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991.
992.
An exact and polynomial distance-based algorithm to reconstruct single copy tandem duplication trees
The problem of reconstructing the duplication tree of a set of tandemly repeated sequences which are supposed to have arisen by unequal recombination, was first introduced by Fitch (1977), and has recently received a lot of attention. In this paper, we place ourselves in a distance framework and deal with the restricted problem of reconstructing single copy duplication trees. We describe an exact and polynomial distance based algorithm for solving this problem, the parsimony version of which has previously been shown to be NP-hard (like most evolutionary tree reconstruction problems). This algorithm is based on the minimum evolution principle, and thus involves selecting the shortest tree as being the correct duplication tree. After presenting the underlying mathematical concepts behind the minimum evolution principle, and some of its benefits (such as statistical consistency), we provide a new recurrence formula to estimate the tree length using ordinary least-squares, given a matrix of pairwise distances between the copies. We then show how this formula naturally forms the dynamic programming framework on which our algorithm is based, and provide an implementation in O(n3) time and O(n2) space, where n is the number of copies. 相似文献
993.
994.
995.
996.
Kenneth Weber Vilmar Trevisan Luiz Felipe Martins 《Journal of Algorithms in Cognition, Informatics and Logic》2005,54(2):152-167
This paper describes the first algorithm to compute the greatest common divisor (GCD) of two n-bit integers using a modular representation for intermediate values U, V and also for the result. It is based on a reduction step, similar to one used in the accelerated algorithm [T. Jebelean, A generalization of the binary GCD algorithm, in: ISSAC '93: International Symposium on Symbolic and Algebraic Computation, Kiev, Ukraine, 1993, pp. 111–116; K. Weber, The accelerated integer GCD algorithm, ACM Trans. Math. Softw. 21 (1995) 111–122] when U and V are close to the same size, that replaces U by (U−bV)/p, where p is one of the prime moduli and b is the unique integer in the interval (−p/2,p/2) such that . When the algorithm is executed on a bit common CRCW PRAM with O(nlognlogloglogn) processors, it takes O(n) time in the worst case. A heuristic model of the average case yields O(n/logn) time on the same number of processors. 相似文献
997.
In this work, we consider a public facility allocation problem decided through a voting process under the majority rule. A
location of the public facility is a majority rule winner if there is no other location in the network where more than half
of the voters would have been closer to than the majority rule winner. We develop fast algorithms for interesting cases with
nice combinatorial structures. We show that the computing problem and the decision problem in the general case, where the
number of public facilities is more than one and is considered part of the input size, are all NP-hard. Finally, we discuss
majority rule decision making for related models. 相似文献
998.
M. Van Barel E. Van Camp N. Mastronardi 《Numerical Linear Algebra with Applications》2005,12(10):981-1000
Very recently, an algorithm, which reduces any symmetric matrix into a semiseparable one of semi‐ separability rank 1 by similar orthogonality transformations, has been proposed by Vandebril, Van Barel and Mastronardi. Partial execution of this algorithm computes a semiseparable matrix whose eigenvalues are the Ritz‐values obtained by the Lanczos' process applied to the original matrix. Also a kind of nested subspace iteration is performed at each step. In this paper, we generalize the above results and propose an algorithm to reduce any symmetric matrix into a similar block‐semiseparable one of semiseparability rank k, with k ∈ ?, by orthogonal similarity transformations. Also in this case partial execution of the algorithm computes a block‐semiseparable matrix whose eigenvalues are the Ritz‐values obtained by the block‐Lanczos' process with k starting vectors, applied to the original matrix. Subspace iteration is performed at each step as well. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
999.
投影寻踪模型在国民经济综合评价中的应用 总被引:10,自引:0,他引:10
文章针对区域国民经济发展的多属性,采用投影寻踪评价模型,用加速遗传算法寻找最佳投影方向,将多维属性指标转换为一维投影值.在此基础上,通过建立单属性指标的分类等级区间,给出区域国民经济发展水平分类的投影值区间,从而实现对区域国民经济发展水平的分类.应用表明,它是国民经济评价的一种计算过程简单、直观的新方法. 相似文献
1000.
戴伏生 《数学的实践与认识》2006,36(2):186-192
经典的D IJKSTRA和BELLM AN-F LOYD通信网络路由算法,只能根据特定网络参数得到最佳路由,却无法获得网络存在的全部可用路由,而通信网理论研究及网络管理等方面,往往需要获得节点之间的全部可用路由.研究出一种路由新算法,遵循逻辑代数运算规则、采用关联矩阵中行与行之间整合与删除方式计算,N个节点的网络只需N-1次整合及删除运算,就能得到源节点到任意节点两点之间全部路由结果.详细论证了算法的正确性与合理性,简介了算法的并行运算可行性及与经典路由算法的兼容性等问题.通过算例详细说明算法的计算过程,并验证其正确性. 相似文献