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LPI is not efficient in time and memory which makes it difficult to be applied to very large data set. In this paper, we propose a optimal algorithm called FLPI which decomposes the LPI problem as a graph embedding problem plus a regularized least squares problem. Such modification avoids eigen decomposition of dense matrices and can significantly reduce both time and memory cost in computation. Moreover, with a specifically designed graph in supervised situation, LPI only needs to solve the regularized least squares problem which is a further saving of time and memory. Real and synthetic data experimental results show that FLPI obtains similar or better results comparing to LPI and it is significantly faster. [ABSTRACT FROM AUTHOR]

We consider the following problem known as simultaneous geometric graph embedding (SGE). Given a set of planar graphs on a shared vertex set, decide whether the vertices can be placed in the plane in such a way that for each graph the straight-line drawing is planar. We partially settle an open problem of Erten and Kobourov [5] by showing that even for two graphs the problem is NP-hard. We also show that the problem of computing the rectilinear crossing number of a graph can be reduced to a simultaneous geometric graph embedding problem; this implies that placing SGE in NP will be hard, since the corresponding question for rectilinear crossing number is a long-standing open problem. However, rather like rectilinear crossing number, SGE can be decided in PSPACE. [ABSTRACT FROM AUTHOR]

This paper outlines a general method for allocating a document collection over a distributed storage system. Documents are organized to make up a corporate semantic web featured by a graph G1, each of whose nodes represents a set of documents having a common range of semantic indices. There exists a second graph G2 modelling the distributed storage system. Our approach consists of embedding G1 into G2, under size restrictions. We use a meta-heuristic called ˵Ant Colony Optimization″, to solve the corresponding instances of the graph embedding problem, which is known to be a NP problem. Our solution provides an efficient mechanism for information storage and retrieval. [ABSTRACT FROM AUTHOR]

Optimal network performance is critical to efficient parallel scaling for communication-bound applications on large machines. With wormhole routing, no-load latencies do not increase significantly with number of hops traveled. Yet, we, and others have recently shown that in presence of contention, message latencies can grow substantially large. Hence task mapping strategies should take the topology of the machine into account on large machines. In this paper, we present topology aware mapping as a technique to optimize communication on 3-dimensional mesh interconnects and hence improve performance. Our methodology is facilitated by the idea of object-based decomposition used in Charm++ which separates the processes of decomposition from mapping of computation to processors and allows a more flexible mapping based on communication patterns between objects. Exploiting this and the topology of the allocated job partition, we present mapping strategies for a production code, OpenAtom to improve overall performance and scaling. OpenAtom presents complex communication scenarios of interaction involving multiple groups of objects and makes the mapping task a challenge. Results are presented for OpenAtom on up to 16,384 processors of Blue Gene/L, 8,192 processors of Blue Gene/P and 2,048 processors of Cray XT3. [ABSTRACT FROM AUTHOR]

This chapter surveys recent progress in constant-working-space algorithms for problems related to image processing. An extreme case is when an input image is given as read-only memory in which reading an array element is allowed but writing any value at any array element is prohibited, and also the number of working storage cells available for algorithms is at most some constant. This chapter shows how a number of important fundamental problems can be solved in such a highly constrained situation. [ABSTRACT FROM AUTHOR]

The key to the graph based semi-supervised learning algorithms for classification problems is how to construct the weight matrix of the p-nearest neighbor graph. A new method to construct the weight matrix is proposed and a graph based Subspace Semi-supervised Learning Framework (SSLF) is developed. The Framework aims to find an embedding transformation which respects the discriminant structure inferred from the labeled data, as well as the intrinsic geometrical structure inferred from both the labeled and unlabeled data. By utilizing this framework as a tool, we drive three semi-supervised dimensionality reduction algorithms: Subspace Semi-supervised Linear Discriminant Analysis (SSLDA), Subspace Semi-supervised Locality Preserving Projection (SSLPP), and Subspace Semi-supervised Marginal Fisher Analysis (SSMFA). The experimental results on face recognition demonstrate our subspace semi-supervised algorithms are able to use unlabeled samples effectively. [ABSTRACT FROM AUTHOR]

We introduce the concept of colored simultaneous geometric embeddings as a generalization of simultaneous graph embeddings with and without mapping. We show that there exists a universal pointset of size n for paths colored with two or three colors. We use these results to show that colored simultaneous geometric embeddings exist for: (1) a 2-colored tree together with any number of 2-colored paths and (2) a 2-colored outerplanar graph together with any number of 2-colored paths. We also show that there does not exist a universal pointset of size n for paths colored with five colors. We finally show that the following simultaneous embeddings are not possible: (1) three 6-colored cycles, (2) four 6-colored paths, and (3) three 9-colored paths. [ABSTRACT FROM AUTHOR]

Graph drawing research traditionally focuses on producing geometric embeddings of graphs satisfying various aesthetic constraints. After the geometric embedding is specified, there is an additional step that is often overlooked or ignored: assigning display colors to the graph's vertices. We study the additional aesthetic criterion of assigning distinct colors to vertices of a geometric graph so that the colors assigned to adjacent vertices are as different from one another as possible. We formulate this as a problem involving perceptual metrics in color space and we develop algorithms for solving this problem by embedding the graph in color space. We also present an application of this work to a distributed load-balancing visualization problem. [ABSTRACT FROM AUTHOR]

Considers the problem of mapping a parallel application onto a transputer network consisting of transputers and crossbars with no inter-crossbar links. Methodology of the mapping of a process graph onto a fixed interconnection network; Factors that constraint the mapping; Algorithm used in embedding the guest graph into the system.