Computing the Quartet Distance between Evolutionary Trees in Time O( n log n)

Evolutionary trees describing the relationship for a set of species are central in evolutionary biology, and quantifying differences between evolutionary trees is therefore an important task. The quartet distance is a distance measure between trees previously proposed by Estabrook, McMorris, and Meacham. The quartet distance between two unrooted evolutionary trees is the number of quartet topology differences between the two trees, where a quartet topology is the topological subtree induced by four species. In this paper we present an algorithm for computing the quartet distance between two unrooted evolutionary trees of n species, where all internal nodes have degree three, in time O(n log n. The previous best algorithm for the problem uses time O(n ²).     

O(log n) bimodality analysis

The bimodality of a population P can be measured by dividing its range into two intervals so as to maximize the Fisher distance between the resulting two subpopulations P₁ and P₂. If P is a mixture of two (approximately) Gaussian subpopulations, then P₁ and P₂ are good approximations to the original Gaussians, if their Fisher distance is great enough. Moreover, good approximations to P₁ and P₂ can be obtained by dividing P into small parts; finding the maximum-distance (MD) subdivision of each part; combining small groups of these subdivisions into (approximate) MD subdivisions of larger parts; and so on. This divide-and-conquer approach yields an approximate MD subdivision of P in O(log n) computational steps using O(n) processors, where n is the size of P.     

On the Linear-Cost Subtree-Transfer Distance between Phylogenetic Trees

Different phylogenetic trees for the same group of species are often produced either by procedures that use diverse optimality criteria [16] or from different genes [12] in the study of molecular evolution. Comparing these trees to find their similarities and dissimilarities (i.e., distance ) is thus an important issue in computational molecular biology. Several distance metrics including the nearest neighbor interchange (nni) distance and the subtree-transfer distance have been proposed and extensively studied in the literature. This article considers a natural extension of the subtree-transfer distance, called the linear-cost subtree-transfer distance, and studies the complexity and efficient approximation algorithms for this distance as well as its relationship to the nni distance. The linear-cost subtree-transfer model seems more suitable than the (unit-cost) subtree-transfer model in some applications. The following is a list of our results: 1. The linear-cost subtree-transfer distance is in fact identical to the nni distance on unweighted phylogenies. 2. There is an algorithm to compute an optimal linear-cost subtree-transfer sequence between unweighted phylogenies in O(n ⋅ 2 ^O(d) ) time, where d denotes the linear-cost subtree-transfer distance. Such an algorithm is useful when d is small. 3. Computing the linear-cost subtree-transfer distance between two weighted phylogenetic trees is NP-hard, provided we allow multiple leaves of a tree to share the same label (i.e., the trees are not necessarily uniquely labeled). 4. There is an efficient approximation algorithm for computing the linear-cost subtree-transfer distance between weighted phylogenies with performance ratio 2 . Received May 8, 1997; revised February 20, 1998.     

Bridging across the log(n) Space Frontier

This paper establishes the importance of even the lowest possible level of space bounded computations. We show that DLOG does not coincide with NLOG if and only if there exists a tally set in NSPACE(log log n)\DSPACE(log log n). This result stands in perfect analogy to the related results concerning linear space or exponential time. Moreover, the above problem is equivalent to the existence of a functions(n), with arbitrarily slow or rapid growth rate, that is nondeterministically fully space constructible but cannot be constructed deterministically. We also present a “hardest” fully space constructibles(n)∈O(log log n), a functional counterpart of log-space complete languages. These nonrelativized results are obtained by the use of oracle machines consuming much larger amount of space, in range betweennand 2^d·n.     

O(log logN) Time Algorithms for Hamiltonian Suffix and Min-Max-Pair Heap Operations on the Hypercube

This paper deals with a fast implementation of a heap data structure on a hypercube-connected, synchronous, distributed-memory multicomputer. In particular, we present a communication-efficient mapping of a min-max-pair heap on the hypercube architecture in which the load on each processor's local memory is balanced and propose cost-optimal parallel algorithms which requireO((logN)/p+ logp) time to perform single insertion, deletemin, and deletemax operations on a min-max-pair heap of sizeN, wherepis the number of processors. Our implementation is based on an embedding of complete binary trees in the hypercube and an efficient parallel solution to a special kind of suffix computation, that we call theHamiltonian suffix, along a Hamiltonian path in the hypercube. The binary tree underlying the heap data structure is, however, not altered by the mapping process.     

具有O(n)消息复杂度的协调检查点设置算法

协调检查点设置及回卷恢复技术作为一种有效的容错手段,已广泛地运用在集群等并行/分布计算机系统中.为了进一步降低协调检查点设置的时间和空间开销,提出了一种基于消息计数的协调检查点设置算法.该算法无须对底层消息通道的FIFO特性进行假设,并使同步阶段引入的控制消息复杂度由通常的O(n²)降低到O(n),有效地提高了系统的效率和扩展性.     

