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# Topic: Deterministic algorithm

 Deterministic algorithm - Wikipedia, the free encyclopedia Deterministic algorithms are by far the most studied and familiar kind of algorithm, as well as one of the most practical, since they can be run on real machines efficiently. One simple model for deterministic algorithms is the mathematical function; just as a function always produces the same output given a certain input, so do deterministic algorithms. Formally, deterministic algorithms can be defined in terms of a state machine: a state describes what a machine is doing at a particular instant in time. en.wikipedia.org /wiki/Deterministic_algorithm   (667 words)

 Nondeterministic algorithm - Wikipedia, the free encyclopedia In the theory of computation, a nondeterministic algorithm is an algorithm with one or more choice points where multiple different continuations are possible, without any specification of which one will be taken. Thus, different execution paths of the algorithm arise when it is applied to the same input / initial state, and these paths, when they terminate, generally produce different output / end in different final states. One way to simulate a nondeterministic algorithm N using a deterministic algorithm D is to treat sets of states of N as states of D. en.wikipedia.org /wiki/Nondeterministic_algorithm   (438 words)

 Algorithm - Facts, Information, and Encyclopedia Reference article Algorithms can be implemented by computer programs, although often in restricted forms; mistakes in implementation and limitations of the computer can prevent a computer program from correctly executing its intended algorithm. Algorithms are essential to the way computers process information, because a computer program is essentially an algorithm that tells the computer what specific steps to perform (in what specific order) in order to carry out a specified task, such as calculating employees’ paychecks or printing students’ report cards. Algorithms are not only implemented as computer programs, but often also by other means, such as in a biological neural network (for example, the human brain implementing arithmetic or an insect relocating food), or in electric circuits or in a mechanical device. www.startsurfing.com /encyclopedia/a/l/g/Algorithm.html   (2150 words)

 Algorithm - Recipes Encyclopedia   (Site not responding. Last check: 2007-10-31) Algorithms can be implemented by computer programs, although often in restricted forms; an error in the design of an algorithm for solving a problem can lead to failures in the implementing program. The concept of an algorithm is often illustrated by the example of a recipe, although many algorithms are much more complex; algorithms often have steps that repeat (iterate) or require decisions (such as logic or comparison) until the task is completed. A greedy algorithm is similar to a dynamic programming algorithm, but the difference is that at each stage you don't have to have the solutions to the subproblems, you can make a "greedy" choice of what looks best for the moment. www.recipes.tiptophot.com /recipes/index.php?title=Algorithm   (2174 words)

 NP-complete - Wikipedia, the free encyclopedia Probabilistic: An algorithm that can be proven to yield good average runtime behavior for a given distribution of the problem instancesâ€”ideally, one that assigns low probability to "hard" inputs. Heuristic: An algorithm that works "reasonably well" on many cases, but for which there is no proof that it is both always fast and always produces a good result. One example of a heuristic algorithm is a suboptimal O(n log n) greedy algorithm used for graph coloring during the register allocation phase of some compilers, a technique called graph-coloring global register allocation. en.wikipedia.org /wiki/NP-complete   (1728 words)

 [No title] Build- crease the correlation between deterministic and probabilis- ing on work in [Beck and Wilson, 2004], we con- tic makespan, providing an explanation for its strong perfor- duct an empirical study of a number of algorithms mance. The minimum probabilistic imental results show that the algorithm performs as well as makespan, D(s), of a solution s is the smallest value D such the existing branch-and-bound style of search on small prob- that the probability that all jobs will finish before D is at least lems and significantly out-performs it on larger problems. The Correlation Between Deterministic and Probabilistic served in heuristic algorithms based on using the determin- Makespan The explanatory power of an algorithm's ability istic makespan to filter the solutions which are to be simu- to find good deterministic makespans is, by itself, insufficient lated. www.ijcai.org /papers/0748.txt   (3106 words)

