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51.
Simple, closed form saddlepoint approximations for the distribution and density of the singly and doubly noncentral F distributions are presented. Their overwhelming accuracy is demonstrated numerically using a variety of parameter values. The approximations are shown to be uniform in the right tail and the associated limitating relative error is derived. Difficulties associated with some algorithms used for exact computation of the singly noncentral F are noted. 相似文献
52.
Center and Distinguisher for Strings with Unbounded Alphabet 总被引:2,自引:0,他引:2
Consider two sets
and
of strings of length L with characters from an unbounded alphabet , i.e., the size of is not bounded by a constant and has to be taken into consideration as a parameter for input size. A closest string s* of
is a string that minimizes the maximum of Hamming1
distance(s, s*) over all string s : s
. In contrast, a farthest string t* from
maximizes the minimum of Hamming distance(t*,t) over all elements t: t
. A distinguisher of
from
is a string that is close to every string in
and far away from any string in
. We obtain polynomial time approximation schemes to settle the above problems. 相似文献
53.
Sorting by Reversals (SBR) is one of the most widely studied models of genome rearrangements in computational molecular biology. At present,
is the best known approximation ratio achievable in polynomial time for SBR. A very closely related problem, called Breakpoint Graph Decomposition (BGD), calls for a largest collection of edge disjoint cycles in a suitably-defined graph. It has been shown that for almost all instances SBR is equivalent to BGD, in the sense that any solution of the latter corresponds to a solution of the former having the same value. In this paper, we show how to improve the approximation ratio achievable in polynomial time for BGD, from the previously known
to
for any > 0. Combined with the results in (Caprara, Journal of Combinatorial Optimization, vol. 3, pp. 149–182, 1999b), this yields the same approximation guarantee for n! – O((n – 5)!) out of the n! instances of SBR on permutations with n elements. Our result uses the best known approximation algorithms for Stable Set on graphs with maximum degree 4 as well as for Set Packing where the maximum size of a set is 6. Any improvement in the ratio achieved by these approximation algorithms will yield an automatic improvement of our result. 相似文献
54.
Maria Liazi Ioannis Milis Fanny Pascual Vassilis Zissimopoulos 《Journal of Combinatorial Optimization》2007,14(4):465-474
The Densest k-Subgraph (DkS) problem asks for a k-vertex subgraph of a given graph with the maximum number of edges. The problem is strongly NP-hard, as a generalization of
the well known Clique problem and we also know that it does not admit a Polynomial Time Approximation Scheme (PTAS). In this paper we focus on
special cases of the problem, with respect to the class of the input graph. Especially, towards the elucidation of the open
questions concerning the complexity of the problem for interval graphs as well as its approximability for chordal graphs,
we consider graphs having special clique graphs. We present a PTAS for stars of cliques and a dynamic programming algorithm
for trees of cliques.
M.L. is co-financed within Op. Education by the ESF (European Social Fund) and National Resources.
V.Z. is partially supported by the Special Research Grants Account of the University of Athens under Grant 70/4/5821. 相似文献
55.
利用扩展乘数法构造了 Landau型多项式算子逼近全空间或有界集上无界函数的若干收敛定理 ,给出了具有一般性的结论 ,从而推广了已有文献的若干结果 . 相似文献
56.
Assuming that both birth and death rates are density and time dependent, a diffusion approximation of the generalized birth and death process has been considered in this paper to obtain a suitable stochastic population model describing the population size and its moments. A simple method of estimating the parameters of the model Is discussed. The predictions of the expected size of the population, and the variance are made and compared with the corresponding census figures as well as with another deterministic projection series made for the corresponding period. 相似文献
57.
It is shown that a recursive estimator with the same asymptotic properties as the median has convergence properties in finite samples which depend heavily on the scale of the data. A simple modification which adjusts for the scale is suggested and its application illustrated on simulated data. The modified estimator has much improved properties which are similar to those of the sample (non-recursive) median. 相似文献
58.
We show the second-order relative accuracy, on bounded sets, of the Studentized bootstrap, exponentially tilted bootstrap and nonparametric likelihood tilted bootstrap, for means and smooth functions of means. We also consider the relative errors for larger deviations. Our method exploits certain connections between Edgeworth and saddlepoint approximations to simplify the computations. 相似文献
59.
Many of the available methods for estimating small-area parameters are model-based approaches in which auxiliary variables are used to predict the variable of interest. For models that are nonlinear, prediction is not straightforward. MacGibbon and Tomberlin and Farrell, MacGibbon, and Tomberlin have proposed approaches that require microdata for all individuals in a small area. In this article, we develop a method, based on a second-order Taylor-series expansion to obtain model-based predictions, that requires only local-area summary statistics for both continuous and categorical auxiliary variables. The methodology is evaluated using data based on a U.S. Census. 相似文献
60.
Christopher Field 《Revue canadienne de statistique》1985,13(3):201-210
The approach to normality of an estimate is displayed graphically by the nonlinearity in the derivative of the log density, and this nonlinearity is related to the accuracy of the normal approximation for the tail area. Using techniques from small-sample asymptotics, an alternate proof of the central limit theorem is given and same indices of tail behavior are examined. 相似文献