On fast planning of suboptimal paths amidst polygonal obstacles in plane

The problem of planning a path for a point robot from a source point s to a destination point d so as to avoid a set of polygonal obstacles in plane is considered. Using well-known methods, a shortest path from s to d can be computed with a time complexity of O(n²) where n is the total number of obstacle vertices. The focus here is in

1. (a) planning paths faster at the expense of setting for suboptimal path lengths and

2. (b) performance analysis of simple and/or well-known suboptimal methods.

A method that enables a hierarchical implementation of any path planning algorithm with no increase in the worst-case time complexity, is presented; this implementation enables fast planning of simple paths. Then methods are presented based on the Voronoi diagrams, trapezoidal decomposition and triangulation, which compute (suboptimal) paths in O(n√log n) time with the preprocessing costs of O(n log n), O(n²) and O(n log n), respectively. Using existing navigational algorithms for unknown terrains, algorithms that run in O(n log n) time (after preprocessing) and yield suboptimal paths, are presented. For all these algorithms, upper bounds on the path lengths are estimated in terms of the shortest of the obstacles, etc.     

A time-optimal solution for the path cover problem on cographs

We show that the notoriously difficult problem of finding and reporting the smallest number of vertex-disjoint paths that cover the vertices of a graph can be solved time- and work-optimally for cographs. Our result implies that for this class of graphs the task of finding a Hamiltonian path can be solved time- and work-optimally in parallel.

It was open for more than 10 years to find a time- and work-optimal parallel solution for this important problem. Our contribution is to offer an optimal solution to this important problem. We begin by showing that any algorithm that solves an instance of size n of the problem must take Ω(log n) time on the CREW, even if an infinite number of processors are available. We then go on to show that this time lower bound is tight by devising an EREW algorithm that, given an n-vertex cograph G represented by its cotree, finds and reports all the paths in a minimum path cover in O(log n) time using n/log n processors.     

An optimal distributed algorithm for finding articulation points in a network

This paper presents a distributed algorithm for finding the articulation points in an n node communication network represented by a connected undirected graph. For a given graph if the deletion of a node splits the graph into two or more components then that node is called an articulation point. The output of the algorithm is available in a distributed manner, i.e., when the algorithm terminates each node knows whether it is an articulation point or not. It is shown that the algorithm requires O(n) messages and O(n) units of time and is optimal in communication complexity to within a constant factor.     

An augmented Voronoi roadmap for 3D translational motion planning for a convex polyhedron moving amidst convex polyhedral obstacles

This paper concerns the development of a piecewise linear Voronoi roadmap for translating a convex polyhedron in a three-dimensional (3-D) polyhedral world. In general the Voronoi roadmap is incomplete for motion planning, i.e., it can have several disjoint components in one connected component of free space. An analysis of the roadmap shows that incompleteness is caused by the occurrence of the following simple geometric structure: a polygon in the Voronoi surface containing one or more polygons inside it. We formally bring out the details of this geometric structure and give an efficient augmentation of the roadmap that makes it complete. We show that the roadmap has size e = O(n²Q²l²), where n is the total number of faces on the obstacles, Q is the total number of obstacles and l is the number of faces on the moving object. We also present an algorithm to construct the roadmap in O((n + Ql)e + Q²log Q) time.     

Properties of n-dimensional triangulations

This paper establishes a number of mathematical results relevant to the problem of constructing a triangulation, i.e., a simplical tessellation of the convex hull of an arbitrary finite set of points in n-space.

The principal results of the present paper are

1. (a) A set of n + 2 points in n-space may be triangulated in at most 2 different ways.

2. (b) The ‘sphere test’ defined in this paper selects a preferred one of these two triangulations.

3. (c) A set of parameters is defined that permits the characterization and enumeration of all sets of n + 2 points in n-space that are significantly different from the point of view of their possible triangulations.

4. (d) The local sphere test induces a global sphere test property for a triangulation.

5. (e) A triangulation satisfying the global sphere property is dual to the n-dimensional Dirichlet tessellation, i.e., it is a Delaunay triangulation.

