We consider the problem of scheduling tasks requiring certain processing times on one machine so that the busy time of the machine is maximized. The problem is to find a probabilistic online algorithm with reasonable ...
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We consider the problem of scheduling tasks requiring certain processing times on one machine so that the busy time of the machine is maximized. The problem is to find a probabilistic online algorithm with reasonable worst case performance ratio. We answer an open problem of Lipton and Tompkins concerning the best possible ratio that can be achieved. Furthermore, we extend their results to an m-machine analogue. Finally, a variant of the problem is analyzed, in which the machine is provided with a buffer to store one job.
In a multiple access broadcast network, all network nodes share a single shared communication channel, and there is the possibility of a collision when two or more nodes transmit at overlapping times. We propose a dyn...
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In a multiple access broadcast network, all network nodes share a single shared communication channel, and there is the possibility of a collision when two or more nodes transmit at overlapping times. We propose a dynamic prioritized conflict resolution algorithm in which, when a collision occurs, all colliding messages are retransmitted according to their priority. When a new message arrives, it is allowed to participate in the algorithm as soon as it finds its priority is higher than that of some broadcast message. Using a time-slotted model, for any arrival pattern and priority distribution, we show that our algorithm runs in expected linear time, i.e., O(r), where ris the total number of message transmitted. We also show that the expected waiting time for any message x is O((rank(x) + log s), where rank(x) is the expected number of messages with higher priority which transmit while x is waiting, and s is the minimum of the total number of messages participating in the algorithm and the total number of nodes in the network. The analysis presented in this work also includes an improved analysis of our original (static) prioritized conflict resolution algorithm. This work is applicable to multimedia communications where different priority values could be assigned to different kinds of traffic, and our algorithm ensures that the high-priority real-time traffic has the minimum delay.
A survey of the state of the art in research on algebraic machine learning is presented. The main emphasis is on computational complexity. The key idea is to use lattice theory methods and probabilistic algorithms bas...
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A survey of the state of the art in research on algebraic machine learning is presented. The main emphasis is on computational complexity. The key idea is to use lattice theory methods and probabilistic algorithms based on Markov chains.
We have recently published a new probabilistic algorithm which performs genomic comparisons on a huge scale. In the present paper it was applied to immunodeficiency viral sequences extracted from international gene da...
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We have recently published a new probabilistic algorithm which performs genomic comparisons on a huge scale. In the present paper it was applied to immunodeficiency viral sequences extracted from international gene databanks. During global sequence analysis of human (HIV1 and HIV2) and simian viruses by means of dot-matrix representation, series of homology were obtained which permitted the definition of families of viruses overlapping the species divisions, Sequences of interest were characterized to the lexical base sentence through successive zoomings. Strain-to-strain comparison confirmed subfamily classifications and led, for example, to the identification of divergent LTR sequences, By way of example, we described the application of the algorithm to the ANT70C and MVP5180 HIV1-O viruses, for which the observed differences were shown to correspond to a deletion in the U3 region, situated between the LEF and NF-kappa B sites. It was of interest to consider these data in a tentative phylogenetic interpretation.
If F(q) is a finite field and f member-of F(q)[x], then f is called a permutation polynomial if the mapping F(q) --> F(q) induced by f is bijective. This property can be tested by a probabilistic algorithm whose nu...
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If F(q) is a finite field and f member-of F(q)[x], then f is called a permutation polynomial if the mapping F(q) --> F(q) induced by f is bijective. This property can be tested by a probabilistic algorithm whose number of operations is polynomial (in fact, essentially linear) in the input size, i.e., in deg f . log q. This is extended to "almost permutation polynomials," whose value set consists of almost all elements of F(q).
We consider two-player games played for an infinite number of rounds, with omega-regular winning conditions. The games may be concurrent, in that the players choose their moves simultaneously and independently, and pr...
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We consider two-player games played for an infinite number of rounds, with omega-regular winning conditions. The games may be concurrent, in that the players choose their moves simultaneously and independently, and probabilistic, in that the moves determine a probability distribution for the successor state. We introduce quantitative game mu-calculus, and we show that the maximal probability of winning such games can be expressed as the fixpoint formulas in this calculus. We develop the arguments both for deterministic and for probabilistic concurrent games;as a special case, we solve probabilistic turn-based games with omega-regular winning conditions, which was also open. We also characterize the optimality, and the memory requirements, of the winning strategies. In particular, we show that while memoryless strategies suffice for winning games with safety and reachability conditions, Buchi conditions require the use of strategies with infinite memory. The existence of optimal strategies, as opposed to epsilon-optimal, is only guaranteed in games with safety winning conditions. (C) 2003 Elsevier Inc. All rights reserved.
Two novel efficient algorithms for placing a total order on messages in an asynchronous fault-tolerant distributed system are presented. The algorithms are resilient to fewer than n/3 and n/2 faulty processes in an n-...
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Two novel efficient algorithms for placing a total order on messages in an asynchronous fault-tolerant distributed system are presented. The algorithms are resilient to fewer than n/3 and n/2 faulty processes in an n-process system. Partial correctness and probabilistic termination are demonstrated;it is also shown that there does not exist a total ordering algorithm that is guaranteed to terminate. A comparison of the complexity of the algorithms is given.
In the forthcoming paper of Beltran and Pardo, the average complexity of linear homotopy methods to solve polynomial equations with random initial input (in a sense to be described below) was proven to be finite, and ...
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In the forthcoming paper of Beltran and Pardo, the average complexity of linear homotopy methods to solve polynomial equations with random initial input (in a sense to be described below) was proven to be finite, and even polynomial in the size of the input. In this paper, we prove that some other higher moments are also finite. In particular, we show that the variance is polynomial in the size of the input.
We propose a probabilistic algorithm to reduce computing the greatest common divisor of m polynomials over a finite field (which requires computing m - 1 pairwise greatest common divisors) to computing the greatest co...
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We propose a probabilistic algorithm to reduce computing the greatest common divisor of m polynomials over a finite field (which requires computing m - 1 pairwise greatest common divisors) to computing the greatest common divisor of two polynomials over the same field. (C) 2003 Elsevier Science (USA). All rights reserved.
A probabilistic test of Boolean functions for k-dimensionality is constructed. The test has a less time complexity and a smaller first kind error probability (with the same upper bound for the second kind error probab...
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A probabilistic test of Boolean functions for k-dimensionality is constructed. The test has a less time complexity and a smaller first kind error probability (with the same upper bound for the second kind error probability) in comparison with a well-known previously proposed test.
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