Improved Approximation Algorithms for Maximum Resource Bin Packing and Lazy Bin Covering Problems

In this paper, we study two variants of the bin packing and covering problems called Maximum Resource Bin Packing (MRBP) and Lazy Bin Covering (LBC) problems, and present new approximation algorithms for them. For the offline MRBP problem, the previous best known approximation ratio is frac65frac{6}{5} (=1.2) achieved by the classical First-Fit-Increasing (FFI) algorithm (Boyar et al. in Theor. Comput. Sci. 362(1–3):127–139, 2006). In this paper, we give a new FFI-type algorithm with an approximation ratio of frac8071frac{80}{71} (≈1.12676). For the offline LBC problem, it has been shown in Lin et al. (COCOON, pp. 340–349, 2006) that the classical First-Fit-Decreasing (FFD) algorithm achieves an approximation ratio of frac7160frac{71}{60} (≈1.18333). In this paper, we present a new FFD-type algorithm with an approximation ratio of frac1715frac{17}{15} (≈1.13333). Our algorithms are based on a pattern-based technique and a number of other observations. They run in near linear time (i.e., O(nlog n)), and therefore are practical.     

改进的装炉组合问题建模与优化算法

针对罩式炉退火生产中的钢卷组合堆垛优化问题,建立了以最小化钢卷组炉总加热时间为目标的数学模型。模型综合考虑了钢卷自身属性以及生产工艺约束条件等因素对钢卷组炉加热处理时间的影响。在分析罩式炉退火加热工艺规范的基础上,提出了一种改进自适应遗传算法对模型求解。算法首先类比装炉组合问题与一维装箱问题的相似点分组编码染色体,借鉴装箱问题的优化思想改善初始解种群质量;然后在工艺规则的指导下对遗传基因进行启发式交叉和变异,变异率和交叉率随种群收敛程度自适应调整以保证种群多样性和全局收敛性;最后结合局部穷举搜索方法实现了对上述模型的优化计算。仿真对比实验以及现场实际应用效果均表明该算法相对其他算法的优越性。     

带权Matching和Packing问题的一种固定参数可解算法

带权的m-D MATCHING和m-SET PACKING问题(m≥3)以前是用近似算法来求解的.本文首先根据参数计算理论对这两个带权问题进行了参数化定义,然后运用最新的着色技术和动态规划技术对带权的m-SET PACKING问题设计了一个时间复杂度为O*(12.8mk)的固定参数可解算法, 接着在此基础上利用问题本身的结构特点对带权的m-D MATCHING问题提出了一个时间复杂度为O*(12.8(m-1)k)的固定参数可解算法,表明带权的m-SET PACKING问题和带权的m-D MATCHING问题都是固定参数可解的.     

气象应用网格中改进遗传负载均衡算法研究

根据气象应用网格的特点和影响负载均衡的因素,对基于气象应用网格的负载均衡技术进行分析和探讨,提出一种气象应用网格中的负载均衡算法,实验结果表明该算法提高网格的负载能力.     

Improved Algorithms for Dynamic Shortest Paths

We describe algorithms for finding shortest paths and distances in outerplanar and planar digraphs that exploit the particular topology of the input graph. An important feature of our algorithms is that they can work in a dynamic environment, where the cost of any edge can be changed or the edge can be deleted. In the case of outerplanar digraphs, our data structures can be updated after any such change in only logarithmic time. A distance query is also answered in logarithmic time. In the case of planar digraphs, we give an interesting tradeoff between preprocessing, query, and update times depending on the value of a certain topological parameter of the graph. Our results can be extended to n -vertex digraphs of genus O(n ^1-ε ) for any ε>0 . Received September 24, 1996; revised May 13, 1998, and January 20, 1999.     

Use of Genetic Algorithms for Solution of the Rectangle Packing Problem

This paper deals with the problem of packing of rectangles in a given rectangle. Genetic algorithms are proposed for solving the problem. Some details of realization of the approach proposed are given and a high efficiency of the method of genetic algorithms is illustrated by two examples.     

Improved Algorithms for Uniform Partitions of Points

Abstract. We consider the following one- and two-dimensional bucketing problems: Given a set S of n points in \reals ¹ or \reals ² and a positive integer b , distribute the points of S into b equal-size buckets so that the maximum number of points in a bucket is minimized. Suppose at most (n/b) + Δ points lie in each bucket in an optimal solution. We present algorithms whose time complexities depend on b and Δ . No prior knowledge of Δ is necessary for our algorithms. For the one-dimensional problem, we give a deterministic algorithm that achieves a running time of O(b ⁴ (Δ ² +log n) + n) . For the two-dimensional problem, we present a Monte Carlo algorithm that runs in subquadratic time for small values of b and Δ . The previous algorithms, by Asano and Tokuyama [1], searched the entire parameterized space and required Ω ( n ² ) time in the worst case even for constant values of b and Δ . We also present a subquadratic algorithm for the special case of the two-dimensional problem when b=2 .     

New Bounds for Multidimensional Packing

New upper and lower bounds are presented for a multidimensional generalization of bin packing called box packing. Several variants of this problem, including bounded space box packing, square packing, variable-sized box packing and resource augmented box packing are also studied. The main results, stated for d=2 , are as follows: a new upper bound of 2.66013 for online box packing, a new 14/9 + ? polynomial time offline approximation algorithm for square packing, a new upper bound of 2.43828 for online square packing, a new lower bound of 1.62176 for online square packing, a new lower bound of 2.28229 for bounded space online square packing and a new upper bound of 2.32571 for online two-sized box packing.     