 18 The expected behavior of a randomized algorithm is no better than the average behavior of its associated deterministic algorithm and is usually a little worse due to such things as the overhead of calls to a random number generator. The analog of the class NC for sequential algorithms is the class RNC for parallel algorithms. algorithm is a probabilistic algorithm that has a certain probability of returning the correct answer whatever input is considered. www.ececs.uc.edu /~jpaul/472/prob.html   (2907 words)

 Algorithm - DmWiki Advance simply continues execution of the algorithm at the next instruction in the algorithm, while jump continues the algorithm at the passed position. It is easy to see that almost any kind of algorithm will fall into this category, unless you own a computer that has a true random number generator, based on some seemingly random nucleus decay. When talking about algorithms there are a few standard terms that describe the strategy an algorithm uses to solve a problem. www.devmaster.net /wiki/Algorithm   (799 words)

 Professional Opportunities To be sure, the existence of fast randomized algorithms suggested to many that a fast deterministic algorithm must exist, but no one had yet been able to find one. Miller's algorithm was deterministic and ran in time bounded by a polynomial of degree 4, but he needed to assume the Extended Riemann Hypothesis to prove his algorithm correct. Having successfully converted the Agrawal-Biswas probabilistic algorithm into a deterministic algorithm, Agrawal and his students are hopeful that a similar approach might succeed in derandomizing other number theoretic algorithms. www.siam.org /siamnews/09-02/primality.htm   (1463 words)

 Intersections for a 2D Set of Segments Algorithms solving these problems are used in many application areas such as computer graphics, CAD, circuit design, hidden line elimination, computer vision, and so on. However, their algorithm did not achieve the theoretical lower bound; and thus, was only the first of many output-sensitive algorithms for solving the segment intersection problem. These algorithms can be used to perform boolean operations, like intersections or unions, between two different polygons or planar subdivision graphs. geometryalgorithms.com /Archive/algorithm_0108/algorithm_0108.htm   (3391 words)

 Introduction We present a novel variation on the approach of sorting by regular sampling which leads to a new deterministic sorting algorithm that achieves optimal computational speedup with very little communication [15]. In return, our algorithm reduces the problem of poor load balancing because it is able to sustain a high sampling rate at substantially less cost. Our algorithm was implemented in a high-level language and run on a variety of platforms, including the Thinking Machines CM-5, the IBM SP-2, and the Cray Research T3D. www.umiacs.umd.edu /research/EXPAR/papers/3670/node1.html   (616 words)

 Randomized Algorithms [CiteSeer; NEC Research Institute; Steve Lawrence, Kurt Bollacker, Lee Giles]   (Site not responding. Last check: 2007-10-31) The algorithms are "Las Vegas," and their expected bounds are with respect to the random behavior of the algorithms. Research on dynamic algorithms for geometric problems has received increasing attention in the last years, and is motivated by many important applications in circuit layout, computer graphics, and com... We present randomized algorithms for computing many faces in an arrangement of lines or of segments in the plane, which are considerably simpler and slightly faster than the previously known ones. sherry.ifi.unizh.ch /SoftwareEngineering/RandomizedAlgorithms   (6471 words)

 Citations: Towards practical deterministic write-all algorithms - Chlebus, Dobrev, Kowalski, Malewicz, Shvartsman, rto ...   (Site not responding. Last check: 2007-10-31) In Proceedings of the 13 ACM Symposium on Parallel Algorithms and Architectures (SPAA 2001. Deterministic algorithms that solve the CWA problem on an asynchronous system can be used to create simulations that have bounded worst case overhead. When such algorithm is used in a simulation, the simulation of a given synchronous program for p = n processors may be faster, as compared to the simulation that uses an algorithm for p.... citeseer.ifi.unizh.ch /context/1815490/484659   (758 words)

 Primality Proving 4.3: A polynomial-time algorithm Adleman and Hang [AH1992] modified the Goldwasser-Killian algorithm [GK86] to produce a randomized polynomial time algorithm that always produced a certificate of primality... But what is surprising is that in 2002 Agrawal, Kayal and Saxena [AKS2002] found a relatively simple deterministic algorithm which relies on no unproved assumptions. This is perhaps the best source for the present state of the algorithm. primes.utm.edu /prove/prove4_3.html   (720 words)

