David Semé

ALL-TO-ALL BROADCASTING ALGORITHMS ON HONEYCOMB NETWORKS AND APPLICATIONS

This paper presents two simple all-to-all broadcasting algorithms on honeycomb mesh. Consider a network with n processors, one has personalized routing strategy at each node and it requires a 3n communication time complexity. This communication time can be reduced to n because the computation time is always assumed to be much lower than the communication time. The other is based on a Hamiltonian path and has a 2n communication time complexity. We show how they can be used to get parallel solutions to a class of problems on honeycomb networks, among others Prefix Sums, Maximal Vectors, Maximal Sum Subsegment, Parenthesis Matching, Decoding Binary Tree, and Sorting. In our knowledge, these all-to-all broadcast algorithms are the only ones so far exhibited on a honeycomb.

A basis for 3-D cellular networks

We propose to extend the standard concept of planar cellular networks into space. Indeed, in cellular networks the trend is to have a smaller cells to meet the growing number of communication services. The smaller the cells, the more important is the third dimension because this model is more efficient. So, it is better to take the height into account. For instance, to create a cellular network in a building, it makes no sense to have a planar cellular network. It would be better to have antennas placed in the three dimensions. This paper presents some explanations about the reason why hexagons tessellation are used in the theory of cellular networks. It describes the 3-D cellular networks used for this work and also discusses the frequency reuse mechanism and channel allocation schemes.

A coarse-grained multicomputer algorithm for the longest common subsequence problem

The paper presents a coarse-grained multicomputer algorithm that solves the Longest Common Subsequence Problem. This algorithm can be implemented in the CGM with P processors in O(N/sup 2//P) in time and O(P) communication steps. It is the first CGM algorithm for this problem. We present also experimental results showing that the CGM algorithm is very efficient.

Time-Efficient Parallel Algorithms for the Longest Common Subsequence and Related Problems

Recently Aklet al. introduced a new model of parallel computation, called broadcasting with selective reduction (BSR), and showed that it is more powerful than any CRCW PRAM and yet requires no more resources for implementation than even EREW PRAM. The model allows constant time solutions to sorting, parallel prefix, and other problems. In this paper, we describe constant time solutions to the longest common subsequence problem and the sequence alignment problem using the BSR model. These are the first constant time solutions to these problems for any model of computation.

A coarse-grained multicomputer algorithm for the longest repeated suffix ending at each point in a word

The paper presents a Coarse-Grained Multicomputer algorithm that solves the problem of finding the longest repeated suffix ending at each point in a word. This algorithm can be implemented in the CGM with p processors in O(N2/P) in time and O(P) communication steps. It is the first CGM algorithm for this problem. We present also experimental results showing that the CGM algorithm is very efficient.

Optimal BSR Solutions to Several Convex Polygon Problems

This paper focuses on BSR (Broadcasting with Selective Reduction) implementation of algorithms solving basic convex polygon problems. More precisely, constant time solutions on a linear number, max(N, M) (where N and M are the number of edges of the two considered polygons), of processors for computing the maximum distance between two convex polygons, finding critical support lines of two convex polygons, computing the diameter, the width of a convex polygon and the vector sum of two convex polygons are described. These solutions are based on the merging slopes technique using one criterion BSR operations.

A constant time parallel detection of repetitions

Recently Akl and al. introduced a new model of parallel computation, called BSR (broadcasting with selective reduction) and showed that it is more powerful than any CRCW PRAM and yet requires no more resources (asymptotically) for implementation than even EREW PRAM [2,3,4]. The model allows constant time solutions to sorting, parallel prefix and other problems. In this paper, we describe constant time solution to the detection of repetitions (with overlapping) problem using the one criterion BSR model. This is the first constant time solution to this problem on any model of computation. If the problem is only to detect the existence of any repetition then n processors suffice, where n is the length of the string. If all repetitions are to be found then

Work-efficient BSR-based parallel algorithms for some fundamental problems in graph theory

n [\frac{n}{2}]

A Coarse-Grained Multicomputer algorithm for the detection of repetitions

processors suffice in our algorithm.

A one-phase parallel algorithm for the sequence alignment problem

This paper presents BSR-parallel algorithms for some problems in fundamental graph theory : transitive closure, connected components, spanning tree, bridges and articulation points of a graph and bipartite graph recognition. There already exist constant time algorithms to solve these problems on a mesh with reconfigurable bus system using O(N4) processors. Here we show that these problems can be solved in constant time using only O(N2) processors on the BSR model (N is the number of vertices of the graph G). Therefore, our algorithms are more work-efficient. These new results suggest that many other problems in graph theory can be solved in constant time using the BSR model.