41930759
Embedding Hierarchical Hypercube Networks into the Hypercube
The embedding of one interconnection network into another is a very important issue in the design and analysis of parallel algorithms. Through such embeddings, the algorithms originally developed for one architecture can be directly mapped to another architecture. This paper describes a new embedding method, based on matrix transformations, for optimally embedding hierarchical hypercube networks (HHNs) into the hypercube (binary n-cube). Thus, this embedding method has practical importance in enhancing the capabilities and extending the usefulness of the hypercube, since hierarchical hypercube networks have proven to be very cost-effective for a wide range of applications.
17543628
Efficient Implementation of the BSP/CGM Parallel Vertex Cover FPT Algorithm
In many applications NP-complete problems need to be solved exactly. One promising method to treat some intractable problems is by considering the so-called Parameterized Complexity that divides the problem input into a main part and a parameter. The main part of the input contributes polynomially on the total complexity of the problem, while the parameter is responsible for the combinatorial explosion. We consider the parallel FPT algorithm of Cheetham et al. to solve the k-Vertex Cover problem, using the CGM model. Our contribution is to present a refined and improved implementation. In our parallel experiments, we obtained better results and obtained smaller cover sizes for some input data. The key idea for these results was the choice of good data structures and use of the backtracking technique. We used 5 graphs that represent conflict graphs of amino acids, the same graphs used also by Cheetham et al. in their experiments. For two of these graphs, the times we obtained were approximately 115 times better, for one of them 16 times better, and, for the remaining graphs, the obtained times were slightly better. We must also emphasize that we used a computational environment that is inferior than that used in the experiments of Cheetham et al.. Furthermore, for three graphs, we obtained smaller sizes for the cover.
45259546
Efficient Parallel Graph Algorithms For Coarse Grained Multicomputers and BSP
In this paper, we present deterministic parallel algorithms for the coarse grained multicomputer (CGM) and bulk-synchronous parallel computer (BSP) models which solve the following well known graph problems: (1) list ranking, (2) Euler tour construction, (3) computing the connected components and spanning forest, (4) lowest common ancestor preprocessing, (5) tree contraction and expression tree evaluation, (6) computing an ear decomposition or open ear decomposition, (7) 2-edge connectivity and biconnectivity (testing and component computation), and (8) cordai graph recognition (finding a perfect elimination ordering). The algorithms for Problems 1–7 require O(log p) communication rounds and linear sequential work per round. Our results for Problems 1 and 2 hold for arbitrary ratios \(\frac{n}{p}\), i.e. they are fully scalable, and for Problems 3–8 it is assumed that \(\frac{n}{p} \geqslant p^ \in ,{\mathbf{ }} \in {\mathbf{ }} > 0\), which is true for all commercially available multiprocessors. We view the algorithms presented as an important step towards the final goal of O(1) communication rounds. Note that, the number of communication rounds obtained in this paper is independent of n and grows only very slowly with respect to p. Hence, for most practical purposes, the number of communication rounds can be considered as constant. The result for Problem 1 is a considerable improvement over those previously reported. The algorithms for Problems 2–7 are the first practically relevant deterministic parallel algorithms for these problems to be used for commercially available coarse grained parallel machines.
52830861
A Coarse-Grained Parallel Algorithm for Maximal Cliques in Circle Graphs
We present a parallel algorithm for generating the maximal cliques of a circle graph with n vertices and m edges. We consider the Coarse-Grained Multicomputer Model (CGM) and show that the proposed algorithm requires O(log p) communication rounds, where p is the number of processors, independent of n. The main contribution is the use of a new technique based on the unrestricted depth search for the design of CGM algorithms.
14651264
Computing Maximum Subsequence in Parallel
The maximum subsequence problem finds the contiguous subsequence of n real numbers with the highest sum. This is an important problem that arises in several contexts in Computational Biology in the analysis of DNA or protein sequences. The maximum subsequence problem of n given scores can be solved sequentially in O(n) time. In this paper we present an efficient BSP/CGM parallel algorithm that requires a constant number of communication rounds. In the proposed algorithm, the input is partitioned equally among the processors and the sequence stored on each processor is reduced to only five numbers. This reduction is crucial as it allows all the resulting values to be concentrated on a single processor which runs an adaptation of the sequential algorithm to obtain the result. The amount of data transmitted is 5p where p is the number of processors, thus independent of the input size n. The good performance of the parallel algorithm is confirmed by experimental results run on a 64-node Beowulf parallel computer, giving almost linear speedup. Topic of interest: Algorithms and Software Tools for Computational Molecular Biology
13919002
Efficient embeddings into the hypercube using matrix transformations
The embedding of one interconnection network into another is a very important issue in the design and analysis of parallel algorithms. Through such embedding the algorithms originally developed for one architecture can be directly mapped to another architecture. This paper describes novel methods, based on matrix transformations, for e~ciently embedding different networks into the hypercube (binary n-cube). First, we use this method to embed r-ary m-cubes into a binary n-cube of the same size with dilation 1. While our method has the same dilation as traditional methods using rejlected Gray code, it has the additional property of making the layout of the binary n-cube more suitable for divide-and-conquer algorithms. Second, we use our matrix transformation method to optimally embed hierarchical interconnection networks into the binary n-cube which we would not achieve using rejlected Gray code embedding. Thus, this embedding method has signi$cant practical importance in enhancing the capabilities of the hypercube..
17783880
TCUAP: A Novel Approach of Text Clustering Using Asymmetric Proximity
Text documents have sparse data spaces and current existing methods of text clustering use symmetry proximity to measure the correlation of documents. In this paper, we propose a novel approach to strengthen the discriminative feature of document objects, which uses asymmetric proximity for text clustering. We present a measure of asymmetric proximity between documents and between clusters. TCUAP is an agglomerative hierarchical clustering algorithm and carries on the clustering analysis by strong components of sparse matrix. The experimental evaluation on textual data sets demonstrates the validity and efficiency of our approach. The result shows that the measure of asymmetric proximity possesses higher accuracy than that of symmetry proximity.
6926758
Semantic Correlation Network Based Text Clustering
Text documents have sparse data spaces, and nearest neighbors may belong to different classes when using current existing proximity measures to describe the correlation of documents. In this paper, we propose an asymmetric similarity measure to strengthen the discriminative feature of document objects. We construct a semantic correlation network by asymmetric similarity between documents and conjecture the power law feature of the connections distributions. Hub points which exist in semantic correlation network are classified by an agglomerative hierarchical clustering approach named SCN. Both objects similarity and neighbors similarity are considered in the definition of hub points proximity. Finally, we assign the rest text objects to their nearest hub points. The experimental evaluation on textual data sets demonstrates the validity and efficiency of SCN. The comparison with other clustering algorithms shows the superiority of our approach.