     

基于属性的概念格渐进式生成算法

提出了一种新的基于属性的渐进式概念格生成算法 ,通过不断地渐增属性来构造概念格 .该算法不仅为概念格的构造提供了一种新的方法 ,还解决了在已构造好概念格的前提下 ,增加属性所带来的概念格更新问题 .给出了算法的实现方法 ,并结合实例说明了概念格的更新过程 .试验表明 ,在通常情况下 ,基于属性的渐进式概念格生成算法的性能往往更优越     

An optimal algorithm for Gaussian elimination of band matrices on an MIMD computer

This paper describes a parallel algorithm for the LU decomposition of band matrices using Gaussian elimination. The matrix dimension is n × n with 2r−1 diagonals. In the case when 1 r 2 p an optimal number of the processors, , is determined according to the equation . When 2 p r n a number of processors, p, statged by Veldhorst is adopted (see [7]). For band matrix with 2r-1 diagonals (1 r 2p) the task scheduling procedure with the aim to obtain maximal parallelism in system operation, i.e. good load balancing, is defined. The architecture of the system is of MIMD type. The connection between the processors is realised via a common bus. Communication and synchronization is performed by message passing technique.     

The crossing function and its application to zig-zag tool paths

In zig-zag paths, which are used to sweep planar areas in applications such as machining and surveillance, the number of switch-backs in the path is a major contributor to cutting time. We develop algorithms to pick the direction in which a zig-zag path on a polygon will have the minimum number of switch-backs. We introduce the concept of a crossing function of a two-dimensional contour, which is a measure of how many times a finely pitched set of parallel raster-lines at some angle intersects with the contour. We show that minimizing the crossing-function minimizes the number of switch-backs. We then show that for polygons, the crossing-function is minimized at a finite set of orientations parallel to the edges of the polygon. We show that the problem of minimizing the crossing function can be reduced to minimizing the width of an equivalent convex polygon, and develop an algorithm that takes n log(n) time for an n-sided polygon. Finally, we discuss how these algorithms are useful in machining.     

A parallel residue-to-binary conversion algorithm without trial division

In recent years, the conversion of residue numbers to a binary integer has been intensively studied. The Chinese Remainder Theorem (CRT) is a solution to this conversion problem of a number to the Residue Number System with a general moduli set. This paper presents a new division-free conversion approach for the conversion of residue numbers to a binary integer. The algorithm differs from others employing a great number of division instructions by using shift instructions instead. These simple instructions keep the power consumption lower. This algorithm can also be implemented with a lookup table or upon a vector machine. Both make the conversion process efficient. This division-free algorithm employs the concept of Montgomery multiplication algorithm. There are two variations of Montgomery algorithm proposed, which are algorithms MMA and IMA. The algorithm MMA is to transform the input number into the output presentation of Montgomery algorithm. Algorithm IMA is therefore inverse the computation of Montgomery algorithm to obtain the multiplicand. These two algorithms are in the complexity of O(n), where n is log₂ q_i. q_i is a modulus. The proposed algorithm for converting the residues to a binary integer therefore runs on O(n × log m) times on O(m) processors. There are O(log m) iterations of O(n) complexity. Compared with the traditional conversion algorithm, the advantages of this proposed algorithm are not only in employing simpler operations but also in performing fewer iterations.     

On a relaxed maximally disjoint path pair problem: a bicriteria approach

In some application areas in telecommunication and transportation networks, there are problems requiring the determination of pairs of paths, aiming at minimizing the number of links, or link groups that they share, and their total cost. In this paper, a new bicriteria algorithm is proposed to deal with this problem. The algorithm is based on ranking pairs of paths by order of the total cost, using an adaptation of a path‐ranking algorithm, after a suitable modification of the network topology. Nondominated solutions are then filtered by means of a dominance test. First, computational experiments are reported in order to assess the efficiency of the algorithm to calculate the whole set of nondominated pairs of paths. Second, we present computational results focused on the nondominated solutions close to the maximal disjoint pair (i.e., quasi‐disjoint pairs only, for a predefined admissible relaxation value) because in some application problems, such as shared risk link group pairs of paths, only those solutions have practical relevance.     

