhorn Gabow algorithm Gabow s algorithm ... , the algorithm requires V sup 2 sup time. References Alfred V. Aho , John E. Hopcroft , Jeffrey ... and proof of Kosaraju s Algorithm http scienceblogs.com goodmath 2007 10 computing strongly connected ...?title Kosaraju 27s algorithm Java implementation at AlgoWiki.net Category Graph algorithms Category Graph connectivity algorithm stub fa ru th vi ... more details
An adaptive algorithm is an algorithm that changes its behavior based on the resources available. For example, stable partition , using no additional memory is O n lg n but given O n memory, it can be O n in time. As implemented by the C Standard Library , http www.sgi.com tech stl stable partition.html code stable partition code is adaptive and so it acquires as much memory as it can get up to what it would need at most and applies the algorithm using that available memory. Another example is adaptive sort , whose behaviour changes upon the presortedness of its input. Category Algorithms soft eng stub ru fr Algorithme adaptatif uk ... more details
F rer s algorithm is an integer multiplication algorithm for very large numbers possessing a very low asymptotic complexity . It was created in 2007 by Switzerland Swiss mathematician Martin F rer of Pennsylvania State University ref name f rer 1 F rer, M. 2007 . http www.cse.psu.edu furer Papers mult.pdf Faster Integer Multiplication in Proceedings of the thirty ninth annual ACM symposium on Theory of computing, June 11 13, 2007, San Diego, California, USA ref as an asymptotically faster when analysed on a multitape Turing machine algorithm than its predecessor, the Sch nhage Strassen algorithm published in 1971. ref A. Sch nhage and V. Strassen, Schnelle Multiplikation gro er Zahlen , Computing 7 1971 , pp. 281 292. ref The predecessor to the F rer algorithm, the Sch nhage Strassen algorithm, used fast Fourier transform s to compute integer products in time math O n log n log log n math in big O notation and its authors, Arnold Sch nhage and Volker Strassen , also conjectured a lower bound for the problem of nowrap math Omega n log n math . Here, math n math denotes the total number of bits in the two input numbers. F rer s algorithm reduces the gap between these two bounds it can be used to multiply binary integers of length math n math in time math style vertical align 15 n log n ,2 O log n math or by a Boolean circuit circuit with that many logic gates , where nowrap log star n represents the iterated logarithm operation. However, the difference between the math log log n math and math style vertical align 0 2 log n math factors in the time bounds of the Sch nhage Strassen algorithm and the F rer algorithm for realistic values of math n math is very small. ref name f rer .... Symposium on Theory of Computation STOC 2008. arXiv 0801.1416 ref gave a similar algorithm that relies ... Number theoretic transform References reflist Number theoretic algorithms DEFAULTSORT Furer S Algorithm Category Arbitrary precision algorithms algorithm stub fr Algorithme de F rer ru ... more details
The firefly algorithm FA is a metaheuristic algorithm , inspired by the flashing behaviour of firefly ... fireflies. Xin she Yang Xin She Yang formulated this firefly algorithm by assuming ref cite book first ... algorithm is a nature inspired metaheuristic Optimization mathematics optimization algorithm . Algorithm ... fileexchange 29693 firefly algorithm content fa mincon.m ref In some difficult problem, it may ... monotonic variation of math alpha t math will enable the algorithm to escape any local optima when ... code http www.mathworks.com matlabcentral fileexchange 29693 firefly algorithm is available ref A python ... p csc6810project ref Recent studies shows that the firefly algorithm is very efficient, ref cite ... Firefly algorithm for continuous constrained optimization task work ICCCI 2009, Lecture Notes in Artificial ... that firefly algorithm can deal with stochastic test functions ref cite journal last Yang first X. S. title Firefly algorithm, stochastic test functions and design optimisation journal Int ... year 2011 ref A clear demonstration of superiority of firefly algorithm over particle swarm optimization ... using firefly and particle swarm optimization algorithm, Progress in Elelectromagnetic Research B, Vol. 36, 113 131 2012 ref In addition, firefly algorithm can efficiently solve non convex problems with complex nonlinear constraints. ref X. S. Yang, S. S. Hosseini, A. H. Gandomi, Firefly algorithm ... firefly algorithm performance, Int. J. Artificial Intelligence, Vol. 8 S 12 , 97 117 2012 ref ref B. Nasiri, M. R. Meybodi, Speciation based firefly algorithm for optimization in dynamic environments, Int. J. Artificial Intelligence, Vol. 8 S12 , 118 132 2012 ref Variants of Firefly Algorithm Discrete Firefly Algorithm DFA A discrete version of Firefly Algorithm, namely, Discrete Firefly Algorithm ... 7.pdf ref DFA outperforms existing algorithms such as the ant colony algorithm. For image segmentation ... cluster method and firefly algorithm, in Proc. of 7th Int. Conf. on Natural Computation ICNC , pp. 1817 ... more details
