Approximation Algorithms for 3D Orthogonal Knapsack

We study non-overlapping axis-parallel packings of 3D boxes with profits into a dedicated bigger box where rotation is either forbidden or permitted, and we wish to maximize the total profit. Since this optimization problem is NP-hard, we focus on approximation algorithms. We obtain fast and simple algorithms for the non-rotational scenario with approximation ratios 9 ε and 8 ε , as well as an algorithm with approximation ratio 7 ε that uses more sophisticated techniques; these are the smallest approximation ratios known for this problem. Furthermore, we show how the used techniques can be adapted to the case where rotation by 90° either around the z-axis or around all axes is permitted, where we obtain algorithms with approximation ratios 6 ε and 5 ε , respectively. Finally our methods yield a 3D generalization of a packability criterion and a strip packing algorithm with absolute approximation ratio 29/4, improving the previously best known result of 45/4.     

工厂地址集中的k-种产品选址问题的近似算法

k-种产品工厂选址问题是：给定一个客户集合和一个可以建立工厂的地址集合,每个客户需要k-种产品,一个工厂只能为客户提供一种产品。考虑的工厂假设相对集中,即假设任何工厂之间的距离都不大于工厂与客户之间的距离。对于没有建厂费用的问题,当k=2时证明了它是一个NP完全问题,对任意的k给出了一个最坏性能比不大于2-1/k的近似算法。对于有建厂费用的问题,给出了一个最坏性能比不大于2的近似算法。     

The hardness of approximation: Gap location

We refine the complexity analysis of approximation problems by relating it to a new parameter calledgap location. Many of the results obtained so far for approximations yield satisfactory analysis with respect to this refined parameter, but some known results (e.g.,max-k-colorability, max 3-dimensional matching andmax not-all-equal 3sat) fall short of doing so. As a second contribution, our work fills the gap in these cases by presenting new reductions.Next, we present definitions and hardness results of new approximation versions of some NP-complete optimization problems. The problems we treat arevertex cover (for which we define a different optimization problem from the one treated in Papadimitriou & Yannakakis 1991),k-edge coloring, andset splitting.     

互联网通信中的信息选取与分布问题的建模与求解

讨论了互联网通信中的一个信息选取与规划问题。由于内部网的单个Web服务器容量不够大,不能容纳与日剧增的信息内容,如何将众多的信息分布到多个Web服务器上,使得每个服务器上存放的信息总量不超过各个服务器容量且避免访问瓶颈的发生;这是陈卫东等1999年提出的一个新问题,该文建立了该问题的一个优化新模型,在讨论了它的强NP－完全性,难近似性后,给出了一个伪多项式时间最优算法的一个多项式时间近似算法。     

Parameterized Computation and Complexity： A New Approach Dealing with NP-Hardness

The theory of parameterized computation and complexity is a recently developed subarea in theoretical computer science. The theory is aimed at practically solving a large number of computational problems that are theoretically intractable.The theory is based on the observation that many intractable computational problems in practice are associated with a parameter that varies within a small or moderate range. Therefore, by taking the advantages of the small parameters, many theoretically intractable problems can be solved effectively and practically. On the other hand, the theory of parameterized computation and complexity has also offered powerful techniques that enable us to derive strong computational lower bounds for many computational problems, thus explaining why certain theoretically tractable problems cannot be solved effectively and practically. The theory of parameterized computation and complexity has found wide applications in areas such as database systems, programming languages, networks, VLSI design, parallel and distributed computing, computational biology, and robotics. This survey gives an overview on the fundamentals, algorithms, techniques, and applications developed in the research of parameterized computation and complexity. We will also report the most recent advances and excitements, and discuss further research directions in the area.     

