短块移动排序算法研究

用短块移动操作对一个排列进行排序是一种染色体基因重排技术。怎样才能找出使用短块移动次数最少的排序算法是计算生物学等领域最热门的研究问题之一。给出了短块移动的最优解算法,对近似算法进行了修改。实验验证了最优解算法和近似算法在实际运行过程中都有较好的表现。     

地理位置相关移动感知系统任务分配问题研究

随着智能手机应用的普及,移动感知技术已被认为是一种高效且成本低廉的环境数据收集方式.移动感知系统中地理位置相关的最优任务分配问题是一个NP难问题.为了解决该问题,提出了一种多项式时间的近似最优的任务分配算法.该算法首先引入了单位圆盘模型中移动划分的思想,将整个监测地理空间划分为若干个子区间,并使得子区间内的最优分配方案的集合是划分前最优解的1/1+ε,这表明所设计的近似算法是一个多项式时间近似机制.随后,证明了最优任务分配问题在每个子区间内是多项式时间可解的,并设计了枚举算法求出该问题的最优解.最后,仿真实验结果表明所设计的近似最优任务分配算法的实际性能与理论分析相吻合.     

针对经典排序问题的一种新算法的近似比分析

给定m台平行机(同型机),n个工件,寻找一种分配方案,使得把这n个工件分配到m台机器后,整体完工时间尽可能短,这个NP-难问题被称为经典排序问题。如果每个工件的加工时间满足一定的条件,则有望能在多项式时间内有效地得到最优的分配方案。Yue等对加工时间满足整除性质的经典排序问题考虑了一种新的算法,该算法总是能得到这种特殊情况的最优分配。该算法在多项式时间内能够得到最优分配,是对于一般的经典排序问题的近似算法。文章在此基础上,考虑该新算法在一般问题上的近似比。文中考虑了这个新算法的两种版本,分别得到了3/2和2-1/2 ^q(q∈Z⁺)的近似比。紧例子表明,文中对算法的两个版本的分析都是最优的。     

智能规划中的可纳子目标排序

提出了一种称为可纳子目标排序(admissible subgoal ordering,简称ASO)的排序关系,给出了可纳排序的形式化定义并讨论其对增量式规划的重要性.随后介绍了原子依赖关系理论和原子依赖图技术,能够在多项式时间内近似求解可纳子目标排序关系.最后给出了一种计算可纳子目标序列的算法.其所有思想已经在规划系统ASOP中实现.通过在国际规划大赛标准测试领域问题上的实验,其结果表明,该方法能够有效地求解大规模的规划问题,并能极大地改善规划性能.     

基因组一般移位排序问题的多项式时间算法

基因组移位排序在基因组重组排序计算研究中占有重要位置.交互型移位和非交互型移位均为移位的特殊形式.目前见到的多种移位排序算法均是针对交互型移位而得到的,未见基因组一般移位排序计算的研究结果.文中讨论包括交互型移位和非交互型移位的一般移位排序问题的求解方法,给出该问题的一个多项式时间算法.算法的关键在于将一般移位排序问题在线性时间内归约为交互型移位排序问题,利用交互型移位排序的算法来求解一般移位排序.作者的算法证实了Ozery-Flato等关于一般移位排序问题可以多项式时间解决的猜测.     

贪心算法求解k-median问题

文章讨论了用贪心算法解k-m edian问题以及其试验结果。首先提出了一个解k-m edian问题的简单贪心算法,然后对求解质量和求解的近似性能比进行了探讨。主要讨论了公制空间和非公制空间初始解的产生,用贪心算法解k-m edian问题以及全局最优解的计算。试验结果表明:贪心算法解公制空间的k-m edian问题效果要好于解非公制空间的k-m edian问题;用贪心算法解公制空间和非公制空间k-m edian问题都能得到较好的结果。     

改进的最优顶点覆盖贪心边近似算法

最优顶点覆盖问题是6个基本的NP完全问题之一，无法在多项式时间内得到最优解，除非P=NP。文中给出改进的最优顶点覆盖贪心边近似算法的同时，证明并讨论了它的近似因子是一个不大于2的与单点贪心边数和双点贪心边数相关的因子。     

