Batch-Processing Scheduling with Setup Times

The problem is to minimize the total weighted completion time on a single batch-processing machine with setup times. The machine can process a batch of at most B jobs at one time, and the processing time of a batch is given by the longest processing time among the jobs in the batch. The setup time of a batch is given by the largest setup time among the jobs in the batch. This batch-processing problem reduces to the ordinary uni-processor scheduling problem when B = 1. In this paper we focus on the extreme case of B = +, i.e. a batch can contain any number of jobs. We present in this paper a polynomial-time approximation algorithm for the problem with a performance guarantee of 2. We further show that a special case of the problem can be solved in polynomial time.     

Modified Wald statistics for generalized linear models

Summary: Wald statistics in generalized linear models are asymptotically ² distributed. The asymptotic chi–squared law of the corresponding quadratic form shows disadvantages with respect to the approximation of the finite–sample distribution. It is shown by means of a comprehensive simulation study that improvements can be achieved by applying simple finite–sample size approximations to the distribution of the quadratic form in generalized linear models. These approximations are based on a ² distribution with an estimated degree of freedom that generalizes an approach by Patnaik and Pearson. Simulation studies confirm that nominal level is maintained with higher accuracy compared to the Wald statistics.     

Calculating the density and distribution function for the singly and doubly noncentral F

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.     

Center and Distinguisher for Strings with Unbounded Alphabet

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.     

Improved Approximation for Breakpoint Graph Decomposition and Sorting by Reversals

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.     

On Inverse Problems of Optimum Perfect Matching

As far as we know, for most polynomially solvable network optimization problems, their inverse problems under l ₁ or l norm have been studied, except the inverse maximum-weight matching problem in non-bipartite networks. In this paper we discuss the inverse problem of maximum-weight perfect matching in a non-bipartite network under l ₁ and l norms. It has been proved that the inverse maximum-weight perfect matching under l norm can be formulated as a maximum-mean alternating cycle problem of an undirected network, and can be solved in polynomial time by a binary search algorithm and in strongly polynomial time by an ascending algorithm, and under l ₁ norm it can be solved by the ellipsoid method. Therefore, inverse problems of maximum-weight perfect matching under l ₁ and l norms are solvable in polynomial time.     

The densest <Emphasis Type="Italic">k</Emphasis>-subgraph problem on clique graphs

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.     

Landau多项式算子与无界函数逼近

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 .     

Admissible minimum bias estimation of response surfaces

The minimum bias estimator was introduced as an alternative to the least squares estimator for approximating response functions by low-order polynomials. Here we show how to obtain an admissible estimator with smaller squared bias.     

Finite nonparametric grach model for foreign exchange volatility

GARCH model has been commonly used to describe the volatility of foreign exchange returns, which typically depends on returns many lags before, While the GARCH model provides a simple geometric decaying structure for persistence in time, it restricts tiie impact of variables to Quadratic functions. A finite nonparametric GARCH model is proposed that allows the variables' impact to be a smooth function of any form. A direct local polynomial estimation method for this finite GARCH model is proposed based on results on proportional additive model, and is applied to the German Mark (DEM)/US Dollar (USD) daily returns data. Estimators uf both the decaying rate and the impact function are obtained. Diagnostics show satisfactory out-of-sampie prediction based on the proposed model, which helps to better understand the dynamics of foreign exchange volatility.