Vague集（值）间的距离测度

1 引言自从Zadeh提出fuzzy集理论以来,fuzzy集理论就在不断地发展和完善,并在许多领域里得到了成功的应用。但在实际应用中我们也发现它存在一些问题,例如,fuzzy集的隶属度是一个单值,该单值既包含了支持u∈U(U为论域)的证据,也包含了反对u∈U的证据,它不可能表示其中的一个,更不可能同时表示支持和反对的证据。为此,Gau等在文中提出了vague集的概念,用一个真隶属函数t_A和一个假隶属函数f_A来描述vague集,真假隶属函数形成了隶属函     

An O(log n) pyramid hough transform

This paper describes a divide-and-conquer Hough transform technique for detecting a given number of straight edges or lines in an image. This technique is designed for implementation on a pyramid of processors, and requires only O(log n) computational steps for an image of size n × n.     

Build shape-shifting tries for fast IP lookup in O(n) time

Most data structures for packet forwarding are optimized for IPv4, and less capable of handling IPv6 routing tables. Shape-Shifting Trie (SST) is specifically designed to be scalable to IPv6. To reduce the worst-case lookup time that is proportional to the height of SST, it is desirable to construct a minimum-height SST. Breadth-First Pruning (BFP) algorithm takes O(n²) time to construct a minimum-height SST, where n is the number of nodes in the binary trie corresponding to the routing table. In this paper, we propose a Post-Order Minimum-Height Pruning (POMHP) algorithm that takes only O(n) time to construct a minimum-height SST. We further propose nodes merging algorithm to cut down SST size without affecting SST height.     

Exact 3-satisfiability is decidable in time O(20.16254n)

Let F = C ₁ C _m be a Boolean formula in conjunctive normal form over a set V of n propositional variables, s.t. each clause C _i contains at most three literals l over V. Solving the problem exact 3-satisfiability (X3SAT) for F means to decide whether there is a truth assignment setting exactly one literal in each clause of F to true (1). As is well known X3SAT is NP-complete [6]. By exploiting a perfect matching reduction we prove that X3SAT is deterministically decidable in time O(2^0.18674n ). Thereby we improve a result in [2,3] stating X3SAT O(2^0.2072n ) and a bound of O(2^0.200002n ) for the corresponding enumeration problem #X3SAT stated in a preprint [1]. After that by a more involved deterministic case analysis we are able to show that X3SAT O(2^0.16254n ).An extended abstract of this paper was presented at the Fifth International Symposium on the Theory and Applications of Satisfiability Testing (SAT 2002).     

An O(n log n) Average Time Algorithm for Computing the Shortest Network under a Given Topology

In 1992 F. K. Hwang and J. F. Weng published an O(n ² ) time algorithm for computing the shortest network under a given full Steiner topology interconnecting n fixed points in the Euclidean plane. The Hwang—Weng algorithm can be used to improve substantially existing algorithms for the Steiner minimum tree problem because it reduces the number of different Steiner topologies to be considered dramatically. In this paper we present an improved Hwang—Weng algorithm. While the worst-case time complexity of our algorithm is still O(n ² ) , its average time complexity over all the full Steiner topologies interconnecting n fixed points is O (n log n ). Received August 24, 1996; revised February 10, 1997.     

Embedding k(n−k) edge-disjoint spanning trees in arrangement graphs

The arrangement graphs are a class of generalized star graphs. In this paper we construct a graph that consists of the maximum number of directed edge-disjoint spanning trees in an arrangement graph. The paths that connect the common root node to any given node through different spanning trees are node-disjoint, and the lengths of these paths differ from the shortest possible lengths by a small additive constant. This graph can be used to derive fault-tolerant algorithms for broadcasting and scattering problems without prior knowledge of the faulty elements of the network.     

An O ( n 1.5 ) Deterministic Gossiping Algorithm for Radio Networks

   Abstract. We consider the problem of distributed gossiping in radio networks of unknown topology. For radio networks of size n and diameter D , we present an adaptive deterministic gossiping algorithm of time O (

背包类问题的并行O(25n/6)时间-空间-处理机折衷

将串行动态二表算法应用于并行三表算法的设计中,提出一种求解背包、精确的可满足性和集覆盖等背包类NP完全问题的并行三表六子表算法.基于EREW-PRAM模型,该算法可使用O(2^n/8)的处理机在O(2^7n/16)的时间和O(2^13n/48)的空间求解n维背包类问题,其时间-空间-处理机折衷为O(2^5n/6).与现有文献的性能对比分析表明,该算法极大地提高了并行求解背包类问题的时间-空间-处理机折衷性能.由于该算法能够破解更高维数的背包类公钥和数字水印系统,其结论在密钥分析领域具有一定的理论和实际意义.     

