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# Topic: Randomized algorithm

 Randomized Reductions Randomized algorithms (to solve a problem) are allowed to make errors and produce incorrect outputs on some sequences of random bits. For decision problems, if the randomized algorithm also provides a witness along with a yes/no answer, then the correctness of the answer can be verified by evaluating the witness (like search problems). The randomized reductions defined in Definition 6.2 are closed for randomized ap-time and they are transitive. www.uncg.edu /mat/avg/avgnp/node29.html   (491 words)

 Randomized algorithm - Wikipedia, the free encyclopedia Randomized algorithms are particularly useful when faced with a malicious "adversary" or attacker who deliberately tries to feed a bad input to the algorithm (see competitive analysis). The most basic randomized complexity class is RP, which is the class of decision problems for which there is an efficient (polynomial time) randomized algorithm (or probabilistic Turing machine) which recognizes NO-instances with absolute certainty and recognizes YES-instances with a probability of at least 1/2. Historically, the study of randomized algorithms was spurred by the discovery by Miller and Rabin in 1976 that the problem of determining the primality of a number can be solved efficiently by a randomized algorithm. en.wikipedia.org /wiki/Randomised_algorithm   (1754 words)

 Las Vegas algorithm - Wikipedia, the free encyclopedia In computing, a Las Vegas algorithm is a randomized algorithm which is correct; that is, it always produces the correct result. Namely the class RP consists of all decision problems for which a randomized polynomial-time algorithm exists that always answers correctly when the correct answer is "no", but is allowed to be wrong with a certain probability bounded away from one when the answer is "yes". Compare to Monte Carlo algorithms where the resources used are constant (or at least bounded), but the "randomness" or entropy used influences the correctness of the result. en.wikipedia.org /wiki/Las_Vegas_algorithm   (328 words)

 Nat' Academies Press, Probability and Algorithms (1992) A randomized algorithm is one that uses random numbers or bits during the runtime of the algorithm. Randomization in Parallel Algorithms Vijaya Ramachandran1 University of Texas at Austin ABSTRACT A randomized algorithm is one that uses random numbers or bits during the runtime of the algorithm. The randomized algorithm examines each vertex v independently in parallel and assigns the vertex to the independent set with probability 1/(2δ(v)), where δ(v) is the degree of v in the graph. www.nap.edu /openbook.php?record_id=2026&page=149   (3761 words)

 Randomized algorithm Summary Random sampling--if a population space of items to be evaluated is very large so that not every member of the space can be measured, then a randomization procedure is applied to draw a sample whose characteristics are likely to be close to that of the whole population itself. Randomized algorithms are particularly useful when faced with a malicious "adversary" or attacker who deliberately tries to feed a bad input to the algorithm (see competitive analysis). Historically, the study of randomized algorithms was spurred by the discovery by Miller and Rabin in 1976 that the problem of determining the primality of a number can be solved efficiently by a randomized algorithm. www.bookrags.com /Randomized_algorithm   (2722 words)

 Amazon.com: Randomized Algorithms: Books: Rajeev Motwani,Prabhakar Raghavan For many applications, a randomized algorithm is either the simplest or the fastest algorithm available, and sometimes both. Algorithmic examples are also given to illustrate the use of each tool in a concrete setting. In the second part of the book, each chapter focuses on an important area to which randomized algorithms can be applied, providing a comprehensive and representative selection of the algorithms that might be used in each of these areas. www.amazon.com /Randomized-Algorithms-Rajeev-Motwani/dp/0521474655   (810 words)

 Publications by the Algorithms Project The algorithms for these tasks all involve as an intermediate quantity an integer N (dispersion or root of an indicial polynomial) that is potentially exponential in the bit size of their input. The randomized algorithm bases on convolution to find an estimator of the scores; the variance of the estimator is particularly small for scores that are close to M, i.e., for approximate occurrences of the pattern in the text. We give a randomized algorithm in deterministic time O(N log M) for estimating the score vector of matches between a text string of length N and a pattern string of length M, i.e., the vector obtained when the pattern is slid along the text, and the number of matches is counted for each position. algo.inria.fr /papers/bibgen/algobib.html   (9047 words)

 Randomized Algorithms   (Site not responding. Last check: 2007-10-17) By this we mean that there is an element of randomness in the way that the algorithm solves a given problem. Of course, if an algorithm is to be of any use, it must find a solution to the problem at hand, so it cannot really be completely random. Randomized algorithms are said to be methods of last resort. www.brpreiss.com /books/opus4/html/page471.html   (174 words)

 Project Report We can notice that the ratio of time for randomized parallel algorithm and local parallel algorithm is less than 50%, and for sparse graph, randomized parallel algorithm runs much faster than local parallel algorithm. While the time for local parallel algorithm flexes dramatically according to structure of graph, the time for randomized parallel algorithm increases steadily around K*O(log n)  compared with size of graph, no matter what kind of structure the graph has. While the efficiency of local parallel algorithm depends on the specific structure of graph, for those sparse graphs, even we increase the # of PE, we cannot get higher speed, because the algorithm is reduced to sequential algorithm. www.cs.wayne.edu /~lxiscas/csc575/ECE7660/ProjectReport.html   (388 words)