最大简单共享问题的快速近似算法

介绍了一种基于复制结点的消除线路交叉的模型.该模型提出了一个优化问题,就是最小化结点复制的数量.同时提出一个自定义问题——"最大简单共享问题",并证明最小化结点复制的数量与最大共享问题是等价的.证明了最大简单共享问题是NP-hard的,给出了一种简单的贪心算法,并证明该贪心算法的近似度为3.引入一个"最大互斥简单共享问题",该问题是最大简单共享问题的2-近似.将其转化为在一系列图上的完美匹配问题,使该问题可以在多项式时间内得到完美解决.最后,在最大互斥简单共享的基础上,用局部搜索的方法将近似度提高到12/7.     

合取范式3可满足问题的局部搜索近似算法

合取范式最大可满足问题是理论计算机科学的核心问题.局部搜索被许多求解实践证明是解答合取范式最大可满足问题十分有效的方法,但未见关于局部搜索算法解答该问题性能分析的结果.文中讨论最大3可满足问题(Max-(3)-Sat)的局部搜索算法并分析算法性能.证明Max-(3)-Sat问题的一位跳变局部搜索算法的近似性能比为4/3;证明一位跳变局部搜索后跟有条件全体跳变算法,解答Max-(3)-Sat问题的近似性能比为5/4.设计一位跳变加全体跳变的新局部搜索算法,证明新算法解答Max-(3)-Sat问题的近似性能比为8/7.将8/7-近似局部搜索算法推广为解答Max-(k)-Sat问题的局部搜索算法,证明算法的近似性能比为(2k+2)/(2k+1),k≥4.设计解答Max-(k)-Sat问题的两位跳变局部搜索算法,证明两位跳变局部搜索算法的近似性能比为1+1/(2k+1+k(k-1)/(n-k)),k≥4.局部搜索算法经多次运行可进一步提高求解性能.文中结果显示,局部搜索算法在合取范式最大可满足问题求解实践中表现出高性能,有其必然性.     

堆与贪心算法

堆是一种特殊的树,堆的首元素常常是堆中结点的最小或最大值.堆排序是一种比较快的排序方法,贪心算法中常常要找到最小(大)值.本文介绍了堆在贪心算法中的运用,并分析了其时间优越性.     

A 14/11-approximation algorithm for sorting by short block-moves

Block-move is one of the popular operations for genome rearrangement. A short block-move is an operation on a permutation that moves an element at most two positions away from its original position. Heath and Vergara investigated the problem of finding a minimum-length sorting sequence of short block-moves for a given permutation and devised a 4/3-approximation algorithm. In this paper, we present a new 14/11-approximation algorithm for this problem. Firstly, we devise an exact polynomial time alg...     

Sorting by Short Block-Moves

Sorting permutations by operations such as reversals and block-moves has received much interest because of its applications in the study of genome rearrangements and in the design of interconnection networks. A short block-move is an operation on a permutation that moves an element at most two positions away from its original position. This paper investigates the problem of finding a minimum-length sorting sequence of short block-moves for a given permutation. A 4/3 -approximation algorithm for this problem is presented. Woven double-strip permutations are defined and a polynomial-time algorithm for this class of permutations is devised that employs graph matching techniques. A linear-time maximum matching algorithm for a special class of grid graphs improves the time complexity of the algorithm for woven double-strip permutations. Received June 1, 1997; revised July 25, 1998.     

Sorting Unsigned Permutations by Weighted Reversals,Transpositions, and Transreversals

Reversals, transpositions and transreversals are common events in genome rearrangement. The genome rearrangement sorting problem is to transform one genome into another using the minimum number of given rearrangement operations. An integer permutation is used to represent a genome in many cases. It can be divided into disjoint strips with each strip denoting a block of consecutive integers. A singleton is a strip of one integer. And the genome rearrangement problem turns into the problem of sorting a permutation into the identity permutation equivalently. Hannenhalli and Pevzner designed a polynomial time algorithm for the unsigned reversal sorting problem on those permutations with O(log n) singletons. In this paper, first we describe one case in which Hannenhalli and Pevzner’s algorithm may fail and propose a corrected approach. In addition, we propose a (1+ε)-approximation algorithm for sorting unsigned permutations with O(log n) singletons by reversals of weight 1 and transpositions/transreversals of weight 2.     

