Robert Cypher

Algorithms for image component labeling on SIMD mesh-connected computers

Abstract : Two new parallel algorithms are presented for the problem of labeling the connected components of a binary image, which is also known as the connected ones problem. The machine model is an SIMD two-dimensional mesh connected computer consisting of an N x N array of processing elements, each containing a single pixel of an N x N image. Both new algorithms use a shrinking operation defined by Levialdi and have time complexities of O(N log N) bit operations, which makes them the fastest local algorithms for the problem. Compared with other approaches having similar or better time complexities, this local approach dramatically simplifies the algorithms and reduces the constants of proportionality by nearly two orders of magnitude, thus making them the first practical algorithms for the problem. The two algorithms differ in the amount of memory required per processing element; the first uses O(N) bits while the second employs a novel compression scheme to reduce the requirement to O(log N) bits.

Wildcard dimensions, coding theory and fault-tolerant meshes and hypercubes

Hypercubes, meshes and tori are well known interconnection networks for parallel computers. The sets of edges in those graphs can be partitioned to dimensions. It is well known that the hypercube can be extended by adding a wildcard dimension resulting in a folded hypercube that has better fault-tolerant and communication capabilities. First the authors prove that the folded hypercube is optimal in the sense that only a single wildcard dimension can be added to the hypercube. They then investigate the idea of adding wildcard dimensions to d-dimensional meshes and tori. Using techniques from error correcting codes they construct d-dimensional meshes and tori with wildcard dimensions. Finally, they show how these constructions can be used to tolerate edge and node faults in mesh and torus networks.

An EREW PRAM algorithm for image component labeling

An important midlevel task for computer vision is addressed. The problem consists of labeling connected components in N/sup 1/2/*N/sup 2/2/ binary images. This task can be solved with parallel computers by using a simple and novel algorithm. The parallel computing model used is a synchronous fine-grained shared-memory model where only one processor can read from or write to the same memory location at a given time. This model is known as the exclusive-read exclusive-write parallel RAM (EREW PRAM). Using this model, the algorithm presented has O(log N) complexity. The algorithm can run on parallel machines other than the EREW PRAM. In particular, it offers an optimal image component labeling algorithm for mesh-connected computers. >

On the construction of fault-tolerant Cube-Connected Cycles networks

Abstract This paper presents a new approach to tolerating edge faults and node faults in (CCC) networks of Cube-Connected Cycles in a worst-case scenario. Our constructions of fault-tolerant CCC networks are obtained by adding extra edges to the CCC. The main objective is to reduce the cost of the fault-tolerant network by minimizing the degree of the network. Specifically, we have two main results. (i) We have created a fault tolerant CCC that can tolerate any single fault, either a node fault or an edge fault. When the dimension of the CCC is odd, the degree of the fault tolerant graph is 4. In the even case, there is a single node per cycle that is of degree 5 and the rest are of degree 4. (ii) We have created a fault-tolerant CCC, where every node has degree y + 2, which can tolerate any 2 y − 1 cube-edge faults. Our constructions are extremely efficient for the case of edge faults-they result in healthy CCC networks that utilize all of the processors.

Embedding cube-connected cycles graphs into faulty hypercubes

We consider the problem of embedding a cube-connected cycles graph (CCC) into a hypercube with edge faults. Our main result is an algorithm that, given a list of faulty edges, computes an embedding of the CCC that spans all of the nodes and avoids all of the faulty edges. The algorithm has optimal running time and tolerates the maximum number of faults (in a worst-case setting). Because ascend-descend algorithms can be implemented efficiently on a CCC, this embedding enables the implementation of ascend-descend algorithms, such as bitonic sort, on hypercubes with edge faults. We also present a number of related results, including an algorithm for embedding a CCC into a hypercube with edge and node faults and an algorithm for embedding a spanning torus into a hypercube with edge faults. >

A lower bound on the size of shellsort sorting networks

Shellsort is a sorting algorithm that is based on a set of parameters called increments. Shellsort has been used both as a sequential sorting algorithm and as a sorting network. The central result of this paper is that all Shellsort sorting networks based on monotonically decreasing increments require

The Hough transform has O(N) complexity on N×-N mesh connected computers

Omega (Nlog ^2 {N / {log log N}})

Requirements for Deadlock-Free, Adaptive PacketRouting

comparators. Previously, only the trivial

Cubesort: An Optimal Sorting Algorithm for Feasible Parallel Computers

Omega (Nlog N)

Apex: two architectures for generating parametric curves and surfaces

bound was known for this class of networks. The lower bound obtained in this paper nearly matches the upper bound of