A radio network is a distributed system with no central shared resource, consisting of n stations each equipped with a radio transceiver. One of the most important parameters to evaluate protocols in the radio network...
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We present three randomized pseudo-polynomial algorithms for the problem of finding a base of specified value in a weighted represented matroid subject to parity conditions. These algorithms, the first two being an im...
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We present three randomized pseudo-polynomial algorithms for the problem of finding a base of specified value in a weighted represented matroid subject to parity conditions. These algorithms, the first two being an improved version of those presented by P. M. Camerini et al. (1992, J. algorithms 13, 258-273) use fast arithmetic working over a finite field chosen at random among a set of appropriate fields. We show that the choice of a best algorithm among those presented depends on a conjecture related to the best value of the so-called Linnik constant concerning the distribution of prime numbers in arithmetic progressions. This conjecture, which we call the C-conjecture, is a strengthened version of a conjecture formulated in 1934 by S. Chowla. If the C-conjecture is true, the choice of a best algorithm is simple, since the last algorithm exhibits the best performance;either when the performance is measured in arithmetic operations, or when it is measured in bit operations and mild assumptions hold. If the C-conjecture is false we are still able to identify a best algorithm, but in this case the choice is between the first two algorithms and depends on the asymptotic growth of m with respect to those of U and n, where 2n, 2m, U are the rank, the number of elements;and the maximum weight assigned to the elements of the matroid, respectively. (C) 1999 Academic Press.
Probability, be it inherent or explicitly introduced, has become an important issue in the verification of programs. In this paper we study a formalism which allows reasoning about programs which can act probabilistic...
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Probability, be it inherent or explicitly introduced, has become an important issue in the verification of programs. In this paper we study a formalism which allows reasoning about programs which can act probabilistically. To describe probabilistic programs, a basic programming language with an operator for probabilistic choice is introduced and a denotational semantics is given for this language. To specify propertics of probabilistic programs, standard first order logic predicates are insufficient, so a notion of probabilistic predicates is introduced. A Hoare-style proof system to check properties of probabilistic programs is given. The proof system for a sublanguage is shown to be sound and complete; the properties that can be derived are exactly the valid properties. Finally some typical examples illustrate the use of the probabilistic predicates and the proof system.
In recent years, a great deal of attention has been devoted to iterative control as an efficient methodology for the design of highly-performing controllers. In this paper, we propose a new iterative scheme which expl...
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In recent years, a great deal of attention has been devoted to iterative control as an efficient methodology for the design of highly-performing controllers. In this paper, we propose a new iterative scheme which explicitly accounts for the presence of uncertainty. At each step, the designed controller is the best possible one relative to the existing level of uncertainty and uncertainty is reduced through steps. In this way, the achieved performance rapidly improves from one step to the next, while preserving the robust stability of the closed-loop system. The controller design is performed at a low computational effort thanks to the use of randomized algorithms.
We adapt some randomized algorithms of Clarkson [3] for linear programming to the framework of so-called LP-type problems, which was introduced by Sharir and Welzl [10]. This framework is quite general and allows a un...
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We adapt some randomized algorithms of Clarkson [3] for linear programming to the framework of so-called LP-type problems, which was introduced by Sharir and Welzl [10]. This framework is quite general and allows a unified and elegant presentation and analysis. We also show that LP-type problems include minimization of a convex quadratic function subject to convex quadratic constraints as a special case, for which the algorithms can be implemented efficiently, if only linear constraints are present. We show that the expected running times depend only linearly on the number of constraints, and illustrate this by some numerical results. Even though the framework of LP-type problems may appear rather abstract at first, application of the methods considered in this paper to a given problem of that type is easy and efficient. Moreover, our proofs are in fact rather simple, since many technical details of more explicit problem representations are handled in a uniform manner by our approach. In particular, we do not assume boundedness of the feasible set as required in related methods.
We show that the well-known random incremental construction of Clarkson and Shor(18) can be adapted to provide efficient external-memory algorithms for some geometric problems. In particular, as the main result, we ob...
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We show that the well-known random incremental construction of Clarkson and Shor(18) can be adapted to provide efficient external-memory algorithms for some geometric problems. In particular, as the main result, we obtain an optimal randomized algorithm for the problem of computing the trapezoidal decomposition determined by a set of N line segments in the plane with K pairwise intersections, that requires Theta((N)/(B) log(M/B) (N)/(B) + (K)/(B)) expected disk accesses, where M is the size of the available internal memory and B is the size of the block transfer. The approach is sufficiently general to derive algorithms for other geometric problems: 3-d half-space intersections, 2-d and 3-d convex hulls, 2-d abstract Voronoi diagrams and batched planar point location;these algorithms require an optimal expected number of disk accesses and are simpler than the ones previously known. The results extend to an external-memory model with multiple disks.
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...
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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. A direct application is approximate string matching. The randomized algorithm uses 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. No assumption is made about the probabilistic characteristics of the input, or about the size of the alphabet. The solution extends to string matching with classes, class complements, "never match" and "always match" symbols, to the weighted case and to higher dimensions.
Line detection is very important in image processing. In this paper, a new randomized algorithm for detecting lines is presented. The proposed algorithm is quite different from the previous parameter-based methods whi...
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Line detection is very important in image processing. In this paper, a new randomized algorithm for detecting lines is presented. The proposed algorithm is quite different from the previous parameter-based methods which vote on the parameter space. Our proposed novel algorithm does not need extra storage to maintain an accumulator array for representing parameter space. The main concept used in the proposed algorithm is that we first randomly select three edge points in the image and use a distance criterion to determine whether there is a candidate line in the image;after finding that candidate line, we apply an evidence-collecting process to further determine whether the candidate line is the desired line. Some experiments have been carried out to demonstrate the computational and robust advantages of the proposed algorithm when compared with the previous algorithms. (C) 2001 Academic Press.
We consider the problem of on-line call admission and routing on trees and meshes. Previous work gave randomized on-line algorithms for these problems and proved that they have optimal ( up to constant factors) compet...
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We consider the problem of on-line call admission and routing on trees and meshes. Previous work gave randomized on-line algorithms for these problems and proved that they have optimal ( up to constant factors) competitive ratios. However, these algorithms can obtain very low profit with high probability. We investigate the question of devising for these problems on-line competitive algorithms that also guarantee a good solution with good probability. We give a new family of randomized algorithms with asymptotically optimal competitive ratios and good probability to get a profit close to the expectation. We complement these results by providing bounds on the probability of any optimally competitive randomized on-line algorithm for the problems we consider to get a profit close to the expectation. To the best of our knowledge, this is the rst study of the relationship between the tail distribution and the competitive ratio of randomized on-line benefit algorithms.
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