多色点集直线划分的复杂性及其近似算法

多色点集划分研究如何将含有不同颜色点的平面划分为各个区域,每个区域中只包含一种颜色的点。这是计算几何中的一种组合优化问题。但是现有的多边形划分方式性能较差。为此,提出用直线来划分平面。针对平面上多色点集的直线划分,将其离散化,证明其可以被非确定性图灵机在多项式时间内判定。并将Max2SAT问题在多项式时间内归约到组合优化问题,证明多色点集直线划分为NP难,从而证明其是NP完全的。利用最优化版本的特有性质,运用贪心方法构造出多项式时间的近似算法,并L归约到Setcover问题,以此证明算法的近似比为O( lgn)。     

基于相位约束的低复杂度稳健宽带波束形成算法

针对传统空时结构宽带波束形成器结构复杂、计算量大和稳健性差的问题,提出低复杂度的稳健宽带波束形成算法。首先给出频率变化时阵列响应相位,分析频率变化与角度变化对阵列响应相位的影响。通过对期望信号不同频点施加阵列响应幅度和相位约束,补偿不同频率间的阵列响应相位差来实现无需延迟线或FIR/IIR滤波器结构的稳健宽带波束形成。然后分析频率和角度同时变化对阵列响应相位的影响,在期望信号来向附近引入辅助方位角,进一步提高期望信号来向趋于零度和相对带宽较小时算法的稳健性。理论分析与仿真实验表明,本文算法结构简单,计算复杂度较低且具有较好的稳健性。     

欧氏空间货郎担问题的一个多项式时间近似方案的改进与实现

货郎担问题的实例是给定n个结点和任意一对结点{i,j}之间的距离di,j,要求找出一条封闭的回路,该回路经过每个结点一次且仅一次,并且费用最小,这里的费用是指回路上相邻结点间的距离和.货郎担问题是NP难的组合优化问题,是计算机算法研究的热点之一.在过去几十年中,这一经典问题成为许多重要算法思想的测试平台,并促使一些研究领域的出现,如多面体理论和复杂性理论.欧氏空间上的货郎担问题,结点限制在欧氏空间,距离定义为欧氏距离.即使是这样,欧氏空间上的货郎担问题仍然是NP难的.1996年,Arora提出欧氏空间上货郎担问题的第1个多项式时间近似方案.对其中货郎担问题的算法进行了改进：提出一种新的构造方法,使应用于该算法的“补丁引理”结论由常数6改进到常数3,从而使算法的时间复杂度大幅减少;同时,编程实现了该算法,并对实验结果进行了分析.     

一类两阶段杂交流水作业的近似算法?

讨论了一类两台机流水作业要求最后完工工件完工时间最早的排序问题.问题中每个工件包含两个加工任务：第1个任务可以在任何一台机器上加工,第2个任务只能在第1个任务完成后在第2台机器上加工.如果要求在加工同一个工件的两个任务时,两个任务之间不能有停顿,则称其为不可等待的模型,记作 NSHFS.如果第2个任务可以在第1个任务完成后的任意时间加工,则称其为允许等待的模型,记作SHFS.对于SHFS模型,在魏麒和何勇工作的基础上给出了一种改进的最坏情况界为8/5的多项式时间近似算法.对于NSHFS模型,首先证明它是NP-难的,并且给出了一种最坏情况界为5/3的多项式时间近似算法.     

一类两阶段杂交流水作业的近似算法

讨论了一类两台机流水作业要求最后完工工件完工时间最早的排序问题.问题中每个工件包含两个加工任务:第1个任务可以在任何一台机器上加工,第2个任务只能在第1个任务完成后在第2台机器上加工.如果要求在加工同一个工件的两个任务时,两个任务之间不能有停顿,则称其为不可等待的模型,记作NSHFS.如果第2个任务可以在第1个任务完成后的任意时间加工,则称其为允许等待的模型,记作SHFS.对于SHFS模型,在魏麒和何勇工作的基础上给出了一种改进的最坏情况界为8/5的多项式时间近似算法.对于NSHFS模型,首先证明它是NP-难的,并且给出了一种最坏情况界为5/3的多项式时间近似算法.     

Lower Bounds on Learning Decision Lists and Trees

k-Decision lists and decision trees play important roles in learning theory as well as in practical learning systems.k-Decision lists generalize classes such as monomials,k-DNF, andk-CNF, and like these subclasses they are polynomially PAC-learnable [R. Rivest,Mach. Learning2(1987), 229–246]. This leaves open the question of whetherk-decision lists can be learned as efficiently ask-DNF. We answer this question negatively in a certain sense, thus disproving a claim in a popular textbook [M. Anthony and N. Biggs, “Computational Learning Theory,” Cambridge Univ. Press, Cambridge, UK, 1992]. Decision trees, on the other hand, are not even known to be polynomially PAC-learnable, despite their widespread practical application. We will show that decision trees are not likely to be efficiently PAC-learnable. We summarize our specific results. The following problems cannot be approximated in polynomial time within a factor of 2^{logδ n}for anyδ<1, unlessNP⊂DTIME[2^{polylog n}]: a generalized set cover,k-decision lists,k-decision lists by monotone decision lists, and decision trees. Decision lists cannot be approximated in polynomial time within a factor ofn^δ, for some constantδ>0, unlessNP=P. Also,k-decision lists withl0–1 alternations cannot be approximated within a factor log^l nunlessNP⊂DTIME[n^{O(log log n)}] (providing an interesting comparison to the upper bound obtained by A. Dhagat and L. Hellerstein [in“FOCS '94,” pp. 64–74]).     