Improved Algorithms for Uniform Partitions of Points

We consider the following one- and two-dimensional bucketing problems: Given a set S of n points in \reals ¹ or \reals ² and a positive integer b , distribute the points of S into b equal-size buckets so that the maximum number of points in a bucket is minimized. Suppose at most (n/b) + Δ points lie in each bucket in an optimal solution. We present algorithms whose time complexities depend on b and Δ . No prior knowledge of Δ is necessary for our algorithms. For the one-dimensional problem, we give a deterministic algorithm that achieves a running time of O(b ⁴ (Δ ² +log n) + n) . For the two-dimensional problem, we present a Monte Carlo algorithm that runs in subquadratic time for small values of b and Δ . The previous algorithms, by Asano and Tokuyama [1], searched the entire parameterized space and required Ω ( n ² ) time in the worst case even for constant values of b and Δ . We also present a subquadratic algorithm for the special case of the two-dimensional problem when b=2 .     

Improved Bounds on Quantum Learning Algorithms

In this article we give several new results on the complexity of algorithms that learn Boolean functions from quantum queries and quantum examples.

基于Ahn改进遗传算法的路由优化算法的研究

论述了用Ahn改进遗传算法解决路由路径的优化问题,采用可变长度染色体路由串和它的基因节点应用于编码问题,交叉操作在交叉点进行部分染色体部分路由交换,变异操作维持种群的多样性。该算法采用简单维护操作,维护好所有的不可行的染色体。交叉操作和变异操作相结合保证了最优解的搜索能力和解的全局收敛性。计算机仿真实验表明该算法快速有效、可靠性高。     

二维板材圆形下料的邻居关系算法

二维圆形排样问题是工业设计与生产中经常遇到的问题.常规下料问题主要针对矩形或圆形等规则板材,常用算法包括模拟退火、遗传算法等.本文在分析规则板材下料算法的基础上,针对实际生产应用中更为复杂的、具有不规则边界板材下料问题,提出了一种基于人工下料思维的仿生下料算法--邻居关系算法.该算法具有很好的利用率和时效性,较好地满足了实际应用的需要.实际板材下料结果表明,平均面积利用率为75.56％,平均计算时间为13.84s.所得排样利用率与模拟退火算法相当,但排样运算时间大大缩小,适应了实际下料需求,已应用于某跨国企业优化下料中.     

网络最短路问题的改进算法

本文着重研究著名的Dijkstra网络最短路算法的实现效率，提出算法实现的若干技巧，大大提高了Dijkstra最短路算法的适用性和时间空间效率。     

改进RRT-人工势场法的机械臂堆垛运动方法

快速拓展随机树算法(RRT)在机械臂路径规划中存在随机性强、搜索效率低、规划路径长等问题,不能在货柜堆垛场景中取得相对最优的光滑路径.对此,该文提出了一种改进RRT-人工势场法混合算法进行货柜堆垛机械臂运动规划.首先,对传统快速拓展随机树算法进行改进,在传统快速拓展随机树算法的全局搜索的基础上引入目标搜索,增强了随机树...     

构造二叉树的两个改进算法

在数据结构中,已知一棵二叉树的先序序列和中序序列,可唯一确定此二叉树.本文在分析建立二叉树经典算法的时间复杂度的基础上,给出了两个改进算法:①利用哈希函数,使得改进后的算法在最差情况下,时间复杂度由O(n2)降为O(n);②利用栈和控制输入的结点序列构造二叉树,时间复杂度也由O(n2)降为O(n).     

Approximation Algorithms and Hardness Results for Packing Element-Disjoint Steiner Trees in Planar Graphs

We study the problem of packing element-disjoint Steiner trees in graphs. We are given a graph and a designated subset of terminal nodes, and the goal is to find a maximum cardinality set of element-disjoint trees such that each tree contains every terminal node. An element means a non-terminal node or an edge. (Thus, each non-terminal node and each edge must be in at most one of the trees.) We show that the problem is APX-hard when there are only three terminal nodes, thus answering an open question. Our main focus is on the special case when the graph is planar. We show that the problem of finding two element-disjoint Steiner trees in a planar graph is NP-hard. Similarly, the problem of finding two edge-disjoint Steiner trees in a planar graph is NP-hard. We design an algorithm for planar graphs that achieves an approximation guarantee close to 2. In fact, given a planar graph that is k element-connected on the terminals (k is an upper bound on the number of element-disjoint Steiner trees), the algorithm returns $\lfloor\frac{k}{2} \rfloor-1$ element-disjoint Steiner trees. Using this algorithm, we get an approximation algorithm for the edge-disjoint version of the problem on planar graphs that improves on the previous approximation guarantees. We also show that the natural LP relaxation of the planar problem has an integrality ratio approaching?2.     

Improved Algorithms for Even Factors and Square-Free Simple b-Matchings

Given a digraph G=(VG,AG), an even factor M?AG is a set formed by node-disjoint paths and even cycles. Even factors in digraphs were introduced by Geelen and Cunningham and generalize path matchings in undirected graphs. Finding an even factor of maximum cardinality in a general digraph is known to be NP-hard but for the class of odd-cycle symmetric digraphs the problem is polynomially solvable. So far the only combinatorial algorithm known for this task is due to Pap; its running time is O(n ⁴) (hereinafter n denotes the number of nodes in G and m denotes the number of arcs or edges). In this paper we introduce a novel sparse recovery technique and devise an O(n ³logn)-time algorithm for finding a maximum cardinality even factor in an odd-cycle symmetric digraph. Our technique also applies to other similar problems, e.g. finding a maximum cardinality square-free simple b-matching.