 Comparison of two Methods / Overview of Monte Carlo algorithm Otherwise a new ray direction is chosen deterministically (in case of specular event when next ray direction is unique) or stochastically (in case of diffuse scattering). Also, as was mentioned in the previous chapter, the deterministic algorithm does not account for light refraction (Figure 1a). Illumination by light reflected by such surfaces is accounted in the deterministic algorithm with use of "virtual source" method while the Monte Carlo algorithm treats this light in its general scheme, as a secondary illumination. www.keldysh.ru /pages/cgraph/articles/cmgia/monte_carlo.htm   (1396 words)

 INI : Abstracts : LAA : A deterministic subexponential algorithm for solving parity games   (Site not responding. Last check: 2007-10-31) The existence of polynomial time algorithms for the solution of parity games is a major open problem. The fastest known algorithms for the problem are randomized algorithms that run in subexponential time. Our deterministic algorithm is almost as fast as the randomized algorithms mentioned above. www.newton.cam.ac.uk /programmes/LAA/jurdzinski.html   (107 words)

 SecureRandom Many implementations are in the form of a pseudo-random number generator (PRNG), which means they use a deterministic algorithm to produce a pseudo-random sequence from a true random seed. Many SecureRandom implementations are in the form of a pseudo-random number generator (PRNG), which means they use a deterministic algorithm to produce a pseudo-random sequence from a true random seed. RNG algorithm, as supplied from the specified provider, if such a RNG implementation is available from the provider. java.sun.com /javase/6/jcp/beta/apidiffs/java/security/SecureRandom.html   (2037 words)

 PRIMES is in P little FAQ   (Site not responding. Last check: 2007-10-31) Note that there is no deterministic or randomized algorithm that is known to be able to solve the "subset sum problem" on arbitrary inputs in time bounded by a polynomial in the size of the inputs. Note that a nondeterminstic algorithm does not constitute a reasonable definition of an algorithm in practice, contrary to randomized algorithms which are very reasonable in practice (and often used). A non-deterministic algorithm can, however, be simulated by a deterministic algorithm by trying all possible choices and making sure that it doesn't get stuck prematurely in a non-terminating computation, but this is very inefficient (not bounded by a polynomial in the size of the input). crypto.cs.mcgill.ca /~stiglic/PRIMES_P_FAQ.html   (2589 words)

 Optimal Deterministic Sorting on Parallel Disks   (Site not responding. Last check: 2007-10-31) We present a load balancing technique that leads to an optimal deterministic algorithm called Balance Sort for external sorting on multiple disks. Our algorithm improves upon the randomized optimal algorithm of Vitter and Shriver as well as the (non-optimal) commonly-used technique of disk striping. It also improves upon our earlier merge-based sorting algorithm in that it has smaller constants hidden in the big-oh notation, and it is possible to implement using only striped writes (but independent reads). www.cs.duke.edu /~jsv/Papers/catalog/node15.html   (162 words)

 ResearchChannel - Deterministic Network Coding by Matrix Completion A algorithm for this problem was developed at MSR by Jaggi, Chou, Jain, et al., using graph theoretic methods. We present a new algorithm that is based on algebraic methods and matroid theory. Our main tool is a new deterministic algorithm for maximum-rank completion of mixed matrices---taking a matrix whose entries are a mixture of numeric values and symbolic variables, and assigning values to the variables so as to maximize the resulting matrix rank. www.researchchannel.org /prog/displayseries.asp?collid=804   (240 words)

 Compgeom Blog   (Site not responding. Last check: 2007-10-31) Maintaining such nonparametric depth notions under updates is an interesting problem in the area of non-parametric geometry: if you want to use notions like data depth to process data, you need a dynamic notion in order to be efficient (you can't recompute each time). If one define things approximately, there are various fairly standard techniques one can use to update contours, and there are even streaming algorithms for maintaining center points. Most of the effort is involved un engineering and hardware design (ugh), and I think there is still a while to go before the algorithms become the main source of difficulty in practice. compgeom.poly.edu /blogs/archives/4-Deterministic-algorithm-for-smal...   (1407 words)