The condensation algorithm Con ditional Dens ity Propag ation is a computer vision algorithm. The principal application is to detect and video tracking track the contour of objects moving in a cluttered environment. Object tracking is one of the more basic and difficult aspects of computer vision and is generally a prerequisite to object recognition. Being able to identify which pixels in an image make up the contour of an object is a non trivial problem. Condensation is a probabilistic algorithm that attempts to solve this problem. The algorithm itself is described in detail by Isard and Andrew Blake scientist Blake in a publication in the International Journal of Computer Vision in 1998. One of the most interesting facets of the algorithm is that it does not compute on every pixel of the image. Rather, pixels to process are chosen at random, and only a subset of the pixels end up being processed. Multiple hypotheses about what is moving where are supported naturally by the probabilistic nature of the approach. The evaluation functions come largely from previous work in the area and include many standard statistical approaches. The original part of this work is the application of particle filter estimation techniques. See also Particle filter Condensation is the application of Sampling Importance Resampling SIR estimation to contour tracking External links http www.robots.ox.ac.uk misard condensation.html Condensation homepage http www.springerlink.com link.asp?id xl887466h454318k Condensation conditional density propagation for visual tracking , by Michael Isard and Andrew Blake International Journal of Computer Vision 29 1 5 28, August 1998 Signal processing stub Category Computer vision no Condensation algoritmen ... more details
Featherstone s algorithm is a technique used for computing the effects of forces applied to a structure of joints and links an open kinematic chain such as a skeleton used in ragdoll physics . The Featherstone s algorithm uses a reduced coordinate representation. This is in contrast to the more popular Lagrange multiplier method, which uses maximal coordinates. http www.kuffner.org james software dynamics mirtich Brian Mirtich s PhD Thesis has a very clear and detailed description of the algorithm. Baraff s paper http www.cs.cmu.edu baraff papers index.html Linear time dynamics using Lagrange multipliers has a discussion and comparison of both algorithms. References cite book first R. last Featherstone title Robot Dynamics Algorithms publisher Kluwer location Boston year 1987 isbn 0 89838 230 0 External links http www.kuffner.org james software Source code for implementation of Featherstone s algorithm http www.thyrix.com documentation featherstone method.php Description and references http www.kuffner.org james software dynamics mirtich Mirtich s Thesis http www.cs.cmu.edu baraff papers index.html Baraff s Lagrange multiplier method Category Mechanics Category Computational physics Category Computer physics engines algorithm stub ... more details
The HS Algorithm is named after Dan Hirschberg and J. B. Sinclair . It is a distributed algorithm designed for the leader election Leader Election problem in a Synchronous Ring . The algorithm requires the use of unique IDs UID for each process. The algorithm works in phases and sends its UID out in both directions. The message goes out a distance of 2 sup Phase Number sup hops and then the message heads back to the originating process. While the messages are heading out each receiving process will compare the incoming UID to its own. If the UID is greater than its own UID then it will continue the message on. Otherwise if the UID is less than its own UID, it will not pass the information on. At the end of a phase, a process can determine if it will send out messages in the next round by if it received both of its incoming messages. Phases continue until a process receives both of its out messages, from both of its neighbors. At this time the process knows it is the largest UID in the ring and declares itself the leader. References Nancy A. Lynch, Distributed Algorithms, Morgan Kaufmann Publishers, Inc. 1996 pp. 31 35. algorithm stub Category Distributed algorithms ... more details
