2,376 research outputs found
Compressive Mining: Fast and Optimal Data Mining in the Compressed Domain
Real-world data typically contain repeated and periodic patterns. This
suggests that they can be effectively represented and compressed using only a
few coefficients of an appropriate basis (e.g., Fourier, Wavelets, etc.).
However, distance estimation when the data are represented using different sets
of coefficients is still a largely unexplored area. This work studies the
optimization problems related to obtaining the \emph{tightest} lower/upper
bound on Euclidean distances when each data object is potentially compressed
using a different set of orthonormal coefficients. Our technique leads to
tighter distance estimates, which translates into more accurate search,
learning and mining operations \textit{directly} in the compressed domain.
We formulate the problem of estimating lower/upper distance bounds as an
optimization problem. We establish the properties of optimal solutions, and
leverage the theoretical analysis to develop a fast algorithm to obtain an
\emph{exact} solution to the problem. The suggested solution provides the
tightest estimation of the -norm or the correlation. We show that typical
data-analysis operations, such as k-NN search or k-Means clustering, can
operate more accurately using the proposed compression and distance
reconstruction technique. We compare it with many other prevalent compression
and reconstruction techniques, including random projections and PCA-based
techniques. We highlight a surprising result, namely that when the data are
highly sparse in some basis, our technique may even outperform PCA-based
compression.
The contributions of this work are generic as our methodology is applicable
to any sequential or high-dimensional data as well as to any orthogonal data
transformation used for the underlying data compression scheme.Comment: 25 pages, 20 figures, accepted in VLD
Unifying mesh- and tree-based programmable interconnect
We examine the traditional, symmetric, Manhattan mesh design for field-programmable gate-array (FPGA) routing along with tree-of-meshes (ToM) and mesh-of-trees (MoT) based designs. All three networks can provide general routing for limited bisection designs (Rent's rule with p<1) and allow locality exploitation. They differ in their detailed topology and use of hierarchy. We show that all three have the same asymptotic wiring requirements. We bound this tightly by providing constructive mappings between routes in one network and routes in another. For example, we show that a (c,p) MoT design can be mapped to a (2c,p) linear population ToM and introduce a corner turn scheme which will make it possible to perform the reverse mapping from any (c,p) linear population ToM to a (2c,p) MoT augmented with a particular set of corner turn switches. One consequence of this latter mapping is a multilayer layout strategy for N-node, linear population ToM designs that requires only /spl Theta/(N) two-dimensional area for any p when given sufficient wiring layers. We further show upper and lower bounds for global mesh routes based on recursive bisection width and show these are within a constant factor of each other and within a constant factor of MoT and ToM layout area. In the process we identify the parameters and characteristics which make the networks different, making it clear there is a unified design continuum in which these networks are simply particular regions
Rectangular Layouts and Contact Graphs
Contact graphs of isothetic rectangles unify many concepts from applications
including VLSI and architectural design, computational geometry, and GIS.
Minimizing the area of their corresponding {\em rectangular layouts} is a key
problem. We study the area-optimization problem and show that it is NP-hard to
find a minimum-area rectangular layout of a given contact graph. We present
O(n)-time algorithms that construct -area rectangular layouts for
general contact graphs and -area rectangular layouts for trees.
(For trees, this is an -approximation algorithm.) We also present an
infinite family of graphs (rsp., trees) that require (rsp.,
) area.
We derive these results by presenting a new characterization of graphs that
admit rectangular layouts using the related concept of {\em rectangular duals}.
A corollary to our results relates the class of graphs that admit rectangular
layouts to {\em rectangle of influence drawings}.Comment: 28 pages, 13 figures, 55 references, 1 appendi
Tag-Cloud Drawing: Algorithms for Cloud Visualization
Tag clouds provide an aggregate of tag-usage statistics. They are typically
sent as in-line HTML to browsers. However, display mechanisms suited for
ordinary text are not ideal for tags, because font sizes may vary widely on a
line. As well, the typical layout does not account for relationships that may
be known between tags. This paper presents models and algorithms to improve the
display of tag clouds that consist of in-line HTML, as well as algorithms that
use nested tables to achieve a more general 2-dimensional layout in which tag
relationships are considered. The first algorithms leverage prior work in
typesetting and rectangle packing, whereas the second group of algorithms
leverage prior work in Electronic Design Automation. Experiments show our
algorithms can be efficiently implemented and perform well.Comment: To appear in proceedings of Tagging and Metadata for Social
Information Organization (WWW 2007
A tight layout of the cube-connected cycles
Preparata and Vuillemin proposed the cubeconnected cycles (CCC) in 1981 [lS], and in the same paper, gave an asymptotically-optimal layout scheme for the CCC. We give a new layout scheme for the CCC which requires less than half of the area of th,e Preparata- Vuillemin layout. We also give a non-trivial lower bound on the layout area of the CCC. There is a constant factor of 2 between the new layout and the lower bound. We conjectur.e that the new layout is optimal (minimal).published_or_final_versio
A tight layout of the cube-connected cycles
Preparata and Vuillemin proposed the cubeconnected cycles (CCC) in 1981 [lS], and in the same paper, gave an asymptotically-optimal layout scheme for the CCC. We give a new layout scheme for the CCC which requires less than half of the area of th,e Preparata- Vuillemin layout. We also give a non-trivial lower bound on the layout area of the CCC. There is a constant factor of 2 between the new layout and the lower bound. We conjectur.e that the new layout is optimal (minimal).published_or_final_versio
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