复杂社会网络的介数性质近似计算方法研究

随着计算机和互联网的迅猛发展,面向互联网的社会网络挖掘和分析成为一个新的课题。从互联网挖掘的社会网络往往规模巨大,这对网络分析算法的性能提出了更高的要求 。介数值作为图的重要结构性质,广泛应用于基于图的聚类、分类算法,如何降低其计算的复杂性是急需解决的问题。目前,常用的方法是利用对最短路径长度的近似来降低低网络分析算法的复杂性,但已有的近似方法没有考虑现实大规模网络的复杂网络特性,对最短路径长度的近似方 近似计算方法,其基本思想是结合复杂网络的结构特性,利用通过网络中枢节点的路径来近似最短路径,以近似的最短路径求得介数的近似值。这为图的结构性质的近似估算算提供了一种新颖的思路。通过与传统的介数计算方法和近的分析得到了若干有益的结论,为进一步的研究工作奠定了基础。     

一般设施定位问题计算复杂度和近似算法研究

设施定位问题即UFL问题是NP-hard的组合优化问题,是聚类问题领域的热点问题之一,在数据挖掘和分类识别方面有着重要应用.多年来其近似算法研究一直是计算机科学工作者关注的焦点,然而现有研究结果大多关于Metric空间,一般距离空间中该问题结果始终未见.针对最大连接费用至多是最小连接费用ω＞1倍的一般距离空间中设施定位问题,简称一般设施定位问题,借助集合覆盖问题,利用问题归约方法证明其不存在近似性能比小于1.243 0.316ln(ω-1)的多项式时间近似算法,除非NPDTIME(nO(log log n));设计了一般设施定位问题的局部搜索算法,证明算法近似性能比是(1 ω)/α,ω＞1,1≤α≤2.仿真实验表明,一般设施定位问题局部搜索算法的求解质量极高;通过实验进一步研究了该算法并给出了改进方法.     

欠驱动柔性机器人的振动可控性分析

欠驱动柔性机器人的可控性分析是对其进行有效控制的关键问题. 本文以具有柔性杆的3DOF平面欠驱动机器人为例, 分两步分析系统的可控性. 首先,忽略杆件的弹性变形, 研究欠驱动刚性系统在不同驱动电机位置的状态可控性;然后, 考虑柔性因素, 研究欠驱动柔性系统的结构振动可控性. 结果表明振动可控性是随机器人关节位形和驱动电机位置而变化的, 并且欠驱动刚性机器人的状态可控性对相应的柔性系统的振动可控性有很重要的影响. 最后, 将上述研究方法扩展到具有一个被动关节的N自由度平面欠驱动柔性机器人.     

Some Computational Aspects of distance-sat

In many AI fields, one must face the problem of finding a solution that is as close as possible to a given configuration. This paper addresses this problem in a propositional framework. We introduce the decision problem distance-sat, which consists in determining whether a propositional formula admits a model that disagrees with a given partial interpretation on at most d variables. The complexity of distance-sat and of several restrictions of it are identified. Two algorithms based on the well-known Davis/Logemann/Loveland search procedure for the satisfiability problem sat are presented so as to solve distance-sat for CNF formulas. Their computational behaviors are compared with the ones offered by sat solvers on sat encodings of distance-sat instances. The empirical evaluation allows us to draw firm conclusions about the respective performances of the algorithms and to relate the difficulty of distance-sat with the difficulty of sat from the practical side. A preliminary version of this paper appeared with the title “distance-sat: Complexity and Algorithms” in the proceedings of the 16 ^th National Conference on Artificial Intelligence (AAAI’99), pages 642–647, 1999.