In theoretical computer science , a Markov algorithm is a string rewriting system that uses Formal grammar grammar like rules to operate on string computer science strings of symbols. Markov algorithms have been shown to be Turing complete , which means that they are suitable as a general model of computation and can represent any mathematical expression from its simple notation. Markov algorithms are named after the mathematician Andrey Markov, Jr. Refal is a programming language based on Markov algorithms. Algorithm The Rules is a sequence of pair of strings, usually presented in the form of pattern &rarr replacement . Some rules may be terminating. Given an input string Check the Rules in order from top to bottom to see whether any of the patterns can be found in the input string. If none is found, the algorithm stops. If one or more is found, use the first of them to replace the leftmost matching text in the input string with its replacement . If the applied rule was a terminating one, the algorithm stops. Return to step 1 and carry on. Example The following example shows the basic operation of a Markov algorithm. Rules A apple B bag S shop T the the shop my brother a never used . terminating rule Symbol string I bought a B of As from T S. Execution If the algorithm is applied to the above example, the Symbol string will change in the following manner. I bought a B of apples from T S. I bought a bag of apples from T S. I bought a bag of apples from T shop. I bought a bag of apples from the shop. I bought a bag of apples from my brother. The algorithm will then terminate. Another Example These rules give a more interesting example. They rewrite binary numbers to their unary ... 0 0 Symbol string 101 Execution If the algorithm is applied to the above example, it will terminate ... utility markov rewriter Online Markov algorithm interpreter http sourceforge.net projects markov Markov algorithm interpreter http nic nac project.de jcm index.php?nav projects Markov algorithm interpreter ... more details
In mathematics , Gosper s algorithm is a procedure for finding sums of Hypergeometric identities hypergeometric terms that are themselves hypergeometric terms. That is suppose we have a 1 ... a n S n &minus S 0 , where S n is a hypergeometric term i.e., S n 1 S n is a rational function of n then necessarily a n is itself a hypergeometric term, and given the formula for a n Gosper s algorithm finds that for S n . Outline of the algorithm Step 1 Find a polynomial p such that, writing b n a n p n , the ratio b n b n &minus 1 has the form q n r n where q and r are polynomials and no q n has a nontrivial factor with r n j for j 0, 1, 2, ... . This is always possible, whether or not the series is summable in closed form. Step 2 Find a polynomial &fnof such that S n q n 1 p n &fnof n a n . If the series is summable in closed form then clearly a rational function &fnof with this property exists in fact it must always be a polynomial, and an upper bound on its degree can be found. Determining &fnof or finding that there is no such &fnof is then a matter of solving a system of linear equations. Relationship to Wilf&ndash Zeilberger pairs Gosper s algorithm can be used to discover Wilf&ndash Zeilberger pair s, where they exist. Suppose that F n 1, k &minus F n ... a k F n 1, k &minus F n , k into Gosper s algorithm. Treat ... in the algorithm works in this setting. If it successfully finds S k with S k &minus ... . Definite versus indefinite summation Gosper s algorithm finds where possible a hypergeometric closed ... s algorithm and Petkov ek s algorithm may be used to find closed forms for the sum over k of a n , k . History Bill Gosper discovered this algorithm in the 1970s while working on the Macsyma ... 75 1 40.pdf Gosper s 1977 article in PNAS reporting on the algorithm. Category Computer algebra ... more details
Bat inspired algorithm is a metaheuristic search optimization developed by Xin She Yang in 2010. ref Yang, X. S., A New Metaheuristic Bat Inspired Algorithm, in Nature Inspired Cooperative Strategies for Optimization NISCO 2010 Eds. J. R. Gonzalez et al. , Studies in Computational Intelligence, Springer Berlin, 284, Springer, 65 74 2010 . http arxiv.org abs 1004.4170 ref This bat algorithm is based on the echolocation behaviour of microbats with varying pulse rates of emission and loudness. ref Altringham, J. D., Bats Biology and Behaviour, Oxford Univesity Press, 1996 . ref ref Richardson, P., Bats. Natural History Museum, London, 2008 ref Algorithm Description The idealization of echolocation can be summarized as follows Each virtual bat flies randomly with a velocity math v i math at position