Constant factor approximation algorithms for the densest k-subgraph problem on proper interval graphs and bipartite permutation graphs

The densest k-subgraph problem asks for a k-vertex subgraph with the maximum number of edges. This problem is NP-hard on bipartite graphs, chordal graphs, and planar graphs. A 3-approximation algorithm is known for chordal graphs. We present -approximation algorithms for proper interval graphs and bipartite permutation graphs. The latter result relies on a new characterisation of bipartite permutation graphs which may be of independent interest.     

Power Assignment in Radio Networks with Two Power Levels

We study the power-assignment problem in radio networks, where each radio station can transmit in one of two possible power levels, corresponding to two ranges—short and long. We show that this problem is NP-hard, and we present an O(n²)-time assignment algorithm such that the number of transmitters that are assigned long range by the algorithm is at most (11/6) times the number of transmitters that are assigned long range by an optimal algorithm. We also present a (9/5)-approximation algorithm for this problem whose running time is considerably higher.     

Linear programming based approximation algorithms for feedback set problems in bipartite tournaments

We consider the feedback vertex set and feedback arc set problems on bipartite tournaments. We improve on recent results by giving a 2-approximation algorithm for the feedback vertex set problem. We show that this result is the best that we can attain when using optimal solutions to a certain linear program as a lower bound on the optimal value. For the feedback arc set problem on bipartite tournaments, we show that a recent 4-approximation algorithm proposed by Gupta (2008) [8] is incorrect. We give an alternative 4-approximation algorithm based on an algorithm for the feedback arc set on (non-bipartite) tournaments given by van Zuylen and Williamson (2009) [14].     

Maximizing the Total Profit of Rectangles Packed into a Rectangle

We consider the following rectangle packing problem. Given a set of rectangles, each of which is associated with a profit, we are requested to pack a subset of the rectangles into a bigger rectangle so that the total profit of rectangles packed is maximized. The rectangles may not overlap. This problem is strongly NP-hard even for packing squares with identical profits. We first present a simple (3 + ε)-approximation algorithm. Then we consider a restricted version of the problem and show a (2 + ε)-approximation algorithm. This restricted problem includes the case where rotation by 90° is allowed (and is possible), and the case of packing squares. We apply a similar technique to the general problem, and get an improved algorithm with a worst-case ratio of at most 5/2 + ε. Finally, we devise a (2 + ε)-approximation algorithm for the general problem.     

Approximating MIN 2-SAT and MIN 3-SAT

We obtain substantially improved approximation algorithms for the MIN k-SAT problem, for k = 2,3. More specifically, we obtain a 1.1037-approximation algorithm for the MIN 2-SAT problem, improving a previous 1.5-approximation algorithm, and a 1.2136-approximation algorithm for the MIN 3-SAT problem, improving a previous 1.75-approximation algorithm for the problem. These results are obtained by adapting techniques that were previously used to obtain approximation algorithms for the MAX k-SAT problem. We also obtain some hardness of approximation results.     

An approximation algorithm for the three-machine scheduling problem with the routes given by the same partial order

The paper considers a three-machine shop scheduling problem to minimize the makespan, in which the route of a job should be feasible with respect to a machine precedence digraph with three nodes and one arc. For this NP-hard problem that is related to the classical flow shop and open shop models, we present a simple 1.5-approximation algorithm and an improved 1.4-approximation algorithm.     

An approximation algorithm for the precedence constrained scheduling problem with hierarchical communications

We study the problem of minimizing the makespan for the precedence multiprocessor constrained scheduling problem with hierarchical communications (Parallel Process. Lett. 10(1) (2000) 133). We propose an -approximation algorithm for the Unit Communication Time hierarchical problem with arbitrary but integer processing times and an unbounded number of biprocessor machines. We extend this result in the case where each cluster has m processors (where m is a fixed constant) by presenting a (2−2/(2m+1))-approximation algorithm.