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In this paper, we study parallel branch and bound on fine grained hypercube multiprocessors. Each processor in a fine grained system has only a very small amount of memory available. Therefore, current parallel branch and bound methods for coarse grained systems (⩽ 1000 nodes) cannot be applied, since all these methods assume that every processor stores the path from the node it is currently processing back to the node where the process was created (the back-up path). Furthermore, the much larger number of processors available in a fine grained system makes it imperative that global information (e.g. the current best solution) is continuously available at every processor; otherwise the amount of unnecessary search would become intolerable. We describe an efficient branch-and-bound algorithm for fine grained hypercube multiprocessors. Our method uses a global scheme where all processors collectively store all back-up paths such that each processor needs to store only a constant amount of information. At each iteration of the algorithm, all current nodes may decide whether they need to create new children, be pruned, or remain unchanged. We describe an algorithm that, based on these decisions, updates the current back-up paths and distributes global information in O(log m) steps, where m is the current number of nodes. This method also includes dynamic allocation of search processes to processors and provides optimal load balancing. Even if very drastic changes in the set of current nodes occur, our load balancing mechanism does not suffer any slow down.

We present parallel computational geometry algorithms that are scalable, architecture independent, easy to implement, and have, with high probability, an optimal time complexity for uniformly distributed random input data. Our methods apply to multicomputers with arbitrary interconnection network or bus system. The following problems are studied in this paper: (1) lower envelope of line segments, (2) visibility of parallelepipeds, (3) convex hull, (4) maximal elements, (5) Voronoi diagram, (6) all-nearest neighbors, (7) largest empty circle, and (8) largest empty hyperrectangle. Problems 2-8 are studied for d-dimensional space, d=O(1). We implemented and tested the lower envelope algorithm and convex hull algorithm (for d=3 and d=4) on a CM5. The results indicate that our methods are of considerable practical relevance. >

In this paper we study the parallel implementation of a traditional frame based knowledge representation system for a general purpose massively parallel hypercube architecture (such as the Connection Machine CM-2). We show that, using a widely available parallel system (instead of a special purpose architecture), it is possible to provide multiple users with efficient shared access to a large scale knowledge-base. Parallel algorithms are presented for answering multiple inference, assert and retract queries on both single and multiple inheritance hierarchies. In addition to theoretical time complexity analysis, empirical results obtained from extensive testing of a prototype implementation are presented.

In this paper we consider a new form of connectivity in binary images, called k -width connectivity. Two pixels a and b of value “1” are in the same k -width component if and only if there exists a path of width k such that a is one of the k start pixels and b is one of the k end pixels of this path. We present characterizations of the k -width components and show how to determine the k -width components of an n × n image in O(n) and O (log 2 n ) time on a mesh of processors and hypercube, respectively, when the image is stored with one pixel per processor. Our methods use a reduction of the k -width-connectivity problem to the 1-width-connectivity problem. A distributed, space-efficient encoding of the k -width components of small size allows us to represent the solution using O (1) registers per processor. Our hypercube algorithm also implies an algorithm for the shuffle-exchange network.

The authors present a parallel algorithm for solving the next element search problem on a set of line segments, using a BSP like model referred to as the coarse grained multicomputer (CGM). The algorithm requires O(1) communication rounds (h-relations with h=O(n/p)), O((n/p) log n) local computation, and O((n/p) log n) storage per processor. The result implies solutions to the point location, trapezoidal decomposition and polygon triangulation problems. A simplified version for axis parallel segments requires only O(n/p) storage per processor, and they discuss an implementation of this version. As in a previous paper by Develliers and Fabri (1993), their algorithm is based on a distributed implementation of segment trees which are of size O(n log n). The paper improves on the work of Develliers and Fabri which presented a CGM algorithm for the special case of trapezoidal decomposition only and requires O((n/p)*log p*log n) local computation.