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.
17819894
Bus-Based Parallel Computers: A Viable Way for Massive Parallelism
In most distributed memory MIMD multiprocessors, processors are connected by a point-to-point interconnection network. Since interprocessor communication frequently constitutes serious bottlenecks, several architectures were proposed that enhance point-to-point topologies with the help of multiple bus systems so as to improve the communication efficiency. In this paper we study global communication on parallel architectures where the communication means are constituted solely by busses. We focus on the hyperpath and the hypergrid architectures, which are the bus-based versions of the well used point-to-point linear and grid interconnection networks. Using (hyper) graph theoretic concepts in order to model inter-processor communication in such networks, we developed a new tool called simplification in order to give extremely efficient algorithms for gossiping (all-to-all or total exchange communications).
2233122
New Techniques for Cycle Shrinking
Several loop transformations techniques have been designed to extract parallelism from nested loop structures. We first review two important approaches, known as Generalized Cycle Shrinking presented by Shang, O'Keefe and Fortes and the Index Shift Method introduced by Liu, Ho and Sheu. The main result of the paper is a new methodology that permits to combine cycle shrinking techniques with the index shift method. We present a new optimization method that produces the best scheduling vector, and we show that we can outperform previous results by an arbitrary speedup factor.
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..
17321479
Achieving optimality for gate matrix layout and PLA folding: a graph theoretic approach
Abstract We present O(n3) heuristic algorithms for multiple/ simple PLA folding, which also apply to the matrix layout problem. Our heuristic is based on a new approach, where both problems are shown to be composed by a permutation step followed by a compaction step. Therefore we are able to show that the exponential complexity of the problem stems from the permutation step—where a good configuration is searched—, since the compaction step—where the actual folding takes place—is optimally solved in polynomial time. We discuss bounds on the distance of the obtained solution to the optimal and give sufficient conditions for the solution to be optimal. Verification of the sufficient conditions constitutes part of the proposed algorithms, and is in fact used to construct the heuristic solution. An example showing the multiple folding of a 58 × 19 PLA produced by the proposed algorithm is presented.
11500592
BSP/CGM Algorithms for Maximum Subsequence and Maximum Subarray
The maximum subsequence problem finds the contiguous subsequence of n real numbers with the highest sum. This problem appears in the analysis of DNA or protein sequences. It can be solved sequentially in O(n) time. In the 2-D version, given an n × n array A, the maximum subarray of A is the contiguous subarray that has the maximum sum. The sequential algorithm for the maximum subarray problem takes O(n 3) time. We present efficient BSP/CGM parallel algorithms that require a constant number of communication rounds for both problems. In the first algorithm, the sequence stored on each processor is reduced to only five numbers, so that the resulting values can be concentrated on a single processor which runs an adaptation of the sequential algorithm to obtain the result. The parallel algorithm requires O(n/p) computing time. In the second algorithm, the input array is partitioned equally among the processors and we first reduce each subarray to a sequence, and then apply the first algorithm to solve it. The parallel algorithm takes O(n 3/p) computing time. The good performance of the parallel algorithms is confirmed by experimental results run on a 64-node Beowulf parallel computer.
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.
2193712
Similarity Joins of Text with Incomplete Information Formats
Similarity join over text is important in text retrieval and query. Due to the incomplete formats of information representation, such as abbreviation and short word, similarity joins should address an asymmetric feature that these incomplete formats may contain only partial information of their original representation. Current approaches, including cosine similarity with q-grams, can hardly deal with the asymmetric feature of similarity between words and their incomplete formats. In order to find this type of incomplete format information with asymmetric features, we develop a new similarity join algorithm, namely IJoin. A novel matching scheme is proposed to identify the overlap between two entities with incomplete formats. Other than q-grams, we reconnect the sequence of words in a string to reserve the abbreviated information. Based on the asymmetric features of similar entities with incomplete formats, we adopt a new similarity function. Furthermore, an efficient algorithm is implemented by using the join operation in SQL, which reduces pairs of tuples in similarity comparison. The experimental evaluation demonstrates the effectiveness and the efficiency of our approach.