Transitive node similarity: predicting and recommending links in signed social networks

Online social networks (OSNs) like Facebook, Myspace, and Hi5 have become popular, because they allow users to easily share content. OSNs recommend new friends to registered users based on local features of the graph (i.e., based on the number of common friends that two users share). However, OSNs do not exploit the whole structure of the network. Instead, they consider only pathways of maximum length 2 between a user and his candidate friends. On the other hand, there are global approaches, which detect the overall path structure in a network, being computationally prohibitive for huge-size social networks. In this paper, we define a basic node similarity measure that captures effectively local graph features (i.e., by measuring proximity between nodes). We exploit global graph features (i.e., by weighting paths that connect two nodes) introducing transitive node similarity. We also derive variants of our method that apply to different types of networks (directed/undirected and signed/unsigned). We perform extensive experimental comparison of the proposed method against existing recommendation algorithms using synthetic and real data sets (Facebook, Hi5 and Epinions). Our experimental results show that our FriendTNS algorithm outperforms other approaches in terms of accuracy and it is also time efficient. Finally, we show that a significant accuracy improvement can be gained by using information about both positive and negative edges.     

一个基于Web访问路径聚类的智能推荐系统

提出了一个基于Web用户访问路径聚类的智能推荐系统．系统使用基于代理技术的结构，由离线的数据预处理和基于用户访问路径的URL聚类以及在线推荐引擎两部分组成．提出了一个基于用户浏览兴趣的推荐规则集生成算法，在度量用户浏览兴趣时综合考虑了用户浏览时间和对该页面的访问次数．提出了一个基于推荐规则集和站点URL路径长度的URL推荐算法．实验表明，该算法比使用基于关联规则和基于用户事务的推荐算法的精确性有较大幅度的提高．     

Efficient algorithms for single- and two-layer linear placement of parallel graphs

This paper outlines an algorithm for optimum linear ordering (OLO) of a weighted parallel graph with O(n log k) worst-case time complexity, and O(n + k log(n/k) log k) expected-case time complexity, where n is the total number of nodes and k is the number of chains in the parallel graph. Next, the two-layer OLO problem is considered, where the goal is to place the nodes linearly in two routing layers minimizing the total wire length. The two-layer problem is shown to subsume the maxcut problem and a befitting heuristic algorithm is proposed. Experimental results on randomly generated samples show that the heuristic algorithm runs very fast and outputs optimum solutions in more than 90% instances.     

Minimal fault diameter for highly resilient product networks

We present a number of results related to the fault tolerance of Cartesian product networks. We start by presenting a method for building containers (i.e., sets of node-disjoint paths) between any two nodes of a product network based on given containers for the factor networks. Then, we show that the best achievable fault diameter (i.e., diameter under maximum fault conditions), under reasonable network regularity and connectivity conditions, is equal to the fault-free diameter plus one. The concept of high fault resilience is then defined. We then prove that if each factor network is highly resilient, then their Cartesian product has minimal fault diameter. We derive from these results that Cartesian products of several popular networks are highly resilient and have minimal fault diameter equal to diameter plus one. These results spare future efforts that would be needed to individually determine the fault diameter of such networks as has been the practice with previously studied networks.     

On optimal monitor placement for localizing node failures via network tomography

We investigate the problem of placing monitors to localize node failures in a communication network from binary states (normal/failed) of end-to-end paths, under the assumption that a path is in normal state if and only if it contains no failed nodes. To uniquely localize failed nodes, the measurement paths must show different symptoms (path states) under different failure events. Our goal is to deploy the minimum set of monitors to satisfy this condition for a given probing mechanism. We consider three families of probing mechanisms, according to whether measurement paths are (i) arbitrarily controllable, (ii) controllable but cycle-free, or (iii) uncontrollable (i.e., determined by the default routing protocol). We first establish theoretical conditions that characterize network-wide failure identifiability through a per-node identifiability measure that can be efficiently evaluated for the above three probing mechanisms. Leveraging these results, we develop a generic monitor placement algorithm, applicable under any probing mechanism, that incrementally selects monitors to optimize the per-node measure. The proposed algorithm is shown to be optimal for probing mechanism (i), and provides upper and lower bounds on the minimum number of monitors required by the other probing mechanisms. In the special case of single-node failures, we develop an improved monitor placement algorithm that is optimal for probing mechanism (ii) and has linear time complexity. Using these algorithms, we study the impact of the probing mechanism on the number of monitors required for uniquely localizing node failures. Our results based on real network topologies show that although more complicated to implement, probing mechanisms that allow monitors to control measurement paths substantially reduce the required number of monitors.     

