Book reviews

We propose two moment ratios based on the first four moments. These moment ratios are useful in identifying different members from a class of discrete or continuous distributions. These ratios are also useful in approximating the Neyman type A and the generalized Poisson distribution by the negative binomial distribution.     

随机效应半参数logit模型的惩罚似然估计研究

 在颇具争议的收入差距和健康关系研究中,为了降低可能存在的模型设定和遗漏变量偏误,本文提出了随机效应半参数logit模型,其中非参数的设定还可用于数据的初探性分析。随后本文提出了模型非参数和参数部分的估计方法。这里涉及的难点是随机效应的存在导致似然函数中的积分没有解析式,而非参数的存在更加大了估计难度。本文基于惩罚样条非参数估计方法和四阶Laplace近似方法建立了惩罚对数似然函数,其最大化采用了Newton_Raphson近似方法。文章还建立了惩罚样条中重要光滑参数的选取准则。模型在收入差距和健康实例中的估计结果表明数据支持收入差距弱假说,且非参数估计结果表明其具有U型形式,与实例估计结果的比较指出本文提出的估计方法是较准确的。     

Approximation algorithms for connected facility location problems

We study Connected Facility Location problems. We are given a connected graph G=(V,E) with nonnegative edge cost c _e for each edge e∈E, a set of clients D⊆V such that each client j∈D has positive demand d _j and a set of facilities F⊆V each has nonnegative opening cost f _i and capacity to serve all client demands. The objective is to open a subset of facilities, say , to assign each client j∈D to exactly one open facility i(j) and to connect all open facilities by a Steiner tree T such that the cost is minimized for a given input parameter M≥1. We propose a LP-rounding based 8.29 approximation algorithm which improves the previous bound 8.55 (Swamy and Kumar in Algorithmica, 40:245–269, 2004). We also consider the problem when opening cost of all facilities are equal. In this case we give a 7.0 approximation algorithm.     

On minimum <Emphasis Type="Italic">m</Emphasis>-connected <Emphasis Type="Italic">k</Emphasis>-dominating set problem in unit disc graphs

Minimum m-connected k-dominating set problem is as follows: Given a graph G=(V,E) and two natural numbers m and k, find a subset S⊆V of minimal size such that every vertex in V∖S is adjacent to at least k vertices in S and the induced graph of S is m-connected. In this paper we study this problem with unit disc graphs and small m, which is motivated by the design of fault-tolerant virtual backbone for wireless sensor networks. We propose two approximation algorithms with constant performance ratios for m≤2. We also discuss how to design approximation algorithms for the problem with arbitrarily large m. This work was supported in part by the Research Grants Council of Hong Kong under Grant No. CityU 1165/04E, the National Natural Science Foundation of China under Grant No. 70221001, 10531070 and 10771209.     

Approximation hardness of edge dominating set problems

We provide the first interesting explicit lower bounds on efficient approximability for two closely related optimization problems in graphs, MINIMUM EDGE DOMINATING SET and MINIMUM MAXIMAL MATCHING. We show that it is NP-hard to approximate the solution of both problems to within any constant factor smaller than . The result extends with negligible loss to bounded degree graphs and to everywhere dense graphs. An extended abstract of this paper was accepted at the 14th Annual International Symposium on Algorithms and Computation, ISAAC 2003.     

Scheduling tool changes and special jobs on a single machine to minimize makespan

This paper considers a variation of the classical single machine scheduling problem with tool changes. In the variation, two sets of jobs, namely special jobs and normal jobs, are considered. By special jobs, we mean that each special job must be processed within the first prefixed time units of a tool life. To solve the scheduling problem with small size and moderate size, we propose two mathematical programming models. To solve the scheduling problem with large size, we propose three sets of algorithms and focus on the performance of six algorithms based on the studies of a new bin packing problem. Worst-case analysis is conducted. Numerical experiment shows that each of the six algorithms can solve instances with up to 5000 jobs in about 0.5 s with an average relative error less than 4%.     

Probabilistic graph-coloring in bipartite and split graphs

We revisit in this paper the stochastic model for minimum graph-coloring introduced in (Murat and Paschos in Discrete Appl. Math. 154:564–586, 2006), and study the underlying combinatorial optimization problem (called probabilistic coloring) in bipartite and split graphs. We show that the obvious 2-coloring of any connected bipartite graph achieves standard-approximation ratio 2, that when vertex-probabilities are constant probabilistic coloring is polynomial and, finally, we propose a polynomial algorithm achieving standard-approximation ratio 8/7. We also handle the case of split graphs. We show that probabilistic coloring is NP-hard, even under identical vertex-probabilities, that it is approximable by a polynomial time standard-approximation schema but existence of a fully a polynomial time standard-approximation schema is impossible, even for identical vertex-probabilities, unless P=NP. We finally study differential-approximation of probabilistic coloring in both bipartite and split graphs. Part of this research has been performed while the second author was with the LAMSADE on a research position funded by the CNRS.