 Citations: A simple randomized parallel algorithm for list-ranking - Anderson, Miller (ResearchIndex)   (Site not responding. Last check: 2007-10-17) ....algorithm is due to Cole and Vishkin [13] Another optimal deterministic algorithm is given by Anderson and Miller [4] Parallel list ranking algorithms using randomization were proposed by Miller and Reif [25, 26] The algorithms use O(n) processors. In the above model, our algorithm uses considerably fewer communication rounds than [1, 2, 4, 5, 7, 15, 17, 18, 20, 21, 25] The simple version of our algorithm is a generalization of the algorithm used in ReidMiller s [21] empirical study of parallel list ranking for the Cray C 90. In the above model, our algorithm uses considerably fewer communication rounds than [1, 2, 4, 5, 7, 15, 17, 18, 20, 21, 25] The simple version of our algorithm is a generalization of the algorithm used in ReidMiller s [21] empirical study of parallel list ranking for the Cray C 90 in shared.... citeseer.ist.psu.edu /context/119308/0   (3136 words)

 PRIMES is in P little FAQ   (Site not responding. Last check: 2007-10-17) 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). In 1986, Goldwasser and Killian proposed a randomized algorithm, based on elliptic curves, running in expected polynomial-time on almost all inputs, that produces a certificate for primality (a certificate of primality is some sort of evidence that proves that an integer is prime, which can be verified in polynomial time). crypto.cs.mcgill.ca /~stiglic/PRIMES_P_FAQ.html   (2589 words)

 CIS 786: Advanced Algorithms (Selected Topics in CS, Fall 2004) Randomized algorithms has proven itself to be a useful resource for developing provably efficient algorithms and it has been certainly among the central discoveries in the foundations of computer science over the last three decades. Randomized algorithms are algorithms that make random choices as they proceed, and have had a fundamental impact on several areas of computer science (e.g., distributed algorithms, cryptography, resource allocation, approximation algorithms). Randomized algorithm for linear programming that uses geometric properties of the problem: to solve the problem with n variables and m constraints we will need expected time O(m n!), which is linear(!) for constant n. web.njit.edu /~czumaj/TEACHING/CIS786-F04.html   (4338 words)

 Biased Randomized Algorithm for Fast Model-Based Diagnosis In a typical prior local-search algorithm for solving the SAT problem, one guesses at a complete solution and then, through a sequence of partly random and partly greedy flips, tries to adjust the guess to reduce the number of unsatisfied clauses while increasing, or leaving unchanged, the number of satisfied clauses. The prior local-search algorithms used to solve the SAT problem sometimes flounder in the search space without converging to the solution, making it necessary to restart the algorithms from time to time. In the present algorithm, one biases this otherwise random assignment toward FALSE in the effort to make the subsequent random and greedy flips lead to a solution in which the fewest variables are TRUE. www.nasatech.com /Briefs/Mar05/NPO40065.html   (632 words)

 Polygon Triangulation In computer graphics, polygon triangulation algorithms are widely used for tessellating curved geometries, as are described by splines [Kumar and Manocha 1994]. Furthermore, the algorithm generates a query structure that can be used to determine the location of a point in logarithmic time. The randomized algorithm is used to create the trapezoidal decomposition of the X-Y plane arising due the segments of set S. www.cs.unc.edu /~dm/CODE/GEM/chapter.html   (837 words)

 An Efficient Randomized Algorithm for Input-Queued Switch Scheduling Randomizing algorithms have proved particularly effective in providing good scalable solutions to problems where decisions need to be made within a limited amount of time and/or with little information. The main idea of randomized algorithms is simply stated: Basing decisions on a few randomly chosen samples is often a good surrogate for basing decisions with complete knowledge of the state. We begin by examining the difficulty of implementing well-known deterministic solutions like the maximum weight matching algorithm, discuss a simple randomized proposed by Tassiulas [1], develop a suite of novel randomized algorithms, and discuss their theory and performance. csdl.computer.org /comp/proceedings/hoti/2001/1357/00/13570003abs.htm   (268 words)

 CPSC516 Project Report   (Site not responding. Last check: 2007-10-17) Among these approaches, incremental algorithms are the easiest to implement, yet on the other hand, it can be easily generalized to higher dimension [5]. But if the input sites are randomized and evenly distributed, the complexity will be dominated by the point location method [1]. To keep the algorithm effective, I guess that some point location approach rather than simple walking should be adopted. www.cs.ubc.ca /~szwang/Research/516Project/delaunay.htm   (1149 words)

 A Survey of Randomized Algorithms   (Site not responding. Last check: 2007-10-17) We introduce randomized algorithm as an alternative method to solving these problems. Randomized algorithms save time by choosing a starting point arbitrarily, rather than deciding where the best starting point is. As a result, the algorithm will have a high probability of producing the correct solution. Several iterations may be required to ensure a correct solution, but this is often much faster than executing a complicated, deterministic algorithm one time. www.cs.wvu.edu /~wallacec/a3/a3.html   (114 words)

