Shi-Nine Yang

An efficient distributed algorithm for minimal connected dominating set problem

The authors propose an efficient distributed algorithm for finding a minimal connected dominating set of an asynchronous communication network. An asynchronous communication network can be modeled by a connected undirected graph G=(V, E) where the nodes correspond to the sites and the edges correspond to bidirectional communication links. No common memory is shared by the sites. Each node receives messages from its neighbors, performs some computation, and sends messages to its neighbors. Thus the distributed algorithms considered here are primarily message driven. Furthermore, each message sent by a node is assumed to be error free and to arrive in sequence to its neighbors after an unpredictable finite delay. The worst case message complexity of the algorithm is O(n/sup 2/), where n is the number of processors of the network.<<ETX>>

A parallel algorithm for finding congruent regions

In this paper, we study the problem for finding all the regions, which are congruent to a testing region R, in an input planar figure F. In a shared memory system with m processors, we propose an el~cient MAX { O(mn), O(n log n)} time parallel algorithm, where n, m are the numbers of edges of F and R, respectively. Furthermore, our algorithm does not require to read from or write into the same memory location simultaneously, hence it can be implemented on an exclusive-read, exclusive-write (EREW) model.

A new linear octree construction by filling algorithms

A novel linear octree construction based on filling the closed voxel-based border is proposed. The algorithm is based on a sweeping strategy. First it is proved that if an octant contains no border voxel then its attribute can be determined by examining the attributes of all its processed neighbors. Then a data structure called active front is used to keep track of the attributes of the corresponding neighbors as the sweeping process is carried out octant by octant. Compared with the existing algorithm, the main advantage of this approach is that it does not require prior blocking information of the boundary voxels. The time complexity of the algorithm is proportional to the ratio of boundary voxels. It is optimal in the sense that all boundary voxels are traversed only once and all octants of the octree are also examined once.<<ETX>>

On mapping Bezier curve and surface subdivision algorithms into a hypercube with geometric adjacency constraint

The authors discuss the Bezier curve and surface generation algorithms on a hypercube computer. They show that the computation structures of Bezier curve and surface generation based on subdivision method can be modeled as binomial trees and extended binomial trees respectively. Properties of binomial trees and extended binomial trees are explored and mappings from these tree structures to hypercubes are discussed. As the spatial coherence plays an important role in computer graphics and geometric algorithms, the authors imposed the geometric adjacency on these mappings and proved that there exist adjacency preserving mappings. Moreover, they show that their mappings are optimal with respect to expansion, dilation and congestion.<<ETX>>

Network partition and its application to distributed selection problem

The authors discuss the network partition and the distributed selection problems for a general tree network. The distributed selection problem is to select the k-th smallest element of a set N of elements distributed among nodes of a point-to-point asynchronous communication network. The distributed algorithms considered are primarily message driven. All the messages have a fixed length, and may carry only a limited amount of information. The authors assume the network is sufficiently reliable so that the messages sent in a link are received error free by the receiver node in first-in-first-out (FIFO) order with finite but totally unpredictable delays. The authors present an improved selection algorithm for general tree networks. Based on the conventional reduction strategy, they introduce a tree partition technique to localize the message passing and therefore to reduce the total message complexity.<<ETX>>

A new 3D-border algorithm by neighbor finding

The authors propose a new algorithm for finding the three-dimensional border of linear octrees stored in a one dimensional array. A simple method is proposed to check whether an octant is a border octant. Then, the border finding procedure can be carried out node by node according to their location code ordering. In order to improve the performance of the algorithm, a new and efficient neighbor finding technique is proposed. The time complexity of the proposed neighbor finding method is analyzed and proved to be O(1) on the average. Compared with the existing border algorithms, the proposed algorithm has the following advantages: (1) no preprocessing is required to arrange the input data according to their grouping factors, (2) the border found is already a sorted sequence of border voxels with no extra sorting required, and (3) the average time complexity is improved from O(N log N) to O(N), where N is the number of nodes in the linear octree.<<ETX>>

A systolic algorithm for extracting regions from a planar graph

In this paper, we describe a systolic algorithm for extracting all of the fundamental regions in a planar graph. It takes O(n) computation time and uses O(n) processing elements, where n is the number of edges of the input planar graph.

Distributed algorithms on edge connectivity problems

Connectivity of a network dictates the routability and survivability of a network. The paper investigates the edge connectivity problems in distributed environments. For a given network or graph G, one can distributively find bridges in the network first then find the 2-edge connected components. Both algorithms proposed, bridge finding and 2-edge connected component identifying, require only O(m) message complexity, where m is the number of edge in G. The paper also shows an efficient distributed 2-edge cutset algorithm that has O(n/sup 2/) message complexity, where n is the number of nodes in G.<<ETX>>

A New Shape Control and Classification for Cubic Bézier Curves

In this paper, a new shape control method called one-point shape control is proposed for cubic Bezier curves. First, we show that a Bezier curve, with given boundary points and tangent directions, can be uniquely determined by a point called the shape point. Then the advantages of this shape control method are discussed and shape classification with respect to the shape point is also studied. Furthermore, by using this one-point shape control method, we introduce a new offset algorithm for Bezier curves. Empirical tests will be given. It shows that our offset algorithm is not only simple and direct but also effective and efficient.

A unidirectional ring partition problem

Let R = (V, E) be a unidirectional ring network where V corresponds to the set of nodes and E corresponds to the set of directed communication links. A partition of R divides R into several disjoint chains. For each partition P, there is associated a communication cost C(P). The optimal ring partition problem is to find a partition P* of R such that C(P*) = minpC(P). In this paper, we first formulate the ring partition problem into a recurrence relation. By solving the recurrence relation, we show that the ring partition can be accomplished distributively in one pass, i.e., the message complexity of our distributed ring partition algorithm is O(|V|), which is optimal.