Computing steady state probabilities in λ(n)/G/1/K queue

In this paper a recursive method is developed to obtain the steady state probability distribution of the number in system at arbitrary and departure time epochs of a single server state-dependent arrival rate queue λ(n)/G/1/K in which the arrival process is Markovian with arrival rates λ(n) which depend on the number of customers n in the system and general service time distribution. It is assumed that there exists an integer K such that λ(n) > 0 for all 0 n < K and λ(n) = 0 for all n K. Numerical results have been presented for many queueing models by suitably defining the function λ(n). These include machine interference model, queues with balking, queues with finite waiting space and machine interference model with finite waiting space. These models have wide application in computer/communication networks.     

一种O(2.983n)时间复杂度的最优联盟结构生成算法

首先,在有限整数集上建立有效拆分关系,在联盟集上建立有效二部分解关系,并设计了一种EOCS(effective optimal coalition structure)算法.该算法采用自底向上方式,只对具有有效二部分解关系的联盟进行二部分解来求联盟的优值,从而降低了二部分解的数量.随后,利用函数的克林闭包特性证明了EOCS算法的正确性,利用积分极限定理证明了EOCS算法时间复杂度的下界是O(2.818n),用时间序列分析方法求出了EOCS算法的上界是O(2.983n).最后,将EOCS算法与其他算法作了对比,指出无论联盟值满足何种概率分布,EOCS算法都能在O(2.983n)时间内找出最优联盟结构.Rothkopf提出的DP(dynamic programming)算法和Rahwan提出的IDP(improved dynamic programming)算法能够在O(3n)时间内求出最优联盟结构.所作的EOCS算法设计、正确性证明、时间复杂度的上下界分析都是对Rothkopf及Rahwan等人相关工作的改进和提高.     

A simple O(n log n) algorithm for finding the maximum distance between two finite planar sets

A simple O(n log n) algorithm is presented for computing the maximum Euclidean distance between two finite planar sets of n points. When the n points form the vertices of simple polygons this complexity reduces to O(n).     

On the uniform finite generation of SO(n, )

A Lie group G, generated by two one-parameter subgroups is said to be uniformly finitely generated by them if there exists a positive integer N such that every element of G can be expressed as a product of at most N elements chosen alternately from the two one-parameter subgroups. In this paper we construct pairs of generators of so(n) whose one-parameter subgroups uniformly finitely generate SO(n) and as a consequence, we put an upper bound on the number of switches required to join any two points on a manifold M trajectories of two particular vector fields on M.     

Quaternion representations of the O(3) group, and their applications in robotics

Abstract algebraic methods for solving different mathematical tasks have found widespread applications in theoretical physics and in several technical applications. Though group theory can be used to achieve the most simple and transparent formulation of different tasks, it is not very well known by engineers. The aim of this paper is to discuss quaternion representations of the O⁺(3) Lie group from the aspect of robotics. The main features of these representations, as well as their advantages over the pure 3 × 3 matrix (self-)representation, are discussed in the formulation and solution of the direct and inverse kinematic tasks for robots of general wrist-joint structure. To illustrate the convenience of quaternion formulations a particular solution of the inverse kinematic task has been developed on the basis of the concept of non-Euclidean (curved) spaces. A possible Hopfield-type neural-network application appropriate to the proposed solution is also considered.     

Teachers' pedagogical change mechanism – Pattern of structural relations between teachers' pedagogical characteristics and teachers' perceptions of transactional distance (TTD) in different teaching environments

In this study we examined how the variables: teaching autonomy, teaching goals teaching style and teachers' perceptions of transactional distance (TTD) work together within the pedagogical decision-making process in different teaching environments. The independent variable was the teaching environment, which was divided into three: entirely distance environment (Distance-E); blended distance environment (Distance-B); and the traditional environment (Traditional). The dependent variables were teaching autonomy, teaching goals, teaching style and TTD, i.e. teachers' evaluation of their ability to communicate with the students, explain the content and their satisfaction from the teaching environment. One hundred and sixty faculty members who teach in distance environments and one hundred and sixty faculty members who teach in a traditional environment answered a five-part study questionnaire. The finding indicated that teaching autonomy, teaching goal and teaching style are significant predictors of TTD. Furthermore, teaching style serves as a mediator variable connecting teaching autonomy and the teaching goal to the TTD. This pattern was repeated in both structural and measurement models in all three teaching environments, indicating the centrality of the teaching style as well as teaching goal and teaching autonomy in the teachers' pedagogical decision-making process and teaching outputs. We concluded that affecting the teachers' pedagogical characteristics, which serve as mechanisms that influence the results of teaching, is an important component in the process of the technological change in 21st century education.