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...     

Constrained total least squares algorithm for passive location based on bearing-only measurements

The constrained total least squares algorithm for the passive location is presented based on the bearing-only measurements in this paper. By this algorithm the non-linear measurement equations are firstly transformed into linear equations and the effect of the measurement noise on the linear equation coefficients is analyzed, therefore the problem of the passive location can be considered as the problem of constrained total least squares, then the problem is changed into the optimized question without restraint which can be solved by the Newton algorithm, and finally the analysis of the location accuracy is given. The simulation results prove that the new algorithm is effective and practicable.     

Robust graph coloring based on the matrix semi-tensor product with application to examination timetabling

This paper investigates the robust graph coloring problem with application to a kind of examination timetabling by using the matrix semi-tensor product, and presents a number of new results and algorithms. First, using the matrix semi-tensor product, the robust graph coloring is expressed into a kind of optimization problem taking in an algebraic form of matrices, based on which an algorithm is designed to find all the most robust coloring schemes for any simple graph. Second, an equivalent problem of robust graph coloring is studied, and a necessary and sufficient condition is proposed, from which a new algorithm to find all the most robust coloring schemes is established. Third, a kind of examination timetabling is discussed by using the obtained results, and a method to design a practicable timetabling scheme is presented. Finally, the effectiveness of the results/algorithms presented in this paper is shown by two illustrative examples.     

A new algorithm based on the proximity principle for the virtual network embedding problem

The virtual network embedding/mapping problem is a core issue of network virtualization. It is concerned mainly with how to map virtual network requests to the substrate network efficiently. There are two steps in this problem： node mapping and link mapping. Current studies mainly focus on developing heuristic algorithms, since both steps are computationally intractable. In this paper, we propose a new algorithm based on the proximity principle, which considers the distance factor besides the capacity factor in the node mapping step. Thus, the two steps of the embedding problem can be better integrated and the substrate network resource can be used more efficiently. Simulation results show that the new algorithm greatly enhances the performance of the revenue/cost （R/C） ratio, acceptance ratio, and runtime of the embedding problem.     

Reduct and attribute order

Based on the principle of discernibility matrix, a kind of reduction algorithm with attribute order has been developed and its solution has been proved to be complete for reduct and unique for a given attribute order. Being called the reduct problem, this algorithm can be regarded as a mapping R = Reduct(S) from the attribute order space O to the reduct space R for an information system (U, C ∪ D）, where U is the universe and C and D are two sets of condition and decision attributes respectively. This paper focuses on the reverse problem of reduct problem S = Order(R), i.e., for a given reduct R of an information system, we determine the solution of S = Order(R) in the space θ. First, we need to prove that there is at least one attribute order S such that S = Order(R). Then, some decision rules are proposed, which can be used directly to decide whether the pair of attribute orders has the same reduct. The main method is based on the fact that an attribute order can be transformed into another one by moving the attribute for limited times. Thus, the decision of the pair of attribute orders can be altered to the decision of the sequence of neighboring pairs of attribute orders. Therefore,the basic theorem of neighboring pair of attribute orders is first proved, then, the decision theorem of attribute order is proved accordingly by the second attribute.     

Algorithm based on taboo search and shifting bottleneck for job shop scheduling

In this paper, a computational effective heuristic method for solving the minimum makespan problem of job shop scheduling is presented. It is based on taboo search procedure and on the shifting bottleneck procedure used to jump out of the trap of the taboo search procedure. A key point of the algorithm is that in the taboo search procedure two taboo lists are used to forbid two kinds of reversals of arcs, which is a new and effective way in taboo search methods for job shop scheduling. Computational experiments on a set of benchmark problem instances show that, in several cases, the approach, in reasonable time, yields better solutions than the other heuristic procedures discussed in the literature.     

属性维概念及其操作的研究

Dimension member attribute is used to describe the property of dimension members. It is not fully understood and well defined in OLAP research area.This paper focuses on a special kind of dimension member attributes,which can be used as dimensions by themselves. We call them attribute dimensions.In order to facilitate this kind of necessity of multidimensional data modeling in many real-world applications,the traditional multidimensional structure is extended and a group of operations are given to formulate corresponding multidimebsuibak qyerues.     

Second Attribute Algorithm Based on Tree Expression

One view of finding a personalized solution of reduct in an information system is grounded on the viewpoint that attribute order can serve as a kind of semantic representation of user requirements. Thus the problem of finding personalized solutions can be transformed into computing the reduct on an attribute order. The second attribute theorem describes the relationship between the set of attribute orders and the set of reducts, and can be used to transform the problem of searching solutions to meet user requirements into the problem of modifying reduct based on a given attribute order. An algorithm is implied based on the second attribute theorem, with computation on the discernibility matrix. Its time complexity is O（n^2 × m） （n is the number of the objects and m the number of the attributes of an information system）. This paper presents another effective second attribute algorithm for facilitating the use of the second attribute theorem, with computation on the tree expression of an information system. The time complexity of the new algorithm is linear in n. This algorithm is proved to be equivalent to the algorithm on the discernibility matrix.     

