Scalable Parallel Computational Geometry for Coarse Grained Multicomputers

Abstract

We study scalable parallel computational geometry algorithms for the coarse grained multicomputer model: p processors solving a problem on n data items, were each processor has O(n/p)≫O(1) local memory and all processors are connected via some arbitrary interconnection network (e.g. mesh, hypercube, fat tree). We present O(Tsequential/p+Ts(n, p)) time scalable parallel algorithms for several computational geometry problems. Ts(n, p) refers to the time of a global sort operation. Our results are independent of the multicomputer’s interconnection network. Their time complexities become optimal when Tsequential/p dominates Ts(n, p) or when Ts(n, p) is optimal. This is the case for several standard architectures, including meshes and hypercubes, and a wide range of ratios n/p that include many of the currently available machine configurations. Our methods also have some important practical advantages: For interprocessor communication, they use only a small fixed number of one global routing operation, global sort, and all other programming is in the sequential domain. Furthermore, our algorithms use only a small number of very large messages, which greatly reduces the overhead for the communication protocol between processors. (Note however, that our time complexities account for the lengths of messages.) Experiments show that our methods are easy to implement and give good timing results.

Fully Scalable Fault-Tolerant Simulations for BSP and CGM

“…In these models the ratio of memory to processors is fairly small (typically Ç´½µ). Recently, bridging models such as BSP [30,31], CGM [7], and LogP [6,18] have been proposed, where the ratio of memory to processors is non-constant. In particular, the BSP model attracted considerable attention and many algorithms for important problems have been designed on this model [12,13,14,8].…”

Accelerating the Requirement Space Exploration through Coarse-Grained Parallel Execution

“…Frank Dehne presented the method [8], described and proofed the time cost of the method, and employed it to solve Hausdorff Voronoi Diagrams problem [9]. CGM has been widely used, and turned out effective.…”

“…A Coarse-Grained Multicomputer model: p processors solving a problem on n data items, each processor has O(n/p) O(1) local memory, and all the processors are connected via some arbitrary interconnection network [8], can be represented as CGM (n, p). In the MIS method, each hyperbox is one data item, thus the key is to assign the hyperboxes to the processors, and keep loadBalanced for each processor.…”

Efficient Implementation of the BSP/CGM Parallel Vertex Cover FPT Algorithm

“…A CGM (Coarse-Grained Multicomputer) [3] consists of p processors connected by some interconnection network. Each processor has local memory of size O(N/p), where N is the problem size.…”