12034549
On embedding ternary trees into Boolean hypercubes
It is pointed out that the problem of efficiently embedding a k-ary tree into hypercube with k>or=3 has largely remained unsolved, even though optimal embeddings (i.e. embeddings achieving minimum delta , lambda , and in ) of complete and incomplete binary trees into hypercubes have been known for some time. Thus, in their quest for designing efficient embeddings of k-ary trees into hypercube for arbitrary k, the authors present some preliminary results that give efficient embeddings for the situations when k=3, 2/sup p/, 3/sup p/, 2/sup p/*3/sup q/ and p, q>0. The embedding of complete ternary trees and the embedding of complete k-ary trees are considered.<<ETX>>
14459246
On optimal embeddings into incomplete hypercubes
The authors show the embeddings of various types of n-node incomplete binary trees into n-node or (n+1)-node composite hypercubes with dilation of at most 2. They also present lower bound proofs showing optimality of the dilation. They characterize the class of incomplete binary trees which are subgraphs of composite hypercubes. They present dilation 1 embedding of a two-dimensional n-node mesh, where one dimension is a power of two, into its optimal n-node composite hypercube. When neither dimension is a power of two, it is shown that a dilation 1 embedding is not possible; thereby characterizing the class of two-dimensional meshes that can be embedded into composite hypercubes with dilation 1. All two-dimensional meshes are shown to be embeddable with dilation 1 if expansion greater than 1 but less than 2 is allowed. The authors also consider two types of incomplete meshes and their embeddings into their optimal composite hypercubes.<<ETX>>
10426404
Load balanced tree embeddings
Abstract When an n -processor architecture T is embedded into an m -processor architecture H with n > m and every processor of H is assigned at least ⌞n/m⌟ and at most [ n / m ] processors of T , the embedding has a balanced processor load. We present efficient embeddings with a balanced load for the case when both architectures are complete binary trees. We show that T can be embedded into H with a dilation of 1 and congestion of at most min{[ n / m ], 2 log n }. We also consider embeddings that achieve a balanced l/i load; i.e. every processor of H simulates at most [( n + 1)/2 m ] leaves and at most [( n − 1)/2 m ] interior processors of T . We present an embedding that achieves a balanced l/i load, a dilation of 2[log log m ] + 1 and a congestion of O(log n ). We show that every embedding strategy achieving a balanced l/i load must have a dilation of at least 3. We also consider the embedding problem when every edge of T has a weight associated with it.
41859107
Preconditioned Conjugate Gradient Solver for Large Sparse Systems on MPI
35215015
Coarse Grain Preconditioned Conjugate Gradient Solver for Large Sparse Systems
We explore a coarse grain parallel algorithm for the solution of large sparse linear systems with symmetric positive definite matrix, based on a preconditioned conjugate gradient method.
17006088
An Efficient MAP Classifier for Sensornets
The classification phase is computationally intensive and frequently recurs in tracking applications in sensor networks. Most related work uses traditional signal processing classifiers, such as Maximum A Posterior (MAP) classifier. Naive formulations of MAP are not feasible for resource constraint sensornet nodes. In this paper, we study computationally efficient methods for classification. We propose to use one-sided Jacobi iterations for eigen value decomposition of the covariance matrices, the inverse of which are needed in MAP classifier. We show that this technique greatly simplifies the execution of MAP classifier and makes it a feasible and efficient choice for sensornet applications.
8920735
Partition-based decision heuristics for image computation using SAT and BDDs
Methods based on Boolean satisfiability (SAT) typically use a conjunctive normal form (CNF) representation of the Boolean formula, and exploit the structure of the given problem through use of various decision heuristics and implication methods. We propose a new decision heuristic based on separator-set induced partitioning of the underlying CNF graph. It targets those variables whose choice generates clause partitions with disjoint variable supports. This can potentially improve performance of SAT applications by decomposing the problem dynamically within the search. In the context of a recently proposed image computation method combining SAT and BDDs, this results in simpler BDD subproblems. We provide algorithms for CNF partitioning - one based on a clause-variable dependency matrix, and another based on standard hypergraph partitioning techniques, and also for the use of partitioning information in decision heuristics for SAT. The effectiveness of the proposed partition-based heuristic is shown with practical results for reachability analysis of benchmark sequential circuits.
19362396
Finding Largest Common Embeddable Subtrees
We consider the problem of determining the largest tree embeddable in two labeled trees T and T′, where the embedding relation is one of subgraph isomorphism or topological embedding. This problem is a generalization of classical tree pattern matching where the problem is to determine if one labeled tree is isomorphic to a subgraph of another. In this paper, we present a general framework for the variations on the problem, for the two embedding relations and for different assumptions about labeling of nodes in the trees. Our general paradigm provides sequential and parallel algorithms for the various subproblems, many of which have no other known solutions.
2367227
Parallel Algorithms For Vehicle Routing Problems
Vehicle routing problems involve the navigation of one or more vehicles through a network of locations. Locations have associated handling times as well as time windows during which they are active. The arcs connecting locations have time costs associated with them. In this paper, we consider two different problems in single vehicle routing. The first is to find least time cost routes between all pairs of nodes in a network for navigating vehicles; we call this the all pairs routing problem. We show that there is an O(log3 n) time parallel algorithm using a polynomial number of processors for this problem on a CREW PRAM. We next consider the problem in which a vehicle services all locations in a network. Here, locations can be passed through at any time but only serviced during their time window. The general problem is -complete under even fairly stringent restrictions but polynomial algorithms have been developed for some special cases. In particular, when the network is a line, there is no time cost in servicing a location, and all time windows are unbounded at either their lower or upper end, O(n2) algorithms have been developed. We show that under the same conditions, we can reduce this problem to the all pairs routing problem and therefore obtain an O(log3 n) time parallel algorithm on a CREW PRAM.
854648
Approximation algorithms for low-distortion embeddings into low-dimensional spaces
We present several approximation algorithms for the problem of embedding metric spaces into a line, and into the two-dimensional plane. Among other results, we give an O(√n)-approximation algorithm for the problem of finding a line embedding of a metric induced by a given unweighted graph, that minimizes the (standard) multiplicative distortion. We give an improved Õ(n1/3) approximation for the case of metrics generated by unweighted trees. This is the first result of this type.
32208794
Adaptive delivery of E-commerce web sites
Most e-commerce web sites are very large, often confusing and overwhelm the visitor with a huge amount of information. People cannot easily find what they are looking for. Moreover, the web site is presented in the same format to every visitor, irrespective of his needs. This paper proposes a model to solve the above problems. Our model divides the visitors into groups. Then it arranges web pages in the decreasing order of preference for each group and applies path prediction to find sink pages for that group. The results of these algorithms are displayed in a separate frame without modifying the site. Secondly, our paper addresses the need to guide visitors during the configuration of a product. We propose to apply data mining on the quotes for every group and find associations between different components of the product. We can then display these results as suggestions while the prospective buyer is configuring the product. These suggestions will dynamically change as each selection is made. We have discussed the data mining algorithms applicable to our model.