 Deterministic selection   (Site not responding. Last check: 2007-10-17) 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. Recall that quickselect chooses a random "pivot" x, partitions the list into elements less than and greater than x, and calls itself recursively in one of the two sublists. 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)

 A Randomized Algorithm for Solving Quadratic Programs (ResearchIndex)   (Site not responding. Last check: 2007-10-17) The expected running time of the algorithm is O(dd!m) where m is the number of inequality constraints and d is the number of variables. This algorithm is based on the ideas of Seidel's linear programming algorithm (Seidel,1991). It is closely related to algorithms of (Welzl,1991,Yoshiba,1992) and has some features of the one proposed in (Stoer,1992). citeseer.ist.psu.edu /108615.html   (282 words)

 Final review   (Site not responding. Last check: 2007-10-17) Prove approximation factors or correctness of new algorithms that are presented, such as problem 3 in HW 2 (HW2 does not ask you to prove these, but you should be able to). Give tight examples for new algorithms that you are given, such as problem 3 in HW 2. Given a randomized algorithm, derandomize it to yield a deterministic algorithm that performs at least as well as the expected behavior of the randomized one. www.cs.fsu.edu /~asriniva/courses/alg05/FinalReview.html   (413 words)

 Bibliography Listing of G. Persiano Exploiting inherent properties of randomized greedy algorithms, we obtain the first randomized algorithm for the problem that uses at most 7l/5+o(l) colors for coloring any set of paths of maximum load l on binary trees of depth o(l^{1/3}), with high probability. Is arrangement S reachable from R? We present an algorithm that, on input two arrangements of k pebbles on a tree with n vertices, decides in time O(n) whether the two arrangements are reachable from one another. We also prove that no greedy algorithm can in general use less than 5/3L wavelengths for a set of requests of load L in a directed fiber tree, and thus our algorithm is optimal in the class of greedy algorithms. www.dia.unisa.it /~giuper/PAPERS   (2817 words)

 Dictionary of Algorithms and Data Structures This is a dictionary of algorithms, algorithmic techniques, data structures, archetypal problems, and related definitions. We do not include algorithms particular to business data processing, communications, operating systems or distributed algorithms, programming languages, AI, graphics, or numerical analysis: it is tough enough covering "general" algorithms and data structures. Data Structures and Algorithms is a wonderful site with illustrations, explanations, analysis, and code taking the student from arrays and lists through trees, graphs, and intractable problems. www.nist.gov /dads   (686 words)

 Michael Nielsen » Blog Archive » Expander graphs VI: reducing randomness   (Site not responding. Last check: 2007-10-17) Today’s post explains how expander graphs can be used to reduce the number of random bits needed by a randomized algorithm in order to achieve a desired success probability. One surprising application of expanders is that they can be used to reduce the number of random bits needed by a randomized algorithm in order to achieve a desired success probability. I won’t give any concrete examples of one-sided randomized algorithms here, but the reader unfamiliar with them should rest assured that they are useful and important - see, e.g., the book of Motwani and Raghavan (Cambridge University Press, 1995) for examples. www.qinfo.org /people/nielsen/blog?p=223   (790 words)

 A Randomized Algorithm for Approximate String Matching   (Site not responding. Last check: 2007-10-17) We give a randomized algorithm in deterministic time O(N ln(M)) for estimating the score vector of matches between a text string of length N and a pattern string of length M, i.e., the vector obtained when the pattern is slid along the text, and the number of matches is counted for each position. The randomized algorithm bases on convolution to find an estimator of the scores and can be viewed as a randomization of an algorithm by Fischer and Paterson. The variance of our estimator is particularly small for scores that are close to M, i.e., for approximate occurrences of the pattern in the text. algo.inria.fr /dumas/AtChDu99   (155 words)

 A Randomized Sorting Algorithm on the BSP model   (Site not responding. Last check: 2007-10-17) We present a new randomized sorting algorithm on the Bulk-Synchronous Parallel (BSP) model. The algorithm improves upon the parallel slack of previous algorithms to achieve optimality. It uses sample sorting and utilizes recently introduced search algorithms for a class of data structures on the BSP model. csdl.computer.org /comp/proceedings/ipps/1997/7792/00/77920293abs.htm   (153 words)

 Randomizing Reductions and Completeness The randomized reductions defined in Definition 4.2 are closed for randomized ap-time and they are transitive. So randomized reductions are deterministic reductions on good-input domains and so, similarly to Lemma 3.6, it is straightforward to show the following lemma for distributional decision problems. Using ap-time randomized reductions, it was shown by Venkatesan and Levin [VL88] that a certain graph edge coloring problem with a flat distribution is complete for distributional NP search problems, and Blass and Gurevich [BG95] showed that a certain matrix transformation problem with a flat distribution is complete for DistNP. www.uncg.edu /mat/avg/avgcomp/node15.html   (337 words)

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