A Routing Algorithm with Candidate Shortest Path

An improved algorithm based on the next node routing principle is proposed in this paper.In this algorithm there is a column added to the classical routing table, in which the candidateshortest distance to the destination node is the entry. When a link fails, the new shortest path inthe nodes connected directly with the failure link can be found immediately (it is just thecandidate shortest path before failure). For all other nodes in which routing tables should bechanged, the required number of control messages and time for convergence are also less thanTajibnapis' algorithm and Predecessor algorithm. The message looping problem does not existin duplex loop networks and is radically improved in mesh networks. These statements areproved by the analysis and simulation in this paper. From the simulation results of a 30-nodemesh network, when one link goes down, the total number of control messages generatedduring convergence with this algorithm on the average is about 30% of Tajibnapis' algorithm.The iterations required is 50% of Tajibnapis' algorithm. The memory space required andcomputation complexity in nodes are almost the same as the two algorithms mentioned aboveand the algorithm implementation is as easy as well.     

An incremental approach to automatic algorithm design

This paper presents an incremental approach to automatic algorithm design,which can be described by algebraic specifications precisely and conveniently.The definitions of selection operator and extension operator which ca be defined by strategy relations and transformations are given in order to model the process of finding the solution of a problem.Also discussed is its object-oriented implementation.The functional specification and the design specification for an algorithm are given in one framework so that the correctness of the algorithm can be easily proved.     

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.     

A 2-approximation algorithm for genome rearrangements by reversals and transpositions

Recently, a new approach to analyze genomes evolving which is based on comparision of gene orders versus traditional comparision of DNA sequences was proposed (Sankoff et al. 1992). The approach is based on the global rearrangements (e.g., inversions and transpositions of fragments). Analysis of genomes evolving by inversions and transpositions leads to a combinatorial problem of sorting by reversals and transpositions, i.e., sorting of a permutation using reversals and transpositions of arbitrary fragments. We study sorting of signed permutations by reversals and transpositions, a problem which adequately models genome rearrangements, as the genes in DNA are oriented. We establish a lower bound and give a 2-approximation algorithm for the problem.     

A new approximation algorithm for cut-and-paste sorting of unsigned circular permutations

A cut-and-paste operation can be a reversal, a transposition, or a transreversal on circular or linear permutations. There are several approximation algorithms for sorting signed permutations by combinations of these operations. For sorting unsigned permutations, we only know an algorithm with performance ratio 3 and its improved version with performance ratio $2.8386+\delta$ allowing reversals and transpositions. In this paper, we present a 2.25-approximation algorithm for sorting unsigned circular permutations by cut-and-paste operations. A structure called tie is proposed to represent the alternating path of length 5. We can classify the ties into 6 types and find ways to remove the breakpoints for each type of ties, so that every cut-and-paste operation can reduce at least $\frac{4}{3}$ breakpoints averagely. Our algorithm can be used to sort unsigned linear permutations and achieve the performance ratio 2.25 if another operation named revrev is allowed.     

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.     

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。     

短块移动排序的14/11近似算法

块移动是基因重组的一种重要形式.短块移动是将排列中的元素最多移动到偏离原来两个位置的块移动.Heath和Vergara最先给出短块移动排序近似度为4/3的多项式时间算法.本文设计了近似性能比为14/11的短块移动排序新算法.首先讨论了具有伞形结构排列图的子排列的排序方法,并将这种子排列称为‘伞’,设计了特殊子排列伞短块移动排序的多项式时间精确算法.然后给出关联伞子排列短块移动排序的贪心算法.讨论了5种特殊子排列的短块移动排序方法,证明了它们短块移动距离的新下界,从而证明此贪心算法的近似性能比为14/11,这是目前解答短块移动排序问题近似性能比最小的多项式近似算法.     

基因组Translocation排序问题的改进多项式算法

该文给出基因组Transhocation排序问题的一个改进多项式算法，原算法所有存储空间O（n)，时间复杂度为O(n^3)，文中改进算法仍采用O(n)存储空间，时间复杂度为O(n^2logn),具体地，将计算Translocation距离的时间复杂度由O(n^3)改进为O(n^2),将计算Translocation序列的时间复杂度由O(n^3)改进为O(n^2logn).     

A more efficient algorithm for perfect sorting by reversals

We describe a new algorithm for the problem of perfect sorting a signed permutation by reversals. The worst-case time complexity of this algorithm is parameterized by the maximum prime degree d of the strong interval tree, i.e., f(d).nO(1). This improves the best known algorithm which complexity was based on a parameter always larger than or equal to d.