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The simplex method is strongly polynomial for deterministic Markov Decision Processes
 In Proceedings of the 24th ACMSIAM Symposium on Discrete Algorithms, SODA
, 2013
"... We prove that the simplex method with the highest gain/mostnegativereduced cost pivoting rule converges in strongly polynomial time for deterministic Markov decision processes (MDPs) regardless of the discount factor. For a deterministic MDP with n states and m actions, we prove the simplex method ..."
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We prove that the simplex method with the highest gain/mostnegativereduced cost pivoting rule converges in strongly polynomial time for deterministic Markov decision processes (MDPs) regardless of the discount factor. For a deterministic MDP with n states and m actions, we prove the simplex
Edmonds Fukuda Rule And A General Recursion For Quadratic Programming
"... A general framework of nite algorithms is presented here for quadratic programming. This algorithm is a direct generalization of Van der Heyden's algorithm for the linear complementarity problem and Jensen's `relaxed recursive algorithm', which was proposed for solution of Oriented Ma ..."
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Matroid programming problems. The validity of this algorithm is proved the same way as the finiteness of the crisscross method is proved. The second part of this paper contains a generalization of EdmondsFukuda pivoting rule for quadratic programming. This generalization can be considered as a finite
A subexponential lower bound for the Least Recently Considered rule for solving linear programs and games
"... The simplex algorithm is among the most widely used algorithms for solving linear programs in practice. Most pivoting rules are known, however, to need an exponential number of steps to solve some linear programs. No nonpolynomial lower bounds were known, prior to this work, for Cunningham’s Least ..."
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Cited by 3 (1 self)
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.e., of the form 2 Ω( √ n)) lower bound for this rule in a concrete setting. Our lower bound is obtained by utilizing connections between pivoting steps performed by simplexbased algorithms and improving switches performed by policy iteration algorithms for 1player and 2player games. We start by building 2
Deformed Products and Maximal Shadows of Polytopes
 ADVANCES IN DISCRETE AND COMPUTATIONAL GEOMETRY, AMER. MATH. SOC., PROVIDENCE, CONTEMPORARY MATHEMATICS 223
, 1996
"... We present a construction of deformed products of polytopes that has as special cases all the known constructions of linear programs with "many pivots," starting with the famous KleeMinty cubes from 1972. Thus we obtain sharp estimates for the following geometric quantities for ddimensio ..."
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Cited by 35 (1 self)
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for the worstcase behaviour of the simplex algorithm on linear programs with these parameters with the worstpossible, the greatest increase, and the shadow vertex pivot rules. The bounds on the maximal number of vertices on an increasing path or a greatest increase path unify and slightly improve a number
An Enhanced Apriori Algorithm for Discovering Frequent Patterns with Optimal Number of Scans
"... Abstract Data mining is wide spreading its applications in several areas. There are different tasks in mining which provides solutions for wide variety of problems in order to discover knowledge. Among those tasks association mining plays a pivotal role for identifying frequent patterns. Among the ..."
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the number of transactions while calculating the frequency of an item or itempairs. This improved version of Apriori algorithm optimizes the time used for scanning the whole transactional database.
Lexicographic perturbation for multiparametric linear programming with applications to control
 Automatica
, 2007
"... Abstract Optimal control problems for constrained linear systems with a linear cost can be posed as multiparametric linear programs (mpLPs) with a parameter in the cost, or equivalently the righthand side of the constraints, and solved explicitly offline. Degeneracy occurs when the control input, ..."
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Cited by 10 (5 self)
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a set of nonoverlapping polyhedral regions. Furthermore, we introduce a new method for computing the optimal solution in an adjacent region, which is very efficient in all cases and reduces to a single simplex pivot for nondegenerate regions. The proposed algorithm is particularly suited
Volume I: Computer Science and Software Engineering
, 2013
"... Algebraic algorithms deal with numbers, vectors, matrices, polynomials, formal power series, exponential and differential polynomials, rational functions, algebraic sets, curves and surfaces. In this vast area, manipulation with matrices and polynomials is fundamental for modern computations in Sc ..."
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Algebraic algorithms deal with numbers, vectors, matrices, polynomials, formal power series, exponential and differential polynomials, rational functions, algebraic sets, curves and surfaces. In this vast area, manipulation with matrices and polynomials is fundamental for modern computations
Perspective An Online Bioinformatics Curriculum
"... Abstract: Online learning initiatives over the past decade have become increasingly comprehensive in their selection of courses and sophisticated in their presentation, culminating in the recent announcement of a number of consortium and startup activities that promise to make a university educat ..."
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education on the internet, free of charge, a real possibility. At this pivotal moment it is appropriate to explore the potential for obtaining comprehensive bioinformatics training with currently existing free video resources. This article presents such a bioinformatics curriculum in the form of a virtual
Results 11  20
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33