solution math x i math with a varying frequency or wavelength and loudness math A i math . As it searches and finds its prey, it changes frequency, loudness and pulse emission rate math r math . Search is intensified by a local random walk . Selection of the best continues until certain stop criteria are met. A detailed introduction of metaheuristic algorithms including the bat algorithm is given by Yang ref Yang, X. S., Nature Inspired Metaheuristic Algoirthms, 2nd Edition, Luniver Press, 2010 . ref where a demo program in Matlab Octave is available, while a comprehensive review is carried out by Parpinelli and Lopes. ref Parpinelli, R. S., and Lopes, H. S., New inspirations in swarm ... is the development of an evolving bat algorithm EBA with better efficiency. ref P. W. Tsai, J. S. Pan, B. Y. Liao, M. J. Tsai, V. Istanda, Bat algorithm inspired algorithm for solving numerical optimization ... Bat Algorithm MOBA Using a simple weighted sum with random weights, a very effective but yet simple multiobjective bat algorithm MOBA has been developed to solve multiobjective engineering design tasks. ref X. S. Yang, bat algorithm for multi objective optimisation, Int. J. Bio Inspired Computation ... more details
graph search algorithm Kruskal s algorithm is an algorithm in graph theory that finds a minimum spanning ... tree for each Connected component graph theory connected component . Kruskal s algorithm is an example of a greedy algorithm . This algorithm first appeared in Proceedings of the American Mathematical ... for this problem include Prim s algorithm , Reverse Delete algorithm , and Bor vka s algorithm . Description ... of the algorithm , the forest has only one component and forms a minimum spanning tree of the graph ... s algorithm can be shown to run in Big O notation O E binary logarithm log E time, or equivalently ... sort or radix sort , the algorithm can use more sophisticated disjoint set data structure to run ... Algorithm 1.svg 200px AD and CE are the shortest arcs, with length 5, and AD has been Arbitrary arbitrarily chosen, so it is highlighted. Image Kruskal Algorithm 2.svg 200px CE is now the shortest arc that does not form a cycle, with length 5, so it is highlighted as the second arc. Image Kruskal Algorithm ... Kruskal Algorithm 4.svg 200px The next shortest arcs are AB and BE , both with length 7. AB is chosen ... Algorithm 5.svg 200px The process continues to highlight the next smallest arc, BE with length 7. Many ... it would form the loop DEBA , and FE because it would form FEBAD . Image Kruskal Algorithm 6.svg .... Proof of correctness The proof consists of two parts. First, it is proved that the algorithm produces ... of math P math produced by the algorithm. math Y math cannot have a cycle, since the last ... Y math would have been added by the algorithm. Thus, math Y math is a spanning tree of math P math ... If F is the set of edges chosen at any stage of the algorithm, then there is some minimum spanning ... than the weight of e , otherwise the algorithm would have chosen f instead of e . So T &minus f e is a minimum .... See also Reverse Delete algorithm Dijkstra s algorithm Prim s algorithm References Joseph. B ... , Fourth Edition. John Wiley & Sons, Inc., 2006. ISBN 0 471 73884 0. Section 13.7.1 Kruskal s Algorithm ... more details
Bach s algorithm ref Eric Bach Bach, Eric . How to Generate Factored Random Numbers , SIAM Journal of Computing, 17 1988 , pp 179 193. ref is a probabilistic polynomial time algorithm for generating pseudorandom number generator random numbers along with their factoring factorization , named after its discoverer, Eric Bach . It is of interest because no algorithm is known that efficiently factors numbers, so the straightforward method, namely generating a random number and then factoring it, is impractical. The algorithm performs, in expectation, O log n primality tests . A simpler, but less efficient algorithm performing, in expectation, O log sup 2 sup n primality tests , is known and is due to Adam Kalai ref Generating Random Factored Numbers, Easily Adam Kalai, Journal of Cryptology, Vol 16, Number 4, 2003 ref Overview Bach s algorithm produces a number x uniformly at random between a given limit N and N 2, specifically math frac N 2 x le N math , along with its factorization. It does this by picking a prime number p and an exponent a such that math p a le N math , according to a certain distribution. Bach s algorithm is then recursively applied to generate a number y uniformly at random between M and M 2, where math M frac N p a math , along with the factorization of y . It then sets math x p a y math , and appends math p a math to the factorization of y to produce the factorization of x . This gives x which logarithmic distribution over the desired range rejection sampling is then used to get a uniform distribution. References references Eric Bach Bach, Eric . Analytic methods in the Analysis and Design of Number Theoretic Algorithms , MIT Press, 1984. Chapter 2, Generation of Random Factorizations , part of which is available online http www.cs.cmu.edu afs cs.cmu.edu academic class 15750 s02 www dartboard.pdf here . Category Cryptographic algorithms ... more details