Minimal fully adaptive wormhole routing on hypercubes

Wormhole routing is an advanced switching technique used in new generation multicomputers. Since such a machine may suffer serious performance degradation under heavy or uneven traffic load, an adaptive routing method is particularly called upon. In minimal fully adaptive routing, the paths between any source and destination pair to be used are exactly all the shortest paths. We propose in this paper a minimal fully adaptive routing algorithm for n-dimensional hypercube with (n+1)/2 virtual channels per physical channel.     

基于二分图完善匹配的布尔匹配算法

提出了一种改进的基于二分图完善匹配的布尔匹配算法。该算法通过把布尔变量之间的匹配问题转换为二分图的完善匹配问题,避免了原算法中因乘积项过多而导致计算时间过长的缺点。对MCNC标准测试电路的实验结果表明;与原算法相比,改进后的算法可以减少21％左右的计算时间。同时,文中提出了布尔变量强匹配的概念,它是对传统布尔匹配概念的引申。     

Ant-based survivable routing in dynamic WDM networks with shared backup paths

In this paper, we consider the problem of survivable routing in dynamic WDM networks with single link failure model. Our work mainly concerns in how to dynamically determine a protection cycle (i.e., two link-disjoint paths between a node pair) to establish a dependable lightpath with backup paths sharing. This problem is identified as NP-complete, thus a heuristic for finding near optimal solution with reasonable computation time is usually preferred. Inspired from the principle of ant colony optimization, we propose in this paper an ant-based mobile agents algorithm for this problem with improved blocking performance. To enable the new ant-based algorithm, we propose to use on each network node both a routing table that contains a set of feasible protection cycles between source destination nodes and also a pheromone table for mobile agents. By keeping a suitable number of mobile agents in a network to continually and proactively update the routing tables based on the current network congestion state, the routing solution of a connection request can be obtained with a reasonable computation time. Extensive simulation results upon the ns-2 network simulator and two typical network topologies show that our new algorithm can achieve a significantly lower blocking probability than the promising algorithm for dynamic lightpath protection proposed in [11] with a comparable computation complexity.     

Pushing a Disk Using Compliance

This paper addresses the problem of maneuvering an object by pushing it through an environment with obstacles. Instead of only pushing the object through open areas, we also allow it to use compliance, e.g., allowing it to slide along obstacle boundaries. Using compliance has a number of advantages: it extends the number of situations in which a manipulation plan can be found, it allows for simpler (i.e., less complicated) paths in many cases, and it often helps solving narrow-passage problems. Here, we present an approach based on rapidly-exploring random trees. Our approach yields paths through the open space, but also exploits the power of compliance.     

A systolic algorithm for hidden surface removal

With the advent of VLSI it has become possible to map parallel algorithms for compute-bound problems directly on silicon. Systolic architecture is very good candidate for VLSI implementation because of its regular and simple design, and regular communication pattern. In this paper, a systolic algorithm and corresponding systolic architecture, a linear systolic array, for the scanline-based hidden surface removal problem in three-dimensional computer graphics have been proposed. The algorithm is based on the concept of sample spans or intervals. The worst case time taken by the algorithm is O(n), n being the number of segments in a scanline. The time taken by the algorithm for a given scene depends on the scene itself, and on an average considerable improvement over the worst case behaviour is expected. A pipeline scheme for handling the I/O process has also been proposed which is suitable for VLSI implementation of the algorithm.