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.     

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).     

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).     

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.     

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.     

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.     

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.     

A binary algorithm for solving n by n systems of integer equations

We discuss a “binary” algorithm for solving systems of linear equations with integer coefficients. So-called “binary” algorithms differ from ordinary ones in that there is no roundoff error, but only overflow, and the underlying analysis is p-adic analysis rather than conventional real analysis. The advantages of this algorithm are especially apparent when extremely large numbers are involved and no roundoff error can be tolerated.

VLSI implementation of this and other “binary” algorithms is very appealing because of the extreme regularity of the circuits involved.     

指定验证人的(t,n)门限代理签名方案

将指定验证人概念引入门限代理签名,提出了一个指定验证人的(t,n)门限代理签名方案.该方案不仅实现了门限代理签名,而且还能实现只有指定验证人一起才能验证门限代理签名的特性.在普通的门限代理签名方案中,任何人都能验证门限代理签名的有效性.然而,在某些情况下,只希望指定的验证人一起才能验证门限代理签名.这在实际中是需要的,如电子商务中的电子投标等.另外,该方案还具有在原始签名人需要时,收回某个代理签名人代理权的特性.     

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 (

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.     

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.     

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.     

Constant-Time Tree Algorithms on Reconfigurable Meshes on Size n × n

Recently, an elegant and powerful architecture called the reconfigurable mesh has been proposed in the literature. In essence, a reconfigurable mesh consists of a mesh-connected architecture enhanced by the addition of a dynamic bus system whose configuration changes in response to computational and communication needs. In this paper we show that the reconfigurable mesh architecture can be exploited to yield very simple constant-time algorithms to solve a number of important computational problems involving trees. Specifically, we address the problem of generating the computation tree form of an arithmetic expression, the problem of reconstructing a binary tree from its preorder and inorder traversals, and the problem of reconstructing an ordered forest from its preorder and postorder traversals. We show that with an input of size n, all these problems find constant-time solutions on a reconfigurable mesh of size n × n.     

A Two-Step Regularization Framework for Non-Local Means

As an effective patch-based denoising method, non-local means （NLM） method achieves favorable denoising performance over its local counterparts and has drawn wide attention in image processing community. The in, plementation of NLM can formally be decomposed into two sequential steps, i.e., computing the weights and using the weights to compute the weighted means. In the first step, the weights can be obtained by solving a regularized optimization. And in the second step, the means can be obtained by solving a weighted least squares problem. Motivated by such observations, we establish a two-step regularization framework for NLM in this paper. Meanwhile, using the fl-amework, we reinterpret several non-local filters in the unified view. Further, taking the framework as a design platform, we develop a novel non-local median filter for removing salt-pepper noise with encouraging experimental results.     

A Permanent Algorithm with exp[Ω ( n ^{1/3}/2 ln n )] Expected Speedup for 0-1 Matrices

Abstract. This paper outlines a permanent algorithm with mildly exponential expected speedup over Ryser's inclusion and exclusion algorithm for 0-1 matrices. The algorithm is based on a finite-difference formula that is a generalization of Ryser's formula. The matrix is augmented by a column of entries selected to produce zero-valued terms in the formula. The algorithm achieves speedup by avoiding computation of many zero-valued terms.     

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.     

A new way of counting n

In this paper, we shall give a combinatorial proof of the following equation:

,

where m and n are positive integers, m ≤ n, and k₁, k₂, …, k_n-1 are nonnegative integers.     

Security of Wang et al.''s group-oriented (t,n) threshold signature schemes with traceable signers

This paper describes a new forgery attack on the group-oriented (t,n) threshold signature schemes proposed by Wang et al. Our attack is more fundamental than Tseng–Jan's attack in the sense that it cannot be recognized or blocked at the designated clerk level of the signature schemes.     

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).