Unreferenced date October 2011 The CN2 induction algorithm is a Algorithmic learning theory learning algorithm for rule induction . It is designed to work even when the training data is imperfect. It is based on ideas from the AQ algorithm and the ID3 algorithm . As a consequence it creates a rule set like that created by AQ but is able to handle noisy data like ID3. Description of algorithm The algorithm must be given a set of examples, TrainingSet, which have already been classified in order to generate a list of classification rules. A set of conditions, SimpleConditionSet, which can be applied, alone or in combination, to any set of examples is predefined to be used for the classification. routine CN2 TrainingSet let the ClassificationRuleList be empty repeat let the BestConditionExpression be Find BestConditionExpression TrainingSet if the BestConditionExpression is not nil then let the TrainingSubset be the examples covered by the BestConditionExpression remove from the TrainingSet the examples in the TrainingSubset let the MostCommonClass be the most common class of examples in the TrainingSubset append to the ClassificationRuleList the rule if the BestConditionExpression then the class is the MostCommonClass until the TrainingSet is empty or the BestConditionExpression is nil return the ClassificationRuleList routine Find BestConditionExpression TrainingSet let the ConditionalExpressionSet be empty let the BestConditionExpression be nil repeat let the TrialConditionalExpressionSet be the set of conditional expressions, x and y where x belongs to the ConditionalExpressionSet and y belongs to the SimpleConditionSet . remove all formulae in the TrialConditionalExpressionSet that are either in the ConditionalExpressionSet i.e., the unspecialized ones or null e.g., big y and big n for every expression, F, in the TrialConditionalExpressionSet if F is statistically significant ... http www.springerlink.com content k6q2v76736w5039r CN2 Algorithm Description Category Machine learning ... more details
In computer science , a search algorithm is an algorithm for finding an item with specified properties among a Collection computing collection of items. The items may be stored individually as record computer science records in a database or may be elements of a search space defined by a mathematical formula or procedure, such as the root of a function roots of an Diophantine equation equation with integer variable mathematics variables or a combination of the two, such as the Hamiltonian circuit s of a graph theory graph . Classes of search algorithms For virtual search spaces Algorithms for searching ... ways. This class also includes various tree search algorithm s, that view the elements as vertices ... . Examples of algorithms for this class are the minimax algorithm , alpha beta pruning , and the A algorithm ... studied subclass are the graph algorithm s, in particular graph traversal algorithms, for finding specific ... graph theory paths , circuit graph theory circuits , and so on. Examples include Dijkstra s algorithm , Kruskal s algorithm , the nearest neighbour algorithm , and Prim s algorithm . Another important subclass of this category are the string searching algorithm s, that search for patterns within strings. Two famous examples are the Boyer Moore string search algorithm Boyer Moore and Knuth Morris Pratt algorithm s, and several algorithms based on the suffix tree data structure. Search for the maximum ... search methods designed for quantum computer s, like Grover s algorithm , that are theoretically .... Search Algorithm Is A Brief Description About The Crawling,Spidering &Indexing. See also Backward ... to rank results in very large data sets Sorting algorithm s necessary for executing certain search algorithms Selection algorithm No free lunch in search and optimization Search engine computing Linear search problem String searching algorithm References Donald Knuth . The Art of Computer Programming . Volume 3 Sorting algorithm Sorting and Searching . ISBN 0 201 89685 0. External links http ... more details
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