Computing a distance map (distance transform) is an operation that converts a two-dimensional (2-D) image consisting of black and white pixels to an image where each pixel has a value or a pair of coordinates that represents the distance to or location of the nearest black pixel. It is a basic operation in image processing and computer vision fields, and is used for expanding, shrinking, thinning, segmentation, clustering, computing shape, object reconstruction, etc. This paper examines the possibility of implementing the problem of finding a distance map for an image efficiently using an optical bus. The computational model considered is the linear array with a reconfigurable pipelined bus system (LARPBS), which has been introduced recently based on current electronic and optical technologies. It is shown that the problem for an image can be implemented in (log log log ) bus cycles deterministically or in (log ) bus cycles with high probability on an LARPBS with processors. By high probability, we mean a probability of (1 ) for any constant 1. We also show that the problem can be solved in (log log ) bus cycles deterministically or in (1) bus cycles with high probability on an LARPBS with 3 processors. Scalability of the algorithms is also discussed briefly. The same problem can be solved using an LARPBS of processors in (( ) log log log ) time deterministically or in (( ) log ) time with high probability for any practical machine size of . For processor arrays with practical sizes, a bus cycle is roughly the time of an arithmetic operation. Hence, the algorithm compares favorably to the best known parallel algorithms for the same problem in the literature.

Abstract. Hierarchical agglomerative clustering (HAC) is a common clustering method that outputs a dendrogram showing all N levels of agglomerations where N is the number of objects in the data set. High time and memory complexities are some of the major bottlenecks in its application to real-world problems. In the literature parallel algorithms are proposed to overcome these limitations. But, as this paper shows, existing parallel HAC algorithms are inefficient due to ineffective partitioning of the data. We first show how HAC follows a rule where most agglomerations have very small dissimilarity and only a small portion towards the end have large dissimilarity. Partially overlapping partitioning (POP) exploits this principle and obtains efficient yet accurate HAC algorithms. The total number of dissimilarities is reduced by a factor close to the number of cells in the partition. We present pPOP, the parallel version of POP, that is implemented on a shared memory multiprocessor architecture. Extensive theoretical analysis and experimental results are presented and show that pPOP gives close to linear speedup and outperforms the existing parallel algorithms significantly both in CPU time and memory requirements.

The computation model on which the algorithms are developed is the reconfigurable array of processors with wider bus networks (abbreviated to RAPWBN). The main difference between the RAPWBN model and other existing reconfigurable parallel processing systems is that the bus width of each network is bounded within the range e#.