 Dynamic splitting: An algorithm for deterministic and stochastic multiperiod optimization   (Site not responding. Last check: 2007-10-31) A new algorithm for the nonlinear multistage stochastic programming problem (MSP) is presented; one that is reasonable for the large-scale problem (e.g. The algorithm is based on the application of Spingarn's operator splitting method to the saddle point problem associated with the MSP. The algorithm was tested on a hydropower scheduling test problem containing 165,000 control variables. www.cqs.washington.edu /papers/dyn_splitting.html   (167 words)

 Deterministic selection But for theoretical purposes, it's unsatisfying to have only a randomized algorithm, and in some rare circumstances it may more important to be predictable than to be fast. Our deterministic algorithm will use the same idea of choosing x by performing a recursive call. This algorithm has the property we want, that each recursive call only involves a constant fraction of the input. www.ics.uci.edu /~eppstein/161/960130.html   (1409 words)

 algorithm   (Site not responding. Last check: 2007-10-31) probabilistic algorithm, randomized algorithm, deterministic algorithm, nondeterministic algorithm, on-line algorithm, off-line algorithm, external memory algorithm, heuristic. Go to the Dictionary of Algorithms and Data Structures home page. Paul E. Black, "algorithm", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology. www.nist.gov /dads/HTML/algorithm.html   (112 words)

 DFA::Kleene - Kleene's Algorithm for Deterministic Finite Automata DFA::Kleene - Kleene's Algorithm for Deterministic Finite Automata Define the number of states (state #1 is the ``start'' state!) of your Deterministic Finite Automaton and the alphabet used (as a string containing all characters which are part of the alphabet). Actually, a list of regular expressions is generated which describe the same language (set of patterns) as the one accepted by your Deterministic Finite Automaton. cpan.uwinnipeg.ca /htdocs/DFA-Kleene/DFA/Kleene.html   (303 words)

 On an optimal deterministic algorithm for SAT - Sadowski (ResearchIndex) Kraj'icek and P. Pudl'ak proved that an almost optimal deterministic algorithm for TAUT exists if and only if there exists a poptimal proof system for TAUT. In this paper we prove that an almost optimal deterministic algorithm for SAT exists if and only if there exists a p-optimal proof system for SAT. Combining Kraj'icek and Pudl'ak's result with our result we show that an optimal deterministic algorithm for SAT exists if and only if both p-optimal proof systems for TAUT and for... citeseer.ist.psu.edu /240348.html   (560 words)

 Random Number Generator Algorithms A deterministic RNG consists of an algorithm that produces a sequence of bits from an initial value called a seed. The algorithm should make sure that subsequent calls in the same thread or two calls on parallel threads do not produce indentical resuls. Generate the 64-bit block X0 = G(S, K, D) where G is the X9.17 RNG algorithm described in ANSI X9.17 Appendix C/ANSI X9.31 Appendix A, and where S is updated as per that algorithm. www.cryptosys.net /rng_algorithms.html   (2697 words)

 deterministic algorithm   (Site not responding. Last check: 2007-10-31) Note: That is, each time a certain set of input is presented, the algorithm gives the same results as any other time the set of input is presented. For algorithms with state, or that maintain information between inputs, "the input" means everything since the algorithm was started from an initial state. For instance, an algorithm that uses random numbers might not be considered deterministic. www.nist.gov /dads/HTML/determinalgo.html   (150 words)

 week226 It's popular to define it by saying an algorithm is "efficient" if it runs in "polynomial time": the time it takes to run is bounded by some polynomial function of the size of the input data. So, the basic idea is that a pseudorandom number generator should be an efficient algorithm that maps short truly random strings to long pseudorandom strings: we give it a short random "seed" and it cranks out a lot of digits that no efficient algorithm can guess with a success rate higher than chance would dictate. As I already mentioned, a "probabilistic algorithm" is just a deterministic algorithm that's been equipped with access to a (true) random number generator. www.math.ucr.edu /home/baez/week226.html   (6429 words)

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