# Convexity Problems on Meshes with Multiple Broadcasting

@article{Bhagavathi1995ConvexityPO, title={Convexity Problems on Meshes with Multiple Broadcasting}, author={Dharmavani Bhagavathi and Stephan Olariu and James L. Schwing and W. Shen and Larry Wilson and Jingyuan Zhang}, journal={J. Parallel Distributed Comput.}, year={1995}, volume={27}, pages={142-156} }

Abstract Our contribution is twofold. First, we show that Ω(log n) is a time lower bound on the CREW-PRAM and the mesh with multiple broadcasting for the tasks of computing the perimeter, the area, the diameter, the width, the modality, the smallest-area enclosing rectangle, and the largest-area inscribed triangle of a convex n-gon. We show that the same time lower bound holds for the tasks of detecting whether a convex n-gon lies inside another as well as for computing the maximum distance…

## 15 Citations

### Time-Optimal Nearest-Neighbor Computations on Enhanced Meshes

- Computer ScienceJ. Parallel Distributed Comput.
- 1996

This work proposes time-optimal algorithms for constructing the Euclidian Minimum Spanning Tree, the Relative Neighborhood Graph, as well as the Symmetric Further Neighbor Graph of an n-vertex unimodal polygon on meshes with multiple broadcasting.

### Time-optimal visibility-related algorithms of meshes with multiple broadcasting

- Computer ScienceProceedings of 8th International Parallel Processing Symposium
- 1994

The main contribution of this work is to provide time-optimal solutions to this problem for two classes of objects, namely disks and iso-oriented rectangles in the plane with the first instance of time-Optimal solutions for these problems on this architecture.

### A time-optimal solution to planar point location in ordered functional domains, with applications

- Computer ScienceProceedings Second International Symposium on Parallel Architectures, Algorithms, and Networks (I-SPAN'96)
- 1996

This work shows that in a family C of continuous functions stored, in discretized form, one function per row in a mesh with multiple broadcasting of size, an arbitrary collection of m, point location queries can be answered in /spl Theta/(m//spl radic/n) time.

### Time-Optimal Proximity Graph Computations on Enhanced Meshes

- Computer ScienceJ. Parallel Distributed Comput.
- 1996

This work proposes time-optimal algorithms for constructing the Euclidian minimum spanning tree, the all-nearest neighbor graph, the relative neighborhood graph, and the symmetric farthest neighbor graph of ann-vertex unimodal polygon and shows that these algorithms run on meshes enhanced with row and column buses.

### An efficient VLSI architecture for digital geometry

- Computer ScienceProceedings of IEEE International Conference on Application Specific Array Processors (ASSAP'94)
- 1994

A number of fundamental digital geometry tasks can be solved fast on a novel VLSI architecture obtained by augmenting the mesh with multiple broadcast architecture (MMB) with precharged 1-bit row and column buses (MHB).

### The Mesh with Hybrid Buses: An Efficient Parallel Architecture for Digital Geometry

- Computer ScienceIEEE Trans. Parallel Distributed Syst.
- 1999

An efficient VLSI architecture obtained by augmenting the Mesh with Multiple Broadcasting with precharged 1-bit row and column buses is proposed and it is shown that the MHB is extremely well-suited for solving an entire slew of digital geometry tasks.

### A bandwidth-efficient implementation of mesh with multiple broadcasting

- Computer ScienceProceedings of the 1999 International Conference on Parallel Processing
- 1999

A wormhole router design equipped with the virtual bus functions is introduced, the connections among these routers are described, and various virtual bus transactions are presented, proving the effectiveness of thevirtual bus by showing that a representative semigroup computation can be solved very efficiently on it.

### Time- and VLSI-Optimal Sorting on Enhanced Meshes

- Computer Science, PhysicsIEEE Trans. Parallel Distributed Syst.
- 1998

This work addresses the problem of sorting on mesh connected computers enhanced by endowing each row and each column with its own dedicated high-speed bus with the first known adaptive time- and VLSI-optimal sorting algorithm for meshes with multiple broadcasting.

### Square Meshes are not Optimal for Convex Hull Computation

- Computer Science1993 International Conference on Parallel Processing - ICPP'93
- 1993

This paper is to provide yet another example of a fundamental problem for which rectangular meshes with multiple broadcasting yield faster algorithms than their square counterparts.

## References

SHOWING 1-10 OF 62 REFERENCES

### Time-optimal proximity algorithms on meshes with multiple broadcasting

- Computer ScienceProceedings of 8th International Parallel Processing Symposium
- 1994

The all-nearest neighbor problem (ANN) is stated as follows: given a set of points in the plane, determine for every point in S, a point that lies closest to it, even if the points are the vertices of a convex polygon.

### Time-Optimal Nearest-Neighbor Computations on Enhanced Meshes

- Computer ScienceJ. Parallel Distributed Comput.
- 1996

This work proposes time-optimal algorithms for constructing the Euclidian Minimum Spanning Tree, the Relative Neighborhood Graph, as well as the Symmetric Further Neighbor Graph of an n-vertex unimodal polygon on meshes with multiple broadcasting.

### A Time-Optimal All-Nearest Neighbor Algorithm on Meshes with Multiple Broadcasting

- Computer Science
- 1993

This paper establishes an ( )(log n) time lower bound for the task of solving an arbitrary n-point instance of the ANN problem and shows that the bound is tight by exhibiting an algorithm solving the problem in O(logn) time on a mesh with multiple broadcasting of size n x n.

### Square meshes are not always optimal

- Computer ScienceSPAA '89
- 1989

It is shown that in the presence of multiple buses, a skewed configuration may perform better than a square configuration for certain computational tasks.

### Efficient Medain Finding and Its Application to Two-Variable Linear Programming on Mesh-Connected Computers with Multiple Broadcasting

- Computer ScienceJ. Parallel Distributed Comput.
- 1992

### Time-optimal sorting and applications on n*n enhanced meshes

- Computer ScienceCompEuro 1992 Proceedings Computer Systems and Software Engineering
- 1992

Time-optimal sorting and convex hull algorithms are proposed for two classes of enhanced meshes, the mesh with multiple broadcasting and the reconfigurable mesh. The authors show that the fundamental…

### Selection on rectangular meshes with multiple broadcasting

- Computer ScienceBIT
- 1993

This paper presents a fast selection algorithm which runs inO(n1/8 logn) time on a mesh with multiple broadcasting of sizen3/8 ×n5/8 and shows that, just like semigroup computations, selection can be done much faster on a suitably chosen rectangular mesh than on square meshes.

### A Fast Selection Algorithm for Meshes with Multiple Broadcasting

- Computer ScienceIEEE Trans. Parallel Distributed Syst.
- 1994

This work proposes an algorithm design methodology that leads to a selection algorithm that runs in O(n/sup 1/8/(log n)/sup 3/4/)) time on a mesh with multiple broadcasting, showing that selection can be done faster on suitably chosen rectangular meshes than on square meshes.

### A Unifying Look at Semigroup Computations on Meshes with Multiple Broadcasting

- Computer Science, MathematicsParallel Process. Lett.
- 1993

The first lower bound and the first time-optimal algorithm which apply to the entire range of m (2 ≤ m ≤ n) are presented and the bound is tight by designing an algorithm whose running time matches the lower bound.