32901959
Efficient embeddings of ternary trees into hypercubes
In this paper we present efficient graph embeddings for complete k-ary trees into boolean hypercubes. In particular, we describe an efficient embedding of a complete ternary tree (k = 3) of height h into a hypercube, which achieves dilation 3 and expansion Θ(1.0104...h). The previously best-known result is dilation 2 and expansion Θ(1.333...h). Our embedding achieves exponentially better expansion at the cost of an increase of 1 in the dilation. We also describe efficient embeddings of k-ary trees into hypercubes when k = 2p * 3q for some p, q > 0 such that the embeddings achieve small constant dilation.
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.
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.
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>>
41859107
Preconditioned Conjugate Gradient Solver for Large Sparse Systems on MPI
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.
96295
Efficient algorithms for pattern matching on directed acyclic graphs
Recently graph data models have become increasingly popular in many scientific fields. Efficient query processing over such data is critical. Existing works often rely on index structures that store pre-computed transitive relations to achieve efficient graph matching. In this paper, we present a family of stack-based algorithms to handle path and twig pattern queries for directed acyclic graphs (DAGs) in particular. With the worst-case space cost linearly bounded by the number of edges in the graph, our algorithms achieve a quadratic runtime complexity in the average size of the query variable bindings. This is optimal among the navigation-based graph matching algorithms.
9282309
Approximation via cost-sharing: a simple approximation algorithm for the multicommodity rent-or-buy problem
We study the multicommodity rent-or-buy problem, a type of network design problem with economies of scale. In this problem, capacity on an edge can be rented, with cost incurred on a per-unit of capacity basis, or bought, which allows unlimited use after payment of a large fixed cost. Given a graph and a set of source-sink pairs, we seek a minimum-cost way of installing sufficient capacity on edges so that a prescribed amount of flow can be sent simultaneously from each source to the corresponding sink. The first constant-factor approximation algorithm for this problem was recently given by Kumar et al.; however, this algorithm and its analysis are both quite complicated, and its performance guarantee is extremely large. In this paper, we give a conceptually simple 12-approximation algorithm for this problem. Our analysis of this algorithm makes crucial use of cost sharing, the task of allocating the cost of an object to many users of the object in a "fair" manner. While techniques from approximation algorithms have recently yielded new progress on cost sharing problems, our work is the first to show the converse - those ideas from cost sharing can be fruitfully applied in the design and analysis of approximation algorithms.
17115672
Emergent Semantics through Interaction in Image Databases
In this paper, we briefly discuss some aspects of image semantics and the role that it plays for the design of image databases. We argue that images don't have an intrinsic meaning, but that they are endowed with a meaning by placing them in the context of other images and by the user interaction. From this observation, we conclude that, in an image, database users should be allowed to manipulate not only the individual images, but also the relation between them. We present an interface model based on the manipulation of configurations of images.
26737462
The Parallel Complexity of Tree Embedding Problems
Abstract The question of the sequential complexity of various tree embedding problems arises in the recent work of Robertson and Seymour on graph miners; here we consider the parallel complexity of such problems. In particular, we present two CREW PRAM algorithms: an O (log 3 n ) time randomized algorithm for determining whether there is a topological embedding of one rooted tree in another and an O (log 2 n log log n ) time deterministic algorithm for determining whether or not a rooted tree with a degree constraint is a minor of a general rooted tree. These algorithms are two examples of a general technique that can be used for solving other problems on trees.
24549782
Adaptive Fault Tolerant Hospital Resource Scheduling
In a distributed hospital system, different hospitals should collaborate among themselves for sharing their resources to provide better and faster service to the patients. We address the distributed hospital resource scheduling problem and apply the Generalized Partial Global Planning (GPGP) approach used for multiagent systems for the same. An adaptive coordination mechanism based on the contract net protocol is proposed to support inter-hospital collaboration. We have performed simulation studies and the experimental results show that our coordination mechanism performs better than commonly used schemes. Fault handling mechanisms are presented so that the system continues to provide service even in the presence of faults. The proposed approach is applicable in contexts other than the distributed hospital system as well.