15,968 research outputs found
Classification of large partial plane spreads in and related combinatorial objects
In this article, the partial plane spreads in of maximum possible
size and of size are classified. Based on this result, we obtain the
classification of the following closely related combinatorial objects: Vector
space partitions of of type , binary MRD
codes of minimum rank distance , and subspace codes with parameters
and .Comment: 31 pages, 9 table
On Communication Protocols that Compute Almost Privately
A traditionally desired goal when designing auction mechanisms is incentive
compatibility, i.e., ensuring that bidders fare best by truthfully reporting
their preferences. A complementary goal, which has, thus far, received
significantly less attention, is to preserve privacy, i.e., to ensure that
bidders reveal no more information than necessary. We further investigate and
generalize the approximate privacy model for two-party communication recently
introduced by Feigenbaum et al.[8]. We explore the privacy properties of a
natural class of communication protocols that we refer to as "dissection
protocols". Dissection protocols include, among others, the bisection auction
in [9,10] and the bisection protocol for the millionaires problem in [8].
Informally, in a dissection protocol the communicating parties are restricted
to answering simple questions of the form "Is your input between the values
\alpha and \beta (under a predefined order over the possible inputs)?".
We prove that for a large class of functions, called tiling functions, which
include the 2nd-price Vickrey auction, there always exists a dissection
protocol that provides a constant average-case privacy approximation ratio for
uniform or "almost uniform" probability distributions over inputs. To establish
this result we present an interesting connection between the approximate
privacy framework and basic concepts in computational geometry. We show that
such a good privacy approximation ratio for tiling functions does not, in
general, exist in the worst case. We also discuss extensions of the basic setup
to more than two parties and to non-tiling functions, and provide calculations
of privacy approximation ratios for two functions of interest.Comment: to appear in Theoretical Computer Science (series A
Rectilinear partitioning of irregular data parallel computations
New mapping algorithms for domain oriented data-parallel computations, where the workload is distributed irregularly throughout the domain, but exhibits localized communication patterns are described. Researchers consider the problem of partitioning the domain for parallel processing in such a way that the workload on the most heavily loaded processor is minimized, subject to the constraint that the partition be perfectly rectilinear. Rectilinear partitions are useful on architectures that have a fast local mesh network. Discussed here is an improved algorithm for finding the optimal partitioning in one dimension, new algorithms for partitioning in two dimensions, and optimal partitioning in three dimensions. The application of these algorithms to real problems are discussed
Overlap Removal of Dimensionality Reduction Scatterplot Layouts
Dimensionality Reduction (DR) scatterplot layouts have become a ubiquitous
visualization tool for analyzing multidimensional data items with presence in
different areas. Despite its popularity, scatterplots suffer from occlusion,
especially when markers convey information, making it troublesome for users to
estimate items' groups' sizes and, more importantly, potentially obfuscating
critical items for the analysis under execution. Different strategies have been
devised to address this issue, either producing overlap-free layouts, lacking
the powerful capabilities of contemporary DR techniques in uncover interesting
data patterns, or eliminating overlaps as a post-processing strategy. Despite
the good results of post-processing techniques, the best methods typically
expand or distort the scatterplot area, thus reducing markers' size (sometimes)
to unreadable dimensions, defeating the purpose of removing overlaps. This
paper presents a novel post-processing strategy to remove DR layouts' overlaps
that faithfully preserves the original layout's characteristics and markers'
sizes. We show that the proposed strategy surpasses the state-of-the-art in
overlap removal through an extensive comparative evaluation considering
multiple different metrics while it is 2 or 3 orders of magnitude faster for
large datasets.Comment: 11 pages and 9 figure
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