New algorithms based on convex programming are proposed for worst case system identification. The algorithms are optimal within a factor of two asymptotically. Further, model validation, or data consistency is embedde...
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(纸本)0780312988
New algorithms based on convex programming are proposed for worst case system identification. The algorithms are optimal within a factor of two asymptotically. Further, model validation, or data consistency is embedded in the identification process. Explicit worst case identification error bounds in H/sup /spl infin// norm are also derived for both uniformly and nonuniformly spaced frequency response samples.
In this paper we discuss lower bounds for the asymptotic worst case ratio of on-line algorithms for different kind of bin packing problems. Recently, Galambos and Frenk gave a simple proof of the 1.536... lower bound ...
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In this paper we discuss lower bounds for the asymptotic worst case ratio of on-line algorithms for different kind of bin packing problems. Recently, Galambos and Frenk gave a simple proof of the 1.536... lower bound for the 1-dimensional bin packing problem. Following their ideas, we present a general technique that can be used to derive lower bounds for other bin packing problems as well. We apply this technique to prove new lower bounds for the 2-dimensional (1.802...) and 3-dimensional (1.974...) bin packing problem.
We consider a version of the on-line bounded-space bin-packing problem where repacking the items within the active bins is allowed. For this problem, the 1.69103 lower bound of Lee and Lee [7] for the worst case ratio...
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We consider a version of the on-line bounded-space bin-packing problem where repacking the items within the active bins is allowed. For this problem, the 1.69103 lower bound of Lee and Lee [7] for the worst case ratios of bounded-space approximation algorithms still applies. We present a polynomial time approximation algorithm that reaches the best possible worst case ratio matching the Lee and Lee lower bound while using only three active bins.
For a given list of 3m items with positive lengths we look for a partition into m subsets containing 3 elements each, such that the ratio of the largest sum of lengths to the smallest sum of lengths is as small as pos...
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For a given list of 3m items with positive lengths we look for a partition into m subsets containing 3 elements each, such that the ratio of the largest sum of lengths to the smallest sum of lengths is as small as possible. Let rho(G) be the value of this ratio using a Greedy-heuristic and rho* the optimal value of this ratio;furthermore let beta be the ratio of the largest length of an item to the smallest length. Then we will show that for 1 less-than-or-equal-to beta less-than-or-equal-to 4 the inequality rho(G)/rho* less-than-or-equal-to (4beta + 7)(2beta + 5) holds and this bound is tight.
The author presents a sequence of linear-time, bounded-space, on-line, bin-packing algorithms that are based on the ''HARMONIC'' algorithms H(k) introduced by Lee and Lee [J. Assoc. Comput. Mach., 32 (...
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The author presents a sequence of linear-time, bounded-space, on-line, bin-packing algorithms that are based on the ''HARMONIC'' algorithms H(k) introduced by Lee and Lee [J. Assoc. Comput. Mach., 32 (1985), pp. 562-572]. The algorithms in this paper guarantee the worst case performance of H(k), whereas they only use O(log log k) instead of k active bins. For k greater-than-or-equal-to 6. the algorithms in this paper outperform all known heuristics using k active bins. For example, the author gives an algorithm that has worst case ratio less than 17/10 and uses only six active bins.
We consider the problem of assigning a set of jobs to a system of m identical processors in order to maximize the earliest processor completion time. It was known that the LPT-heuristic gives an approximation of worst...
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We consider the problem of assigning a set of jobs to a system of m identical processors in order to maximize the earliest processor completion time. It was known that the LPT-heuristic gives an approximation of worst case ratio at most 3/4. In this note we show that the exact worst case ratio of LPT is (3m - 1)/(4m - 2).
We describe an approximation algorithm for the problem of finding the minimum makespan in a job shop. The algorithm is based on simulated annealing, a generalization of the well known iterative improvement approach to...
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We describe an approximation algorithm for the problem of finding the minimum makespan in a job shop. The algorithm is based on simulated annealing, a generalization of the well known iterative improvement approach to combinatorial optimization problems. The generalization involves the acceptance of cost-increasing transitions with a nonzero probability to avoid getting stuck in local minima. We prove that our algorithm asymptotically converges in probability to a globally minimal solution, despite the fact that the Markov chains generated by the algorithm are generally not irreducible. Computational experiments show that our algorithm can find shorter makespans than two recent approximation approaches that are more tailored to the job shop scheduling problem. This is, however, at the cost of large running times.
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